Statistics

Problem Statement for "SmallestRegular"

Problem Statement

A regular bracket sequence is a sequence of opening ("(") and closing (")") brackets such that it is possible to obtain a correct mathematical expression from it by inserting numbers and operators between the brackets. For example, the sequences "(())()" and "()" are regular bracket sequences while sequences such as ")()" and "(()" are not.

A string is said to be valid if for each of its non-empty prefixes the number of opening brackets >= number of closing brackets. For example, "((()()" and "(())" are valid strings but ")(" is not.

T[a..b] denotes the substring of T formed by characters at 0-based indices a through b, inclusive. E.g., if T = "qwertyuiop" then T[2..5] = "erty".


You are given a regular bracket sequence S of length N. Your goal is to change S into the lexicographically smallest regular bracket sequence possible. Below we define the meaning of an operation. You have to find any sequence of at most 300 operations that reaches your goal.

An operation looks as follows:

  1. Choose a triplet of indices (a,b,c) such that 0 <= a <= b < c <= N-1 and that both substrings S[a..b] and S[b+1..c] are valid strings (as defined above).
  2. Swap the substrings S[a..b] and S[b+1..c].

Lets say the number of operations you needed is X. Then return a int[] res with 3*X elements, where for i-th operation (a, b, c) we have res[3*i]=a, res[3*i+1]=b and res[3*i+2]=c respectively.

Definition

Class:
SmallestRegular
Method:
findLexSmallest
Parameters:
String
Returns:
int[]
Method signature:
int[] findLexSmallest(String S)
(be sure your method is public)

Notes

  • For the purpose of the lexicographic ordering of bracket sequences, the character '(' is smaller than the character ')'.
  • You are not required to minimize the number of operations. Any valid solution will be accepted.

Constraints

  • S will consist of characters '(' and ')' only.
  • S.length will be between 2 and 500, inclusive.
  • S.length will be even.
  • S will be a regular bracket sequence.

Examples

  1. "((()()(())))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 6, 7 }

  2. "()()()()(())"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 8, 9 }

  3. "(())"

    Returns: { }

  4. "()()((((())())))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 10, 11 }

  5. "()()()(())()(())()"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 15, 16 }

  6. "()((()))()()()()()()"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 17, 18 }

  7. "(())((())(())(()))"

    Returns: {0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 8, 9, 0, 9, 10, 0, 12, 13, 0, 13, 14 }

  8. "()()(())"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5 }

  9. "()(()(()))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 5, 6 }

  10. "()(()())()(((())))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13 }

  11. "(((()(()))))"

    Returns: {0, 4, 5, 0, 5, 6 }

  12. "()()()((()))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8 }

  13. "(())"

    Returns: { }

  14. "((((((()))))))"

    Returns: { }

  15. "()()"

    Returns: {0, 1, 2 }

  16. "()()()()()()()"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12 }

  17. "((((()))))"

    Returns: { }

  18. "(((())))(()(()))(())"

    Returns: {0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 15, 16, 0, 16, 17 }

  19. "()(())((()))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 6, 7, 0, 7, 8 }

  20. "(()(()))"

    Returns: {0, 2, 3, 0, 3, 4 }

  21. "(()()((())))((()())(()()((((()))()(((((())())))())))))"

    Returns: {0, 2, 3, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 46, 47 }

  22. "((()())(()))()(()())()()()()"

    Returns: {0, 3, 4, 0, 6, 7, 0, 7, 8, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 25, 26 }

  23. "((()())())()()(()(())((()(())))()(()(((()((()())))))()))()"

    Returns: {0, 3, 4, 0, 6, 7, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 51, 52, 0, 55, 56 }

  24. "()()()((()()(())((())))())"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 22, 23 }

  25. "(())"

    Returns: { }

  26. "((()))()()()(()(())(()(())))"

    Returns: {0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 22, 23 }

  27. "()()((())()(()()((())()()))()(()())())(()((()(((()))(())()())((())))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 20, 21, 0, 22, 23, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 51, 52, 0, 52, 53, 0, 55, 56, 0, 57, 58, 0, 60, 61, 0, 61, 62, 0, 62, 63 }

  28. "((()))"

    Returns: { }

  29. "()()()(((()()((()())(())())())(()()()()())))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 20, 21, 0, 23, 24, 0, 26, 27, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 34, 35, 0, 36, 37, 0, 38, 39 }

  30. "()((())(()((()(((())()((()(((((((())))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33 }

  31. "()()((()))()()((((()()(()))(((()()())(()()))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 36, 37, 0, 37, 38, 0, 39, 40 }

  32. "((()))()(((((())()(()((()(())))()((())((((())())(()())))))))))"

    Returns: {0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 50, 51 }

  33. "(()(()())((())(((()(((()))((()((()()))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 33, 34 }

  34. "()()()()()()()(())(((())))()"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 25, 26 }

  35. "((()))((((()))))()()()(())((((((()(((())))(()())()))))))"

    Returns: {0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 47, 48 }

  36. "(()(())()(())(()())(()))()()()(())(())"

    Returns: {0, 2, 3, 0, 3, 4, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 18, 19, 0, 19, 20, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 34, 35 }

  37. "(((()())()((()())()))()((())()))()()(((((()))()())()))((()()()()())((()(()))))"

    Returns: {0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 16, 17, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 27, 28, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 44, 45, 0, 46, 47, 0, 49, 50, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 71, 72 }

  38. "()()()(())((())())(()(()()))((()))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 14, 15, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 23, 24, 0, 27, 28, 0, 28, 29, 0, 29, 30 }

  39. "()(()())()(()(()()))((())(())())()"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 24, 25, 0, 25, 26, 0, 28, 29, 0, 31, 32 }

  40. "()(((((()))(()))((((((()()())(()()())))))((()((())()((((()((()(()(()()))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 10, 11, 0, 11, 12, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 65, 66, 0, 67, 68 }

  41. "()()((()))()(())(())()()((())())(())(()())()"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 28, 29, 0, 31, 32, 0, 32, 33, 0, 35, 36, 0, 36, 37, 0, 38, 39, 0, 41, 42 }

  42. "(()())()((((((()())()))()())))(()(()())(()()))"

    Returns: {0, 2, 3, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 18, 19, 0, 22, 23, 0, 24, 25, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 38, 39, 0, 39, 40, 0, 41, 42 }

  43. "()()((()()))()()(((()()()()())()))(((())(())()))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 7, 8, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 29, 30, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 40, 41, 0, 43, 44 }

  44. "((((())(())())()())()((())(()())(()))()())()(())()()()()()()(())()()()()()()(())()((()))"

    Returns: {0, 6, 7, 0, 7, 8, 0, 10, 11, 0, 13, 14, 0, 15, 16, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 26, 27, 0, 28, 29, 0, 31, 32, 0, 32, 33, 0, 36, 37, 0, 38, 39, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 49, 50, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 65, 66, 0, 67, 68, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 79, 80, 0, 81, 82, 0, 82, 83, 0, 83, 84 }

  45. "((())((()())))(())((()((()()()(((()))()()))((((()(())(()(()(())((()))())))()((()(((()))))())))))))"

    Returns: {0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 13, 14, 0, 14, 15, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 36, 37, 0, 38, 39, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 88, 89 }

  46. "(((())(())))(()(()(())))"

    Returns: {0, 5, 6, 0, 6, 7, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 18, 19 }

  47. "(())()()((())(()))()((((((()()()(()())))))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 12, 13, 0, 13, 14, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 34, 35 }

  48. "()()(())(())(()(((()()()()()())(()()())(()(())(()()))((()((()()()(()(((())))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 62, 63, 0, 64, 65, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71 }

  49. "(())(((()(()((()()))(())()(()())()()(())))(()())()()(((()())((((((()))))))))))"

    Returns: {0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 19, 20, 0, 20, 21, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 28, 29, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 47, 48, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66 }

  50. "()()()(((())))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 8, 9 }

  51. "()(()()()(()))(()())(())()((()((()()()()())()())))(((()())(((()()())(()))(()))()()((()()(())()(())))())(())(()(()()(((()()(())((((()((()))()())()((())(())(()((((())((((())((((())))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 20, 21, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 37, 38, 0, 39, 40, 0, 42, 43, 0, 44, 45, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 72, 73, 0, 73, 74, 0, 77, 78, 0, 79, 80, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 99, 100, 0, 102, 103, 0, 103, 104, 0, 106, 107, 0, 107, 108, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 122, 123, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 137, 138, 0, 139, 140, 0, 142, 143, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 149, 150, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 170, 171, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 174, 175 }

  52. "()()(()((()(())))(()()(()()()))()((((()((())((())())))((()((()(((()())))))(((((()())()()()))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 48, 49, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 66, 67, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 83, 84, 0, 85, 86, 0, 87, 88 }

  53. "()()()()()((((()())(()())))(()))()()(())()((((()(((()(()((()(()((()))(((()(()))((((()))))()())))))())))))())))()(((()((()))))((()())))()()((())(()))((()(((())))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 26, 27, 0, 27, 28, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 88, 89, 0, 90, 91, 0, 97, 98, 0, 104, 105, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 133, 134, 0, 135, 136, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 142, 143, 0, 143, 144, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 154, 155 }

  54. "(()(()(())()))()()()()(())()((()))(())()()()(())(())()()(()(()())(())()(()))(((())())())(())()(()((()(()()))((((()()(()()()())(((((()()))()))))()())(()()(()((()))())()(()))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 9, 10, 0, 13, 14, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 64, 65, 0, 65, 66, 0, 68, 69, 0, 70, 71, 0, 71, 72, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 81, 82, 0, 84, 85, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 100, 101, 0, 101, 102, 0, 103, 104, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 120, 121, 0, 122, 123, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 132, 133, 0, 136, 137, 0, 142, 143, 0, 144, 145, 0, 147, 148, 0, 148, 149, 0, 150, 151, 0, 152, 153, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 161, 162, 0, 164, 165, 0, 166, 167, 0, 167, 168 }

  55. "()()(())()(((())()())()()())(((((()()))(((((()))((())(()())()((()))((((()))()(()((())((()()(()()(()))))()()))(()))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 17, 18, 0, 20, 21, 0, 22, 23, 0, 24, 25, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 74, 75, 0, 76, 77, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 90, 91, 0, 91, 92, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 102, 103, 0, 104, 105, 0, 108, 109, 0, 109, 110 }

  56. "()()(()()(()((()(()))()()(())()))((())))()(()(()))()()()()(()((()(()()))(()())()(()()))()((()))())(())((()((()(()(((((())()()()(()(())(()()))))))()))(((((())((()()())))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 20, 21, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 28, 29, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 45, 46, 0, 49, 50, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 65, 66, 0, 67, 68, 0, 71, 72, 0, 72, 73, 0, 74, 75, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 94, 95, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 133, 134, 0, 134, 135, 0, 136, 137, 0, 144, 145, 0, 148, 149, 0, 149, 150, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 160, 161, 0, 162, 163 }

  57. "()(())((()((()))))(((((()(((()((())())()))())())(())()))))((()()))(())()(((()(())(()())()))(())()((((((()()))(((())())(()()(()))))()(())())((()(((())())))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 34, 35, 0, 37, 38, 0, 41, 42, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 51, 52, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 65, 66, 0, 66, 67, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 77, 78, 0, 80, 81, 0, 81, 82, 0, 83, 84, 0, 86, 87, 0, 90, 91, 0, 91, 92, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 114, 115, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 135, 136, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 148, 149 }

  58. "()()()(()(())()())()()((()))()(()()((()))(()(()(((()(())(()(()(())(())(()(((())(())(()(()(()(())()(())()())()())()(()())((())))(())())(())(()())(((()))()()(())()(()()()(())(()((()()())))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 12, 13, 0, 14, 15, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 65, 66, 0, 66, 67, 0, 69, 70, 0, 70, 71, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 78, 79, 0, 79, 80, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 91, 92, 0, 92, 93, 0, 95, 96, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 103, 104, 0, 106, 107, 0, 108, 109, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 126, 127, 0, 127, 128, 0, 130, 131, 0, 133, 134, 0, 134, 135, 0, 137, 138, 0, 138, 139, 0, 140, 141, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 150, 151, 0, 152, 153, 0, 154, 155, 0, 155, 156, 0, 158, 159, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 165, 166, 0, 167, 168, 0, 168, 169, 0, 171, 172, 0, 172, 173, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 178, 179, 0, 180, 181 }

  59. "((()))((()((())()(())()()())()(())()()()()))()(()(()()))((())(()))((())((())(((())(()()))())()))()((()((((((())()))(((()))))))()(())))"

    Returns: {0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 20, 21, 0, 22, 23, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 35, 36, 0, 37, 38, 0, 39, 40, 0, 43, 44, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 51, 52, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 60, 61, 0, 61, 62, 0, 65, 66, 0, 66, 67, 0, 67, 68, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 81, 82, 0, 82, 83, 0, 84, 85, 0, 88, 89, 0, 91, 92, 0, 95, 96, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 110, 111, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 125, 126, 0, 127, 128, 0, 128, 129 }

  60. "(()()(()))()(()()(()))()(())()()(()(()())()((()((((()()())()((((((())((((((((())(()()()(()))(((()(()(((((())((()))(((((()(()(((()()(()(())()()((((()))))))))))))))))))))))))))))))))))))))))"

    Returns: {0, 2, 3, 0, 4, 5, 0, 5, 6, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 54, 55, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 133, 134, 0, 134, 135, 0, 137, 138, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 145, 146 }

  61. "()()()((()))((())())()()((()))()(((((()))()))()((()())(()))((()())()(((())((((()))((((()(())(((()))(()())(()(()))()()(((()()(((()()(()(((())))((()(()()())))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 40, 41, 0, 44, 45, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 50, 51, 0, 53, 54, 0, 54, 55, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 112, 113, 0, 114, 115, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 148, 149, 0, 150, 151 }

  62. "(((()())))()()(((()()((()()()()()(())()((()())(()())((((())()()(((()(()))(((()())((((((())())((()((()(()())(()))(()()()())())())())((()())))))))((())()())))))))))))))"

    Returns: {0, 4, 5, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 28, 29, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 36, 37, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 89, 90, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 100, 101, 0, 101, 102, 0, 103, 104, 0, 106, 107, 0, 107, 108, 0, 111, 112, 0, 112, 113, 0, 114, 115, 0, 116, 117, 0, 118, 119, 0, 121, 122, 0, 124, 125, 0, 127, 128, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 148, 149, 0, 150, 151 }

  63. "((((()))()(((()(()()()))()))))(())((())((())))()((((())(((()))()(())((()()))((()))()((())((()()(()))))(()((()())))()())((())))(()(()()())()())(((((((())((()))()))))))))"

    Returns: {0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 23, 24, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 81, 82, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 108, 109, 0, 113, 114, 0, 115, 116, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 131, 132, 0, 133, 134, 0, 136, 137, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 157, 158 }

  64. "(((())((()((()()(()())))()))()()())()(()))(())(()()()())()()()()(()((()((())(()()((())()(((()))((()))()))())))))((((())()()(((()()(((()()()((())))))))))))"

    Returns: {0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 23, 24, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 41, 42, 0, 42, 43, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 50, 51, 0, 52, 53, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 75, 76, 0, 76, 77, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 100, 101, 0, 104, 105, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 118, 119, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 136, 137, 0, 138, 139, 0, 139, 140, 0, 140, 141 }

  65. "((()()((((()()(())))))())())()()(())((((()())((())))))((()))()()((()))((()))()(()())()(())()()(()(()))(())()(()(()()()))(()()()())()(()())(())(())()()(())(()())((((())))())()()()()(())"

    Returns: {0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 21, 22, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 101, 102, 0, 102, 103, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 126, 127, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 137, 138, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 156, 157, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 168, 169, 0, 171, 172, 0, 173, 174, 0, 175, 176, 0, 177, 178, 0, 179, 180, 0, 180, 181 }

  66. "()(()((())(()))())(()()(((()))(()()(())(((()()))()((((((()))())(()))()(()())(((()(((((((())))(()()))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 14, 15, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 59, 60, 0, 62, 63, 0, 63, 64, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 72, 73, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 92, 93, 0, 93, 94, 0, 95, 96 }

  67. "()(())()()()((())(()()(()((()()((()))(())())))))(((()(((((()()((())))()()(())()()))())))((()))((()()()(((()(((()(()()()))))(())())()((())())))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 28, 29, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 36, 37, 0, 37, 38, 0, 40, 41, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 68, 69, 0, 70, 71, 0, 72, 73, 0, 73, 74, 0, 76, 77, 0, 78, 79, 0, 82, 83, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 97, 98, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 114, 115, 0, 116, 117, 0, 122, 123, 0, 123, 124, 0, 126, 127, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 136, 137 }

  68. "()(())()()(()())()(())()(())()(())()()(())()()()(())((()())((())())(())(())((()(())))(())()((()))(()()))((())()((())))()(())()()()((((()(((())(()(()))(())(())()))))))((()))((((())()(())))(()))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 70, 71, 0, 71, 72, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 78, 79, 0, 79, 80, 0, 84, 85, 0, 85, 86, 0, 88, 89, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 117, 118, 0, 119, 120, 0, 120, 121, 0, 123, 124, 0, 125, 126, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 144, 145, 0, 145, 146, 0, 149, 150, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 157, 158, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 178, 179, 0, 180, 181, 0, 181, 182, 0, 186, 187, 0, 187, 188 }

  69. "()((()))(())((()((((()())))))(())()(((()(()(())(()()()))(((()))())()(()()())())))()(()(())))(()())(((()()))(((()(())()(()((()((((())))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 7, 8, 0, 8, 9, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 28, 29, 0, 29, 30, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 46, 47, 0, 47, 48, 0, 49, 50, 0, 51, 52, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 62, 63, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 72, 73, 0, 75, 76, 0, 80, 81, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 102, 103, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 115, 116, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129 }

  70. "(()(((()(())))))()((((()))()()(()(())(())))()())()((())((((()(()))(()()()))())()((((())(((()))(()())()()))()(((())())((())(()))(((((((())((((()()(()())())))())((())))))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 36, 37, 0, 37, 38, 0, 42, 43, 0, 44, 45, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 70, 71, 0, 74, 75, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 99, 100, 0, 101, 102, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 113, 114, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 122, 123, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 142, 143, 0, 144, 145, 0, 145, 146, 0, 147, 148, 0, 150, 151, 0, 155, 156, 0, 158, 159, 0, 159, 160, 0, 160, 161 }

  71. "(()(()((()()()()))))()()()()()((()()((((((()()()()(()))((()()()))))))()()(())(()(()(()(()()))())(()(())((())((()()())))())))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 60, 61, 0, 68, 69, 0, 70, 71, 0, 72, 73, 0, 73, 74, 0, 76, 77, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 92, 93, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 99, 100, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 113, 114, 0, 118, 119 }

  72. "()()(()()(()()))(())()(()()((())))()()(()((()()))(()())((())))(((((()))(()(())())))((()())((()()))))()(()(()(((())()))))()()(()())"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 15, 16, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 33, 34, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 48, 49, 0, 49, 50, 0, 51, 52, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 66, 67, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 77, 78, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 93, 94, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 113, 114, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 126, 127 }

  73. "(())((()((())(()()(((((())(()((()((())()))))))()())((()()()()))(()(()()(()))())()()())()))))()(((())())()()())()(())()(()()(((()))((())((())))()((()(()((((()((())()))((((()))))))))))))"

    Returns: {0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 45, 46, 0, 47, 48, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 56, 57, 0, 58, 59, 0, 62, 63, 0, 63, 64, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 70, 71, 0, 71, 72, 0, 75, 76, 0, 78, 79, 0, 80, 81, 0, 82, 83, 0, 85, 86, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 99, 100, 0, 102, 103, 0, 104, 105, 0, 106, 107, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 115, 116, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 141, 142, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 147, 148, 0, 148, 149, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 161, 162, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 169, 170 }

  74. "(()(()()))()(()(())()(())(())((()((()))())())(()()((()()((()(()))())((()()((())()()))))))()(()))()()()((()))(()())()((()(()(()))()())()())(((((()))())())(((()(()(())())((())())))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 24, 25, 0, 25, 26, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 38, 39, 0, 41, 42, 0, 44, 45, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 78, 79, 0, 80, 81, 0, 88, 89, 0, 90, 91, 0, 91, 92, 0, 95, 96, 0, 97, 98, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 107, 108, 0, 108, 109, 0, 110, 111, 0, 113, 114, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 127, 128, 0, 129, 130, 0, 132, 133, 0, 134, 135, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 146, 147, 0, 149, 150, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 160, 161, 0, 161, 162, 0, 164, 165, 0, 167, 168, 0, 168, 169, 0, 169, 170, 0, 172, 173 }

  75. "()((())(()))()(()())(((()())))()()(())(())()()(((()())))()((()))()()()(()((()))())(((())(((())))((((()()((()(((()))(())()))())())())))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 6, 7, 0, 7, 8, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 50, 51, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 63, 64, 0, 65, 66, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 78, 79, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 114, 115, 0, 115, 116, 0, 118, 119, 0, 122, 123, 0, 125, 126, 0, 128, 129 }

  76. "(())()()(((())()(((((()(())))))()()())))(((()()(())((())))((((()(())()()()())()()(((((()())))(())((())))()))))(((()))(())))())(())((()(())))(())(((())())((()((())))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 30, 31, 0, 32, 33, 0, 34, 35, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 46, 47, 0, 47, 48, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 76, 77, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 92, 93, 0, 93, 94, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 103, 104, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 116, 117, 0, 117, 118, 0, 122, 123, 0, 125, 126, 0, 126, 127, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 133, 134, 0, 134, 135, 0, 139, 140, 0, 140, 141, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 149, 150, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 158, 159 }

  77. "()((()(())(()()())()()(()((())((())(()()(((((()))()(())))())()(())(())((()((()()()(())(()())))((()))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 14, 15, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 48, 49, 0, 50, 51, 0, 51, 52, 0, 56, 57, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 65, 66, 0, 66, 67, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 79, 80, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 93, 94, 0, 94, 95, 0, 95, 96 }

  78. "((((((((((((()()(()()(()))()(()(()(()((())(((()())))(()))()))(()(())))()(((())))())((()))())(((()()()))((((())())((((((())()))))))))))))))))))"

    Returns: {0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 25, 26, 0, 27, 28, 0, 28, 29, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 46, 47, 0, 51, 52, 0, 52, 53, 0, 56, 57, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 79, 80, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 88, 89, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 98, 99, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 109, 110, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 121, 122 }

  79. "()(((())))(())(((((()())()())))()()())()()(())(()(((())())((())()())))(())()(())()()(((())((()))))()((((())()()()())(()(())())))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 9, 10, 0, 10, 11, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 23, 24, 0, 25, 26, 0, 30, 31, 0, 32, 33, 0, 34, 35, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 62, 63, 0, 64, 65, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 79, 80, 0, 81, 82, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 106, 107, 0, 108, 109, 0, 110, 111, 0, 112, 113, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 119, 120, 0, 122, 123 }

  80. "()()()()((()))(())(()())()(())(())(())()()(()()())(())()()()()()(())((())()()())(())((()(())(()(())((((())))(())((()((((())()(((())((((()))()()(((((()()))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 13, 14, 0, 14, 15, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 46, 47, 0, 49, 50, 0, 50, 51, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 72, 73, 0, 74, 75, 0, 76, 77, 0, 79, 80, 0, 80, 81, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 107, 108, 0, 108, 109, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 138, 139, 0, 140, 141, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 149, 150 }

  81. "((()())())(((((()())()(()()(((()(()()(())((()()()())()))())()()((()))())((())(((()))))()(()()()))(()((((())()((()(((()))((((((()()))(()()((((((()(((()(())(()()()())(((()))))()(()())((()))()(((()()(()()(()()())))())))()()(()((())()(((()))())(()()()())()))())(()()(((((())()))()())(()))()))()))()(()()(((((()((()())))))(()(()((((((()))((())))))))))))))))))))))))))))))))"

    Returns: {0, 3, 4, 0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 46, 47, 0, 48, 49, 0, 51, 52, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 90, 91, 0, 92, 93, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 156, 157, 0, 158, 159, 0, 160, 161, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 172, 173, 0, 174, 175, 0, 175, 176, 0, 177, 178, 0, 180, 181, 0, 181, 182, 0, 182, 183, 0, 186, 187, 0, 188, 189, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 193, 194, 0, 195, 196, 0, 196, 197, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 203, 204, 0, 205, 206, 0, 210, 211, 0, 215, 216, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 227, 228, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 236, 237, 0, 239, 240, 0, 240, 241, 0, 242, 243, 0, 244, 245, 0, 246, 247, 0, 249, 250, 0, 253, 254, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 269, 270, 0, 273, 274, 0, 275, 276, 0, 278, 279, 0, 279, 280, 0, 283, 284, 0, 287, 288, 0, 291, 292, 0, 293, 294, 0, 294, 295, 0, 296, 297, 0, 298, 299, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 309, 310, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 332, 333, 0, 333, 334, 0, 334, 335 }

  82. "((()))(()())()()()(())(()()(()()(())()())(()()))()()()()()()()()((()))()()(()((()(()((()((((()(((()))))))(((()(()))()())(((())()()()))())))())()(()((())())((()()((()(((()()()))))))(())((())()))))()))((((())))))"

    Returns: {0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 35, 36, 0, 37, 38, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 47, 48, 0, 49, 50, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 109, 110, 0, 110, 111, 0, 114, 115, 0, 116, 117, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 125, 126, 0, 127, 128, 0, 129, 130, 0, 133, 134, 0, 138, 139, 0, 141, 142, 0, 143, 144, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 151, 152, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 158, 159, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 169, 170, 0, 171, 172, 0, 179, 180, 0, 180, 181, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 188, 189, 0, 194, 195, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 202, 203 }

  83. "(())()(((()(()()())())()()())())(()((((()(((((()))()(()))(((())()()()((()()(()))))))((()))()(()(((()(()(()())(((()()()(()))(((()()((()())))))())))))(())())(((())(())()))(()()))))()(()))())()()(()())(((()))))())()()()()()(()((())))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 18, 19, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 28, 29, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 62, 63, 0, 64, 65, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 72, 73, 0, 74, 75, 0, 75, 76, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 89, 90, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 102, 103, 0, 103, 104, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 117, 118, 0, 118, 119, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 133, 134, 0, 140, 141, 0, 147, 148, 0, 148, 149, 0, 151, 152, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 160, 161, 0, 161, 162, 0, 164, 165, 0, 168, 169, 0, 169, 170, 0, 171, 172, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 184, 185, 0, 187, 188, 0, 189, 190, 0, 191, 192, 0, 192, 193, 0, 194, 195, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 206, 207, 0, 209, 210, 0, 211, 212, 0, 213, 214, 0, 215, 216, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 222, 223, 0, 223, 224, 0, 224, 225 }

  84. "()()(((()()())((()))))()()(())(((())()(()())((((()))))(((())(())()(()((())(())())(()))((()(()))((())(()((()))))()(()()())()((())((()(())()()(((()()))()(()((())(((())()))((()(()))()(()((()))))))()))(()))(((())))())()))())))()()((()))()((()()()))()((()))()()()()()((())((()))(()(())))()()((()))()()()()()()()(())(((()()((()))()))((())(((((())()()())()))()()(()(())()(())(((()))()()))())))()(())(()())()()()()()()()(((()(()))(()()())))()()(()(()()()))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 10, 11, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 74, 75, 0, 77, 78, 0, 80, 81, 0, 81, 82, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 89, 90, 0, 90, 91, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 99, 100, 0, 100, 101, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 110, 111, 0, 112, 113, 0, 113, 114, 0, 115, 116, 0, 117, 118, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 135, 136, 0, 137, 138, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 144, 145, 0, 148, 149, 0, 150, 151, 0, 151, 152, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 164, 165, 0, 168, 169, 0, 169, 170, 0, 170, 171, 0, 172, 173, 0, 173, 174, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 192, 193, 0, 196, 197, 0, 197, 198, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 209, 210, 0, 212, 213, 0, 216, 217, 0, 221, 222, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 231, 232, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 237, 238, 0, 239, 240, 0, 243, 244, 0, 245, 246, 0, 246, 247, 0, 247, 248, 0, 251, 252, 0, 253, 254, 0, 255, 256, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 272, 273, 0, 273, 274, 0, 275, 276, 0, 276, 277, 0, 281, 282, 0, 283, 284, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 291, 292, 0, 293, 294, 0, 295, 296, 0, 297, 298, 0, 299, 300, 0, 301, 302, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 314, 315, 0, 316, 317, 0, 317, 318, 0, 318, 319, 0, 322, 323, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 339, 340, 0, 341, 342, 0, 343, 344, 0, 346, 347, 0, 350, 351, 0, 352, 353, 0, 354, 355, 0, 355, 356, 0, 357, 358, 0, 358, 359, 0, 361, 362, 0, 363, 364, 0, 364, 365, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 370, 371, 0, 374, 375, 0, 376, 377, 0, 380, 381, 0, 385, 386, 0, 387, 388, 0, 388, 389, 0, 391, 392, 0, 392, 393, 0, 394, 395, 0, 397, 398, 0, 399, 400, 0, 401, 402, 0, 403, 404, 0, 405, 406, 0, 407, 408, 0, 409, 410, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 414, 415, 0, 416, 417, 0, 417, 418, 0, 421, 422, 0, 422, 423, 0, 424, 425, 0, 426, 427, 0, 431, 432, 0, 433, 434, 0, 435, 436, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 441, 442, 0, 443, 444 }

  85. "((((()))))()()(())()((((()())(()))()((((()(()()())()))()()()))))()()()(())()()(()(()()()))()(())((()((()(()((((())(()())((()))())))))(())()((((())()()))))(()(()(())))(()()())()((()()((()(())))()())()()(()))()(()()())))()()()()()(((()))())()(())(((())))(())(()())((())()()())((()((()()((((((()())(()()())((()(((()()()(())))))))))))))))"

    Returns: {0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 28, 29, 0, 29, 30, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 46, 47, 0, 49, 50, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 63, 64, 0, 65, 66, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 83, 84, 0, 85, 86, 0, 89, 90, 0, 91, 92, 0, 92, 93, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 103, 104, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 125, 126, 0, 132, 133, 0, 133, 134, 0, 136, 137, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 153, 154, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 159, 160, 0, 160, 161, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 170, 171, 0, 173, 174, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 185, 186, 0, 186, 187, 0, 191, 192, 0, 193, 194, 0, 196, 197, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 205, 206, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 212, 213, 0, 217, 218, 0, 219, 220, 0, 221, 222, 0, 223, 224, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 234, 235, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 246, 247, 0, 251, 252, 0, 252, 253, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 266, 267, 0, 268, 269, 0, 270, 271, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 281, 282, 0, 283, 284, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 291, 292, 0, 294, 295, 0, 295, 296, 0, 297, 298, 0, 299, 300, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 311, 312, 0, 313, 314, 0, 315, 316, 0, 316, 317 }

  86. "()()()()()()(()()())()()((()))(()(()(())()))()()(())(()(()(()()(((())()))))(())((())()))()()()()(((()()()))()(()(())))()(()()()(()()))()()(())(())()()()()()()((((()(())()()))))(((()()(((((()(((())())(()(())(())))()))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 43, 44, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 68, 69, 0, 74, 75, 0, 75, 76, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 83, 84, 0, 87, 88, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 100, 101, 0, 102, 103, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 117, 118, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 129, 130, 0, 133, 134, 0, 135, 136, 0, 137, 138, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 149, 150, 0, 151, 152, 0, 153, 154, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 167, 168, 0, 169, 170, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 192, 193, 0, 195, 196, 0, 198, 199, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 205, 206, 0, 206, 207, 0, 211, 212 }

  87. "()()()(()())()(())(((((((((((())(()(()))(()()()()(())(())(()(((()(()))()((()(()))((((())(()()()((()(())))((())((())((())((()()()()))))(())))()()))))(()))))())))()(()((()()())))))))(()))(()(())(((((((((())((((((()(()((((()))((()(()((((())(()(((()))()(()())()((((((()(())())())(())()))))())))(()((((())))))))))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 44, 45, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 52, 53, 0, 53, 54, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 65, 66, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 87, 88, 0, 88, 89, 0, 90, 91, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 99, 100, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 123, 124, 0, 125, 126, 0, 127, 128, 0, 133, 134, 0, 134, 135, 0, 139, 140, 0, 141, 142, 0, 147, 148, 0, 148, 149, 0, 154, 155, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 170, 171, 0, 179, 180, 0, 180, 181, 0, 184, 185, 0, 185, 186, 0, 187, 188, 0, 188, 189, 0, 191, 192, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 195, 196, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 209, 210, 0, 211, 212, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 227, 228, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 246, 247, 0, 248, 249, 0, 249, 250, 0, 251, 252, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 264, 265, 0, 265, 266, 0, 268, 269, 0, 271, 272, 0, 274, 275, 0, 275, 276, 0, 278, 279, 0, 284, 285, 0, 289, 290, 0, 290, 291, 0, 292, 293, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 296, 297 }

  88. "()(()(()((())))(()((((())))))((()(()((()(((((()))()((((()()))(()))()()()))((((())((()()((()()))))()(()())(())()((((())()()((()))()(((())))((())(()()())())()(())((()))(((((())()())))(()(())())()))())()(())(((())((()()))()()))())()(())())))(())()()()()(((()(())())))((()))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 48, 49, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 60, 61, 0, 61, 62, 0, 65, 66, 0, 67, 68, 0, 69, 70, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 90, 91, 0, 96, 97, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 122, 123, 0, 123, 124, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 147, 148, 0, 150, 151, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 169, 170, 0, 170, 171, 0, 173, 174, 0, 175, 176, 0, 180, 181, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 187, 188, 0, 190, 191, 0, 194, 195, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 209, 210, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 217, 218, 0, 219, 220, 0, 223, 224, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 232, 233, 0, 237, 238, 0, 238, 239, 0, 241, 242, 0, 243, 244, 0, 245, 246, 0, 247, 248, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 254, 255, 0, 255, 256, 0, 258, 259, 0, 263, 264, 0, 264, 265, 0, 265, 266 }

  89. "((()))()()()((((()()()())))(())(((()()()()((()(()())((())))(()))))))(()((())((((())))())()(()))((()(()()))())(()())(((()())(()))(()))()())()()()()(()()((()())))((()(())(((()((()(()(()))()(()(()))(((()(())()()())(())(((((()())))())())(()((()(())))(()())(()()())()))))))))))"

    Returns: {0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 26, 27, 0, 27, 28, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 58, 59, 0, 59, 60, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 84, 85, 0, 87, 88, 0, 89, 90, 0, 90, 91, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 119, 120, 0, 122, 123, 0, 123, 124, 0, 127, 128, 0, 128, 129, 0, 132, 133, 0, 134, 135, 0, 137, 138, 0, 139, 140, 0, 141, 142, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 148, 149, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 167, 168, 0, 168, 169, 0, 169, 170, 0, 170, 171, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 184, 185, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 194, 195, 0, 195, 196, 0, 196, 197, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 203, 204, 0, 205, 206, 0, 207, 208, 0, 210, 211, 0, 211, 212, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 221, 222, 0, 226, 227, 0, 229, 230, 0, 232, 233, 0, 233, 234, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 245, 246, 0, 246, 247, 0, 248, 249, 0, 251, 252, 0, 252, 253, 0, 254, 255, 0, 256, 257, 0, 259, 260 }

  90. "()(((())(()()())(()(((()()()()()())(((()()))())()()))()(((()()())((())((()()())(((()((()()))(()(())()())())())((()((())))))))((()()())))())()(()()())))())(())((((()))(())((())(()(()(()))(()((()))))((((())((((()())))))()))))())((()))((()))(((((())))(())))()((()()()((((((())))((())())))((()))((())(()((()(()((((()()(()()()))((((()(())()()((((()(((())((((()()())))))(())())(()(())()()()(()((((()))))()))))()))))(((())))))()())(((((()))((()))(()()(()(((()))))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 12, 13, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 43, 44, 0, 46, 47, 0, 48, 49, 0, 52, 53, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 64, 65, 0, 65, 66, 0, 66, 67, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 75, 76, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 98, 99, 0, 100, 101, 0, 103, 104, 0, 106, 107, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 130, 131, 0, 135, 136, 0, 138, 139, 0, 140, 141, 0, 141, 142, 0, 143, 144, 0, 145, 146, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 165, 166, 0, 166, 167, 0, 169, 170, 0, 170, 171, 0, 171, 172, 0, 174, 175, 0, 175, 176, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 181, 182, 0, 185, 186, 0, 186, 187, 0, 188, 189, 0, 189, 190, 0, 190, 191, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 209, 210, 0, 216, 217, 0, 222, 223, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 247, 248, 0, 248, 249, 0, 253, 254, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 279, 280, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 290, 291, 0, 291, 292, 0, 292, 293, 0, 295, 296, 0, 296, 297, 0, 298, 299, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 311, 312, 0, 313, 314, 0, 314, 315, 0, 316, 317, 0, 318, 319, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 328, 329, 0, 329, 330, 0, 332, 333, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 340, 341, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 354, 355, 0, 356, 357, 0, 363, 364, 0, 364, 365, 0, 367, 368, 0, 370, 371, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 379, 380, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 390, 391, 0, 396, 397, 0, 402, 403, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 418, 419, 0, 420, 421, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 438, 439, 0, 439, 440, 0, 441, 442, 0, 443, 444, 0, 444, 445, 0, 446, 447, 0, 447, 448, 0, 448, 449, 0, 449, 450 }

  91. "(()()()((()(((())(()()()())))(()(((())(()()())()))())())))()(())()((()))(())()(()((())(())))((()((((()())(((()()(()))()))()))((()((())))(((()()))()))(()))))((()(((((((()))())(()((((())(((()(())())()())()())(())()))()())())()()))()(()()(((()(((())(()()((((()()(()()()())((()())((((())))(((()()()())((()(((((((((((()))))))))))))))))))))))))))))))))"

    Returns: {0, 2, 3, 0, 4, 5, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 42, 43, 0, 45, 46, 0, 49, 50, 0, 52, 53, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 65, 66, 0, 66, 67, 0, 67, 68, 0, 71, 72, 0, 72, 73, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 116, 117, 0, 120, 121, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 140, 141, 0, 144, 145, 0, 148, 149, 0, 149, 150, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 170, 171, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 188, 189, 0, 189, 190, 0, 192, 193, 0, 195, 196, 0, 197, 198, 0, 200, 201, 0, 202, 203, 0, 205, 206, 0, 206, 207, 0, 209, 210, 0, 213, 214, 0, 215, 216, 0, 218, 219, 0, 221, 222, 0, 223, 224, 0, 227, 228, 0, 229, 230, 0, 230, 231, 0, 232, 233, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 245, 246, 0, 246, 247, 0, 248, 249, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 261, 262, 0, 263, 264, 0, 265, 266, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 272, 273, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 289, 290, 0, 291, 292, 0, 293, 294, 0, 296, 297, 0, 297, 298, 0, 298, 299, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312 }

  92. "(()()())(((()))((())((())())()()))(((())(())))((()))((()(()(((()())(())))(()()(())()))))(())()()((()()(())()))()()()()()()((()))((((()(((()(()))))))(((()(())((()))(()(()())((())((()())(((((())(((())))())((((()()(((())(()))()))(())))()(())()((())())))))))))))))"

    Returns: {0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 40, 41, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 81, 82, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 105, 106, 0, 109, 110, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 122, 123, 0, 123, 124, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 138, 139, 0, 139, 140, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 153, 154, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 162, 163, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 191, 192, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 199, 200, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 208, 209, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 216, 217, 0, 217, 218, 0, 221, 222, 0, 225, 226, 0, 226, 227, 0, 231, 232, 0, 233, 234, 0, 234, 235, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 241, 242, 0, 244, 245 }

  93. "((()()()()))((()))()((((())()(((((((())(((())))(())((()()))(()()()))((()()(()())()))(()(()())()()((())))))()()))(((())(((()()(())))()(()())()((())()((((()()()(())(((()((())()()))))()((())(((()()(())(()((())())((()()(())()))(()()(())())))()(()))))))))))))))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 46, 47, 0, 47, 48, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 79, 80, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 89, 90, 0, 92, 93, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 105, 106, 0, 107, 108, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 130, 131, 0, 132, 133, 0, 133, 134, 0, 135, 136, 0, 138, 139, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 150, 151, 0, 151, 152, 0, 153, 154, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 171, 172, 0, 173, 174, 0, 179, 180, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 191, 192, 0, 193, 194, 0, 194, 195, 0, 197, 198, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 205, 206, 0, 208, 209, 0, 209, 210, 0, 210, 211, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 218, 219, 0, 222, 223, 0, 223, 224, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 231, 232, 0, 236, 237, 0, 238, 239, 0, 239, 240 }

  94. "(()(()))((((((()))())((()()))))(()))()((()(())(())((((()(((((())(()((((()()()()()(()))))))()())()))((((())()((()())())((()()(((()))))(()()()(())()())(())))))))((((()()((()()((((())(())(()())()()))(())()()(()()(()(((()((())))()(()((()(((()(())()))()()(()()((()))((())))(()))(()())))((()()((()((((((()(())))(((())()))(())(((())))())))(((()((()))((())))))()))())()((()()))()())())))(()((()(())()(((()(())(())((((()))()))(()(()(())))()())))())()))(((()))))))))))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 17, 18, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 30, 31, 0, 31, 32, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 45, 46, 0, 46, 47, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 72, 73, 0, 74, 75, 0, 76, 77, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 89, 90, 0, 91, 92, 0, 94, 95, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 114, 115, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 132, 133, 0, 133, 134, 0, 135, 136, 0, 137, 138, 0, 139, 140, 0, 140, 141, 0, 143, 144, 0, 145, 146, 0, 148, 149, 0, 149, 150, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 170, 171, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 179, 180, 0, 180, 181, 0, 183, 184, 0, 184, 185, 0, 186, 187, 0, 189, 190, 0, 191, 192, 0, 195, 196, 0, 196, 197, 0, 199, 200, 0, 201, 202, 0, 203, 204, 0, 204, 205, 0, 206, 207, 0, 208, 209, 0, 209, 210, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 214, 215, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 237, 238, 0, 238, 239, 0, 241, 242, 0, 245, 246, 0, 247, 248, 0, 249, 250, 0, 250, 251, 0, 252, 253, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 267, 268, 0, 268, 269, 0, 272, 273, 0, 273, 274, 0, 275, 276, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 284, 285, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 290, 291, 0, 291, 292, 0, 292, 293, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 298, 299, 0, 299, 300, 0, 304, 305, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 310, 311, 0, 314, 315, 0, 315, 316, 0, 318, 319, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 326, 327, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 351, 352, 0, 355, 356, 0, 358, 359, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 364, 365, 0, 368, 369, 0, 370, 371, 0, 373, 374, 0, 378, 379, 0, 379, 380, 0, 381, 382, 0, 382, 383, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 389, 390, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 394, 395, 0, 396, 397, 0, 397, 398, 0, 400, 401, 0, 401, 402, 0, 404, 405, 0, 405, 406, 0, 406, 407, 0, 407, 408, 0, 408, 409, 0, 412, 413, 0, 416, 417, 0, 417, 418, 0, 419, 420, 0, 420, 421, 0, 422, 423, 0, 423, 424, 0, 428, 429, 0, 430, 431, 0, 435, 436, 0, 438, 439, 0, 442, 443, 0, 443, 444, 0, 444, 445, 0, 445, 446 }

  95. "(()(()())()((((()()((()))())()()())))()(())((())(())))()()(())()((()))(((()(()()()))(()))()((((())(())(((()))(((())))((())(()))()(()()()()(())()()))())())()(())((()())()(()))()(()(((())(()()((()()(()()()(())((())()(()()))))((((()))))))))(((())((())(()()()))()()(())))()()((())())(()(())()))))()()(())()(())()(()())()()(()(()))(())((((((())(()()))())(((()(()()((()))))(()(())(())(())()))()))(((())))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 36, 37, 0, 38, 39, 0, 39, 40, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 79, 80, 0, 83, 84, 0, 84, 85, 0, 88, 89, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 122, 123, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 131, 132, 0, 133, 134, 0, 135, 136, 0, 137, 138, 0, 138, 139, 0, 141, 142, 0, 143, 144, 0, 147, 148, 0, 150, 151, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 166, 167, 0, 168, 169, 0, 169, 170, 0, 173, 174, 0, 175, 176, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 184, 185, 0, 185, 186, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 193, 194, 0, 195, 196, 0, 196, 197, 0, 198, 199, 0, 200, 201, 0, 202, 203, 0, 203, 204, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 216, 217, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 247, 248, 0, 248, 249, 0, 250, 251, 0, 252, 253, 0, 256, 257, 0, 258, 259, 0, 260, 261, 0, 261, 262, 0, 266, 267, 0, 268, 269, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 275, 276, 0, 278, 279, 0, 279, 280, 0, 281, 282, 0, 282, 283, 0, 285, 286, 0, 291, 292, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 299, 300, 0, 301, 302, 0, 302, 303, 0, 305, 306, 0, 307, 308, 0, 308, 309, 0, 310, 311, 0, 313, 314, 0, 315, 316, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 325, 326, 0, 326, 327, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 338, 339, 0, 339, 340, 0, 341, 342, 0, 345, 346, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 351, 352, 0, 353, 354, 0, 354, 355, 0, 356, 357, 0, 358, 359, 0, 359, 360, 0, 360, 361, 0, 366, 367, 0, 367, 368, 0, 369, 370, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 378, 379, 0, 381, 382, 0, 385, 386, 0, 389, 390, 0, 390, 391, 0, 391, 392, 0, 392, 393 }

  96. "()()(())()()()()(()((((()((()((()()()((((()()))(())((((())))(()((((()(())((())())))()())()))(((((((()))()()((()(()(())(()()((())()())(((()))((()))(())()())((((()))(()()()()(())()()(()()()(())))))()((()((((()))())()(())()(((()(((())(()()(()))))()()()()(()())()))(()(()))()))(()))(())()(()()))())))())((()())())((()()()(()((()))(())))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 46, 47, 0, 47, 48, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 77, 78, 0, 82, 83, 0, 84, 85, 0, 87, 88, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 102, 103, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 127, 128, 0, 129, 130, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 145, 146, 0, 146, 147, 0, 149, 150, 0, 151, 152, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 162, 163, 0, 163, 164, 0, 165, 166, 0, 167, 168, 0, 169, 170, 0, 171, 172, 0, 172, 173, 0, 175, 176, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 184, 185, 0, 186, 187, 0, 187, 188, 0, 194, 195, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 208, 209, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 230, 231, 0, 231, 232, 0, 233, 234, 0, 235, 236, 0, 236, 237, 0, 242, 243, 0, 244, 245, 0, 246, 247, 0, 248, 249, 0, 250, 251, 0, 251, 252, 0, 253, 254, 0, 256, 257, 0, 260, 261, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 268, 269, 0, 272, 273, 0, 273, 274, 0, 277, 278, 0, 278, 279, 0, 281, 282, 0, 283, 284, 0, 284, 285, 0, 286, 287, 0, 290, 291, 0, 295, 296, 0, 298, 299, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 305, 306, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 312, 313, 0, 314, 315, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 325, 326, 0, 326, 327 }

  97. "(())((((())((()()(()()))))))((((()()((())(()))(()())())((()((()()))(()))()(())((()())((()(())()((()())()))())(()(()))(()(((()())())()))))())(((((()(())))))))())()()()(())()()()()()()(()(((()(()()))())))(()()(()())(())(())()((()(()(()(())())((())()(((())()())(())))()))))()()(()()(()()))()(()(()))()(())(()((((())(()())()(()))()(()(()())(()))(((())((((())))))(()))(()(()))())(()((()((((())(()())))))())()))(()())()(()))()()()(())(((()(((()())())))))"

    Returns: {0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 40, 41, 0, 41, 42, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 51, 52, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 66, 67, 0, 67, 68, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 81, 82, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 101, 102, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 116, 117, 0, 117, 118, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 124, 125, 0, 127, 128, 0, 130, 131, 0, 136, 137, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 156, 157, 0, 159, 160, 0, 161, 162, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 169, 170, 0, 171, 172, 0, 173, 174, 0, 175, 176, 0, 177, 178, 0, 179, 180, 0, 181, 182, 0, 182, 183, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 192, 193, 0, 196, 197, 0, 201, 202, 0, 202, 203, 0, 204, 205, 0, 206, 207, 0, 207, 208, 0, 209, 210, 0, 212, 213, 0, 213, 214, 0, 216, 217, 0, 217, 218, 0, 220, 221, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 227, 228, 0, 229, 230, 0, 230, 231, 0, 232, 233, 0, 233, 234, 0, 236, 237, 0, 239, 240, 0, 240, 241, 0, 241, 242, 0, 244, 245, 0, 246, 247, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 252, 253, 0, 254, 255, 0, 257, 258, 0, 258, 259, 0, 263, 264, 0, 269, 270, 0, 271, 272, 0, 273, 274, 0, 274, 275, 0, 276, 277, 0, 278, 279, 0, 279, 280, 0, 281, 282, 0, 285, 286, 0, 287, 288, 0, 288, 289, 0, 290, 291, 0, 291, 292, 0, 295, 296, 0, 297, 298, 0, 298, 299, 0, 301, 302, 0, 302, 303, 0, 304, 305, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 311, 312, 0, 312, 313, 0, 314, 315, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 324, 325, 0, 326, 327, 0, 327, 328, 0, 329, 330, 0, 330, 331, 0, 332, 333, 0, 335, 336, 0, 336, 337, 0, 340, 341, 0, 341, 342, 0, 342, 343, 0, 343, 344, 0, 346, 347, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 357, 358, 0, 358, 359, 0, 362, 363, 0, 363, 364, 0, 365, 366, 0, 366, 367, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 380, 381, 0, 381, 382, 0, 382, 383, 0, 383, 384, 0, 384, 385, 0, 387, 388, 0, 388, 389, 0, 390, 391, 0, 397, 398, 0, 400, 401, 0, 404, 405, 0, 405, 406, 0, 407, 408, 0, 410, 411, 0, 412, 413, 0, 413, 414, 0, 417, 418, 0, 419, 420, 0, 421, 422, 0, 423, 424, 0, 424, 425, 0, 427, 428, 0, 428, 429, 0, 429, 430, 0, 430, 431, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 435, 436, 0, 437, 438, 0, 440, 441 }

  98. "((((()()(())())(())(())((((()))))(()(())(()())()()((()())()))()()())))(())((()))(()())(()(((((())))))()()((()(()((())()()())((()(()))())))))()()()(((())()(((((()())())())()())(((((())))()(((())))())))))(((()()()())(()()(((()())((((())))))))))(()()())"

    Returns: {0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 11, 12, 0, 14, 15, 0, 15, 16, 0, 18, 19, 0, 19, 20, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 53, 54, 0, 56, 57, 0, 60, 61, 0, 62, 63, 0, 64, 65, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 100, 101, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 116, 117, 0, 118, 119, 0, 120, 121, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 128, 129, 0, 132, 133, 0, 139, 140, 0, 141, 142, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 151, 152, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 160, 161, 0, 163, 164, 0, 166, 167, 0, 169, 170, 0, 171, 172, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 179, 180, 0, 184, 185, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 194, 195, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 206, 207, 0, 208, 209, 0, 210, 211, 0, 213, 214, 0, 214, 215, 0, 216, 217, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 223, 224, 0, 226, 227, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 241, 242, 0, 242, 243, 0, 244, 245, 0, 246, 247 }

  99. "()()()()()()(())((())()(()(((()))(()())))()(()())())(())()(((())((()())((((()()))(((()(()(((()(()))))(((((((()((()()(()))(((())))))()((())))()((())(()))(()(()(())()))))))((())())()((()())((()((((())())(((())(((((()(()))((())()))))()()()())()())(((((((((())((())())()(()(()())())()))()()))((())())((()()())()()((())(()))(()))))))())()(()()()(((()(())((())()((()(()((((()((())())((()(((()((()()())(()(())))))()))))))))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 45, 46, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 67, 68, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 116, 117, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 123, 124, 0, 130, 131, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 146, 147, 0, 147, 148, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 161, 162, 0, 169, 170, 0, 170, 171, 0, 171, 172, 0, 174, 175, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 183, 184, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 191, 192, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 197, 198, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 209, 210, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 223, 224, 0, 229, 230, 0, 231, 232, 0, 233, 234, 0, 235, 236, 0, 238, 239, 0, 240, 241, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 246, 247, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 260, 261, 0, 263, 264, 0, 265, 266, 0, 266, 267, 0, 268, 269, 0, 269, 270, 0, 271, 272, 0, 274, 275, 0, 277, 278, 0, 281, 282, 0, 283, 284, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 292, 293, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 301, 302, 0, 304, 305, 0, 306, 307, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 313, 314, 0, 314, 315, 0, 318, 319, 0, 319, 320, 0, 327, 328, 0, 330, 331, 0, 332, 333, 0, 333, 334, 0, 335, 336, 0, 337, 338, 0, 339, 340, 0, 340, 341, 0, 341, 342, 0, 342, 343, 0, 344, 345, 0, 345, 346, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 353, 354, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 359, 360, 0, 360, 361, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 366, 367, 0, 368, 369, 0, 369, 370, 0, 370, 371, 0, 373, 374, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 380, 381, 0, 381, 382, 0, 382, 383, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 389, 390, 0, 391, 392, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 398, 399, 0, 405, 406 }

  100. "()(()()((()())((((((((()()((((()))))())))((()())((()((()(())()(()()))()))(()())((()()((((()))((()()((())(((())())))((()())(()))((()))))()((())))()())(()))())))(((()()(())()())))()(())(()()(()()()())()()(())()()))))(())))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 10, 11, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 35, 36, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 68, 69, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 109, 110, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 121, 122, 0, 122, 123, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 134, 135, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 143, 144, 0, 145, 146, 0, 148, 149, 0, 149, 150, 0, 153, 154, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 169, 170, 0, 171, 172, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 182, 183, 0, 183, 184, 0, 185, 186, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 192, 193, 0, 194, 195, 0, 197, 198, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 205, 206, 0, 207, 208, 0, 213, 214, 0, 214, 215 }

  101. "((((()))))((())((((()((()((((((())((()()()()(()()()(())((())())()()((())(()))()(()))((((((()())())((((())(())()())()())((()()((((()(())))(()())((()((()())(())()()))()((()()))(())))(()()(()()(()())()(())(()(())(()())(())((())()()())))(()()()()(((()))((((())(()()(((())(())))()(()(()(())()()()()))(((()(())()(()())(()()()()))))(()()()()())(()))((())))))()))(()(()((()())(())(()((((((())()))()()))))())))((())))(())(())(((()))()(()()()(()))))((()()()()())))))))))))))))))))))))"

    Returns: {0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 46, 47, 0, 48, 49, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 59, 60, 0, 62, 63, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 71, 72, 0, 72, 73, 0, 76, 77, 0, 78, 79, 0, 79, 80, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 91, 92, 0, 94, 95, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 110, 111, 0, 113, 114, 0, 115, 116, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 136, 137, 0, 137, 138, 0, 139, 140, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 157, 158, 0, 159, 160, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 169, 170, 0, 173, 174, 0, 174, 175, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 184, 185, 0, 185, 186, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 192, 193, 0, 195, 196, 0, 197, 198, 0, 198, 199, 0, 201, 202, 0, 202, 203, 0, 204, 205, 0, 205, 206, 0, 208, 209, 0, 209, 210, 0, 211, 212, 0, 214, 215, 0, 215, 216, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 223, 224, 0, 225, 226, 0, 227, 228, 0, 232, 233, 0, 233, 234, 0, 235, 236, 0, 237, 238, 0, 239, 240, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 266, 267, 0, 267, 268, 0, 272, 273, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 278, 279, 0, 280, 281, 0, 281, 282, 0, 284, 285, 0, 286, 287, 0, 288, 289, 0, 290, 291, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 308, 309, 0, 311, 312, 0, 312, 313, 0, 314, 315, 0, 316, 317, 0, 318, 319, 0, 324, 325, 0, 325, 326, 0, 327, 328, 0, 329, 330, 0, 331, 332, 0, 333, 334, 0, 336, 337, 0, 337, 338, 0, 341, 342, 0, 342, 343, 0, 343, 344, 0, 350, 351, 0, 354, 355, 0, 355, 356, 0, 357, 358, 0, 358, 359, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 364, 365, 0, 367, 368, 0, 368, 369, 0, 371, 372, 0, 372, 373, 0, 374, 375, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 383, 384, 0, 387, 388, 0, 389, 390, 0, 395, 396, 0, 400, 401, 0, 401, 402, 0, 402, 403, 0, 407, 408, 0, 408, 409, 0, 411, 412, 0, 412, 413, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 422, 423, 0, 424, 425, 0, 425, 426, 0, 427, 428, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 438, 439, 0, 439, 440, 0, 440, 441, 0, 442, 443, 0, 444, 445, 0, 446, 447, 0, 448, 449 }

  102. "()(())(()()(()((((()(()(((()))()(((())(()))()()())((()))())))(()(())((())(((()((()()((()())(())()())))(())()))(()))()))))((((((()(((())()(()()(()()))(()()(((((()()))))(())(()(()(()())())()()))(()))()((())((((()())())((()(())()((()()))()(()()(())())((()(()())(()(()())(())))())())))(((()()((())))((()()())())()))(()()()()())(()))))((((()))))()()()()))(()))(()))()()))()))))()(()()())()()((()(((()(()(()())((()))(()))))))(()))((()()(()(()()(()()()))))())()()"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 42, 43, 0, 44, 45, 0, 46, 47, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 55, 56, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 81, 82, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 90, 91, 0, 91, 92, 0, 94, 95, 0, 96, 97, 0, 101, 102, 0, 102, 103, 0, 105, 106, 0, 109, 110, 0, 110, 111, 0, 114, 115, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 134, 135, 0, 136, 137, 0, 137, 138, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 144, 145, 0, 148, 149, 0, 149, 150, 0, 151, 152, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 160, 161, 0, 166, 167, 0, 167, 168, 0, 170, 171, 0, 171, 172, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 182, 183, 0, 185, 186, 0, 187, 188, 0, 191, 192, 0, 192, 193, 0, 196, 197, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 209, 210, 0, 212, 213, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 229, 230, 0, 233, 234, 0, 235, 236, 0, 236, 237, 0, 238, 239, 0, 240, 241, 0, 241, 242, 0, 244, 245, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 251, 252, 0, 252, 253, 0, 254, 255, 0, 257, 258, 0, 258, 259, 0, 260, 261, 0, 261, 262, 0, 263, 264, 0, 266, 267, 0, 267, 268, 0, 272, 273, 0, 275, 276, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 283, 284, 0, 285, 286, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 298, 299, 0, 300, 301, 0, 303, 304, 0, 306, 307, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 315, 316, 0, 317, 318, 0, 319, 320, 0, 322, 323, 0, 323, 324, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 339, 340, 0, 341, 342, 0, 343, 344, 0, 345, 346, 0, 349, 350, 0, 350, 351, 0, 354, 355, 0, 355, 356, 0, 359, 360, 0, 361, 362, 0, 365, 366, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 376, 377, 0, 378, 379, 0, 381, 382, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 389, 390, 0, 390, 391, 0, 391, 392, 0, 392, 393, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 398, 399, 0, 400, 401, 0, 403, 404, 0, 404, 405, 0, 405, 406, 0, 409, 410, 0, 410, 411, 0, 418, 419, 0, 419, 420, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 427, 428, 0, 429, 430, 0, 430, 431, 0, 432, 433, 0, 433, 434, 0, 435, 436, 0, 437, 438, 0, 438, 439, 0, 440, 441, 0, 442, 443, 0, 448, 449, 0, 451, 452, 0, 453, 454 }

  103. "((()()((())))((())))()(())(((((())()()()()))(((((())(()())))((((()(()(()(()))()((()(()(()()))()()())()()()())))()((()(())()(())()())(((())((((()(()(())))((())))(((()()())(((()())))((()())(((((())(()()))))()(((())))((()())))()))())))())))))((()()))())))()()((()()()(()))))()()(()()(()()())()()(()())(()))(()(()))((()))()()((((((((((())))((()))(()))()(()(())(()()))))))())())())()()()()()()()()((())((())))((()()))()()()((()))((())(()))(()(()))()(())()(()()()())((())())()()(()())"

    Returns: {0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 35, 36, 0, 37, 38, 0, 39, 40, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 76, 77, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 92, 93, 0, 94, 95, 0, 96, 97, 0, 99, 100, 0, 101, 102, 0, 103, 104, 0, 105, 106, 0, 110, 111, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 117, 118, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 126, 127, 0, 128, 129, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 143, 144, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 166, 167, 0, 169, 170, 0, 170, 171, 0, 171, 172, 0, 172, 173, 0, 174, 175, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 183, 184, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 194, 195, 0, 195, 196, 0, 197, 198, 0, 203, 204, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 217, 218, 0, 222, 223, 0, 226, 227, 0, 231, 232, 0, 238, 239, 0, 239, 240, 0, 240, 241, 0, 242, 243, 0, 246, 247, 0, 251, 252, 0, 253, 254, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 270, 271, 0, 272, 273, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 279, 280, 0, 280, 281, 0, 282, 283, 0, 284, 285, 0, 287, 288, 0, 289, 290, 0, 291, 292, 0, 292, 293, 0, 294, 295, 0, 297, 298, 0, 298, 299, 0, 302, 303, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 316, 317, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 335, 336, 0, 336, 337, 0, 337, 338, 0, 341, 342, 0, 342, 343, 0, 346, 347, 0, 348, 349, 0, 349, 350, 0, 351, 352, 0, 352, 353, 0, 355, 356, 0, 356, 357, 0, 358, 359, 0, 366, 367, 0, 369, 370, 0, 372, 373, 0, 375, 376, 0, 377, 378, 0, 379, 380, 0, 381, 382, 0, 383, 384, 0, 385, 386, 0, 387, 388, 0, 389, 390, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 396, 397, 0, 397, 398, 0, 398, 399, 0, 403, 404, 0, 404, 405, 0, 405, 406, 0, 407, 408, 0, 411, 412, 0, 413, 414, 0, 415, 416, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 428, 429, 0, 429, 430, 0, 433, 434, 0, 434, 435, 0, 436, 437, 0, 437, 438, 0, 441, 442, 0, 443, 444, 0, 444, 445, 0, 447, 448, 0, 449, 450, 0, 450, 451, 0, 452, 453, 0, 454, 455, 0, 456, 457, 0, 459, 460, 0, 460, 461, 0, 461, 462, 0, 464, 465, 0, 467, 468, 0, 469, 470, 0, 471, 472, 0, 472, 473, 0, 474, 475 }

  104. "((((()())(((((((())(((((()(((()()(()))(((()((())()(((()(())))(()(((()(()(()())()(((((()))((()())())))))()))(()()()(((((())()(()(()(()())()()((((())()()((()())))(())))(((()))))((())(())))((()()()((()())())))(((()()(()))())))())((()())()()(()((()()()())((((((())())()))(()()))((()((())))((())(()))(()()(((()))(())(()((()))(((()()(()(())(()()())))(()(()))()))((()(()(())())))()((())()))((())((()((()())))(((()))(())((()()))()))()())())))((())(()))))()((()))))())))(())((())))))))))))))))))))))))))"

    Returns: {0, 5, 6, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 55, 56, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 74, 75, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 92, 93, 0, 95, 96, 0, 102, 103, 0, 106, 107, 0, 107, 108, 0, 109, 110, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 132, 133, 0, 135, 136, 0, 137, 138, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 146, 147, 0, 148, 149, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 159, 160, 0, 160, 161, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 179, 180, 0, 180, 181, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 191, 192, 0, 193, 194, 0, 194, 195, 0, 195, 196, 0, 197, 198, 0, 200, 201, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 212, 213, 0, 213, 214, 0, 217, 218, 0, 222, 223, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 229, 230, 0, 232, 233, 0, 234, 235, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 241, 242, 0, 243, 244, 0, 245, 246, 0, 247, 248, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 259, 260, 0, 262, 263, 0, 266, 267, 0, 267, 268, 0, 269, 270, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 289, 290, 0, 290, 291, 0, 294, 295, 0, 295, 296, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 306, 307, 0, 307, 308, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 324, 325, 0, 326, 327, 0, 327, 328, 0, 329, 330, 0, 330, 331, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 338, 339, 0, 343, 344, 0, 344, 345, 0, 346, 347, 0, 347, 348, 0, 351, 352, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 359, 360, 0, 360, 361, 0, 362, 363, 0, 363, 364, 0, 366, 367, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 375, 376, 0, 378, 379, 0, 382, 383, 0, 383, 384, 0, 384, 385, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 395, 396, 0, 400, 401, 0, 401, 402, 0, 402, 403, 0, 403, 404, 0, 407, 408, 0, 408, 409, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 415, 416, 0, 419, 420, 0, 423, 424, 0, 425, 426, 0, 428, 429, 0, 433, 434, 0, 434, 435, 0, 435, 436, 0, 438, 439, 0, 439, 440, 0, 445, 446, 0, 447, 448, 0, 448, 449, 0, 449, 450, 0, 455, 456, 0, 460, 461, 0, 461, 462, 0, 464, 465, 0, 465, 466, 0, 466, 467 }

  105. "()(()())(((((()(()(())())())(())(()((())((()((()))))(((()(())(((())(()((((()(())()()()))()()()(())(())))())())()()(((()((()())(((()())()()))())()()())())(((())(())(()()))())((()((()())())))()())(())))()((())()(()())(())(((())((()(()()(())(())))((())))()(()((((((((())((((()))((()())))))())())(()))))()((()(()))())()()))())))())()))()((()))))))(()))()(()(())())()(()(((()(()()())()(()()()))()))(()(()(()))())((()(())(((((()))()()(()(((())()((((((()(()(())(()()))()))))(())))(()))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 21, 22, 0, 24, 25, 0, 27, 28, 0, 28, 29, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 79, 80, 0, 81, 82, 0, 83, 84, 0, 87, 88, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 97, 98, 0, 98, 99, 0, 103, 104, 0, 106, 107, 0, 109, 110, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 130, 131, 0, 133, 134, 0, 135, 136, 0, 139, 140, 0, 142, 143, 0, 144, 145, 0, 146, 147, 0, 149, 150, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 158, 159, 0, 159, 160, 0, 162, 163, 0, 163, 164, 0, 165, 166, 0, 169, 170, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 183, 184, 0, 188, 189, 0, 190, 191, 0, 193, 194, 0, 194, 195, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 206, 207, 0, 208, 209, 0, 209, 210, 0, 211, 212, 0, 214, 215, 0, 215, 216, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 233, 234, 0, 234, 235, 0, 237, 238, 0, 238, 239, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 250, 251, 0, 252, 253, 0, 253, 254, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 278, 279, 0, 285, 286, 0, 288, 289, 0, 291, 292, 0, 292, 293, 0, 298, 299, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 304, 305, 0, 305, 306, 0, 309, 310, 0, 312, 313, 0, 314, 315, 0, 318, 319, 0, 323, 324, 0, 326, 327, 0, 330, 331, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 342, 343, 0, 343, 344, 0, 347, 348, 0, 349, 350, 0, 350, 351, 0, 352, 353, 0, 353, 354, 0, 356, 357, 0, 359, 360, 0, 361, 362, 0, 362, 363, 0, 364, 365, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 369, 370, 0, 370, 371, 0, 372, 373, 0, 374, 375, 0, 377, 378, 0, 379, 380, 0, 380, 381, 0, 382, 383, 0, 384, 385, 0, 388, 389, 0, 392, 393, 0, 393, 394, 0, 395, 396, 0, 396, 397, 0, 398, 399, 0, 399, 400, 0, 403, 404, 0, 406, 407, 0, 407, 408, 0, 408, 409, 0, 410, 411, 0, 411, 412, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 423, 424, 0, 425, 426, 0, 427, 428, 0, 428, 429, 0, 430, 431, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 444, 445, 0, 446, 447, 0, 447, 448, 0, 449, 450, 0, 450, 451, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 460, 461, 0, 466, 467, 0, 467, 468, 0, 472, 473, 0, 473, 474 }

  106. "(()((()))(()))(((((())))))()((())()()()())()()()()(()(()())())((())((()()(()(()())(()(()()(((()((())()())))))(((()()(((()()((()(())())((()())())(()))))(((()()())()()(((((()))()()))(()())))(())))()(())()()))))))))((((()))(((((((()(())()(()((())())))())()()))))((()((((()()))(((()()))())()())())))()))(())(())())((())()()()((())((()()()((()((()()()()()))((()())))(((())())))()()((((((()((()))())()(())(((()(()()((())))))))))(()())))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 8, 9, 0, 9, 10, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 25, 26, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 32, 33, 0, 34, 35, 0, 36, 37, 0, 38, 39, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 58, 59, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 78, 79, 0, 81, 82, 0, 82, 83, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 99, 100, 0, 101, 102, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 130, 131, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 137, 138, 0, 140, 141, 0, 143, 144, 0, 144, 145, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 155, 156, 0, 157, 158, 0, 160, 161, 0, 162, 163, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 169, 170, 0, 173, 174, 0, 175, 176, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 187, 188, 0, 188, 189, 0, 193, 194, 0, 195, 196, 0, 196, 197, 0, 199, 200, 0, 201, 202, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 232, 233, 0, 234, 235, 0, 235, 236, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 242, 243, 0, 247, 248, 0, 250, 251, 0, 252, 253, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 268, 269, 0, 272, 273, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 281, 282, 0, 284, 285, 0, 286, 287, 0, 289, 290, 0, 294, 295, 0, 298, 299, 0, 299, 300, 0, 302, 303, 0, 303, 304, 0, 306, 307, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 314, 315, 0, 316, 317, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 329, 330, 0, 331, 332, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 341, 342, 0, 343, 344, 0, 345, 346, 0, 347, 348, 0, 351, 352, 0, 352, 353, 0, 353, 354, 0, 355, 356, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 366, 367, 0, 371, 372, 0, 373, 374, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 389, 390, 0, 392, 393, 0, 394, 395, 0, 395, 396, 0, 398, 399, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 403, 404, 0, 404, 405, 0, 406, 407, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 421, 422, 0, 422, 423, 0, 424, 425 }

  107. "(())()()(())()(()())()()()((()))()()(((()(()((())))(()((()(())()())(((((((())()())))())()()(())()(())(((())))()(())()()))))))((()(())())))()()(((((()()((()))())(()(()((()))())((()(((()())((()(())()((((((()()()())))(())(((()(())))(((()())())))()(()))((()))(()((()))((()(()))))())((())(())())(()()))())()())())(())))(((()(()()()(()(()()()()()))())(())))()))()())())))())()()((((()((()(()((()))())))((()(())(((()()())))(((()(()(())))))))))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 31, 32, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 50, 51, 0, 51, 52, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 61, 62, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 76, 77, 0, 78, 79, 0, 83, 84, 0, 86, 87, 0, 88, 89, 0, 90, 91, 0, 91, 92, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 114, 115, 0, 116, 117, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 132, 133, 0, 137, 138, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 148, 149, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 156, 157, 0, 159, 160, 0, 160, 161, 0, 162, 163, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 171, 172, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 183, 184, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 191, 192, 0, 194, 195, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 204, 205, 0, 206, 207, 0, 208, 209, 0, 213, 214, 0, 214, 215, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 222, 223, 0, 223, 224, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 233, 234, 0, 236, 237, 0, 241, 242, 0, 243, 244, 0, 244, 245, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 254, 255, 0, 255, 256, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 267, 268, 0, 268, 269, 0, 274, 275, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 282, 283, 0, 283, 284, 0, 286, 287, 0, 289, 290, 0, 290, 291, 0, 292, 293, 0, 296, 297, 0, 299, 300, 0, 301, 302, 0, 304, 305, 0, 307, 308, 0, 308, 309, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 319, 320, 0, 321, 322, 0, 323, 324, 0, 325, 326, 0, 326, 327, 0, 328, 329, 0, 329, 330, 0, 331, 332, 0, 333, 334, 0, 335, 336, 0, 337, 338, 0, 341, 342, 0, 344, 345, 0, 345, 346, 0, 350, 351, 0, 354, 355, 0, 356, 357, 0, 359, 360, 0, 364, 365, 0, 367, 368, 0, 369, 370, 0, 371, 372, 0, 372, 373, 0, 373, 374, 0, 374, 375, 0, 375, 376, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 381, 382, 0, 382, 383, 0, 384, 385, 0, 385, 386, 0, 386, 387, 0, 390, 391, 0, 395, 396, 0, 396, 397, 0, 397, 398, 0, 399, 400, 0, 400, 401, 0, 403, 404, 0, 404, 405, 0, 405, 406, 0, 406, 407, 0, 408, 409, 0, 410, 411, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 420, 421, 0, 421, 422, 0, 423, 424, 0, 424, 425 }

  108. "()((((((())()())))(()(((()((()()(((()())))(()))()(((())()(((((()(()(())))(()()))(())((()))(()))())(())())(())(()))((()))(())))(()))))(()())())((((()())()(())((((()())()(())())()(((((())))())))))))((()((()((((())()())(((()())))(())))()((((())((((((((((()))((((()(()((()(())(()))))(()())())(())())(())())((()()()((()(())()(()()(((((()())())(((())()()(()()))()(((()))((((((((()()(((((())))()()(()())))))))))))))))))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 10, 11, 0, 12, 13, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 41, 42, 0, 42, 43, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 79, 80, 0, 80, 81, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 89, 90, 0, 90, 91, 0, 94, 95, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 119, 120, 0, 120, 121, 0, 125, 126, 0, 126, 127, 0, 132, 133, 0, 133, 134, 0, 135, 136, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 147, 148, 0, 150, 151, 0, 152, 153, 0, 153, 154, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 162, 163, 0, 165, 166, 0, 167, 168, 0, 168, 169, 0, 171, 172, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 186, 187, 0, 195, 196, 0, 196, 197, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 210, 211, 0, 212, 213, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 220, 221, 0, 225, 226, 0, 226, 227, 0, 231, 232, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 246, 247, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 260, 261, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 267, 268, 0, 268, 269, 0, 271, 272, 0, 272, 273, 0, 278, 279, 0, 279, 280, 0, 281, 282, 0, 284, 285, 0, 287, 288, 0, 288, 289, 0, 291, 292, 0, 294, 295, 0, 295, 296, 0, 298, 299, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 305, 306, 0, 307, 308, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 314, 315, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 322, 323, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 331, 332, 0, 334, 335, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 340, 341, 0, 343, 344, 0, 345, 346, 0, 347, 348, 0, 348, 349, 0, 350, 351, 0, 354, 355, 0, 356, 357, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 370, 371, 0, 371, 372, 0, 373, 374, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 385, 386, 0, 387, 388, 0, 389, 390, 0, 390, 391, 0, 392, 393 }

  109. "()(()())()((())(((((()))())()(((())()))((()()(())()()()()))()((((()))((())())()())(((()))))((()(()((()(((()))(()(())))(()((((()(()())(((())))()(()((((()())))()()((((((())(()))((()))(()(((((()()))))()((((()))()(()())()))((()))()(((()()())()))))()))))))))))()))))()))((())))(()()(()))))()()()()()()()()(()(())((()(()()(()((())()))()))()(())(()(()()))))()(((())))(((()(()))()))(())(()(()))()(())()((()(((()))))()(((()(())()((())(())())((())()((()())()()()()(()(((()(()(()((()(()))()))))(()())())))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 23, 24, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 34, 35, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 44, 45, 0, 45, 46, 0, 48, 49, 0, 50, 51, 0, 52, 53, 0, 54, 55, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 76, 77, 0, 78, 79, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 117, 118, 0, 118, 119, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 129, 130, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 140, 141, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 151, 152, 0, 156, 157, 0, 158, 159, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 169, 170, 0, 170, 171, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 180, 181, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 196, 197, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 206, 207, 0, 208, 209, 0, 209, 210, 0, 211, 212, 0, 214, 215, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 224, 225, 0, 226, 227, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 233, 234, 0, 236, 237, 0, 242, 243, 0, 254, 255, 0, 260, 261, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 276, 277, 0, 277, 278, 0, 283, 284, 0, 285, 286, 0, 287, 288, 0, 289, 290, 0, 291, 292, 0, 293, 294, 0, 295, 296, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 303, 304, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 319, 320, 0, 320, 321, 0, 323, 324, 0, 327, 328, 0, 331, 332, 0, 333, 334, 0, 334, 335, 0, 337, 338, 0, 338, 339, 0, 340, 341, 0, 341, 342, 0, 343, 344, 0, 349, 350, 0, 351, 352, 0, 352, 353, 0, 353, 354, 0, 354, 355, 0, 359, 360, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 364, 365, 0, 365, 366, 0, 369, 370, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 378, 379, 0, 380, 381, 0, 381, 382, 0, 385, 386, 0, 387, 388, 0, 388, 389, 0, 391, 392, 0, 393, 394, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 398, 399, 0, 399, 400, 0, 400, 401, 0, 406, 407, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 413, 414, 0, 414, 415, 0, 417, 418, 0, 419, 420, 0, 420, 421, 0, 421, 422, 0, 424, 425, 0, 425, 426, 0, 428, 429, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 440, 441, 0, 442, 443, 0, 445, 446, 0, 447, 448, 0, 449, 450, 0, 451, 452, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 461, 462, 0, 462, 463, 0, 464, 465, 0, 465, 466, 0, 467, 468, 0, 468, 469, 0, 469, 470, 0, 471, 472, 0, 472, 473, 0, 476, 477, 0, 482, 483, 0, 483, 484, 0, 485, 486, 0, 488, 489 }

  110. "()()(())()()(()()((())())(((()))((()(()))(((((()()(()()))))((())(())()))))))()(((((()())())())))()((((())()))((((()()()))())()()))(())((())())(())()(((()())())())(())()(())()(()()(((())(((()()()()))()((((((())(()))))()()))))(()()()))((()()))((((()))(()(()()())(()())())())(()())))()(())()(()((()))()()())((((((((())((()()(())(((()()()()()((((()())()(())(()()()((())))())(())(()))(()(())))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 21, 22, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 84, 85, 0, 87, 88, 0, 90, 91, 0, 95, 96, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 104, 105, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 114, 115, 0, 116, 117, 0, 120, 121, 0, 123, 124, 0, 125, 126, 0, 129, 130, 0, 130, 131, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 155, 156, 0, 158, 159, 0, 161, 162, 0, 162, 163, 0, 165, 166, 0, 167, 168, 0, 168, 169, 0, 171, 172, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 191, 192, 0, 193, 194, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 208, 209, 0, 209, 210, 0, 215, 216, 0, 217, 218, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 228, 229, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 236, 237, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 248, 249, 0, 249, 250, 0, 251, 252, 0, 252, 253, 0, 254, 255, 0, 256, 257, 0, 259, 260, 0, 260, 261, 0, 262, 263, 0, 265, 266, 0, 268, 269, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 279, 280, 0, 281, 282, 0, 282, 283, 0, 285, 286, 0, 287, 288, 0, 288, 289, 0, 290, 291, 0, 291, 292, 0, 292, 293, 0, 296, 297, 0, 298, 299, 0, 300, 301, 0, 303, 304, 0, 304, 305, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 314, 315, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 329, 330, 0, 331, 332, 0, 333, 334, 0, 335, 336, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 340, 341, 0, 341, 342, 0, 343, 344, 0, 346, 347, 0, 348, 349, 0, 349, 350, 0, 352, 353, 0, 353, 354, 0, 355, 356, 0, 357, 358, 0, 359, 360, 0, 360, 361, 0, 361, 362, 0, 366, 367, 0, 369, 370, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 378, 379, 0, 379, 380, 0, 381, 382, 0, 382, 383 }

  111. "((()())((((()((()(()))())))()()())()))(((()(()))(((())()((((()()())())()))(((()()(())(())))))(()((((()(()(())()()()()((())()()()((()(()()())))(()))))())(())()())(()((((((()())())((())))))()())(()((()(()(())(()()()))()()))()))()))()()()()((())()(())())((())((()(())()))(()()))())))(())()()()((((()(()))((()(()()((()()(()()))(((())(()))())(())(()))))())))(()(()(()))(())(((()((())())))())))()(())()()(()()((())((()()))((()))()))()()((()())())"

    Returns: {0, 3, 4, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 21, 22, 0, 26, 27, 0, 28, 29, 0, 30, 31, 0, 33, 34, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 66, 67, 0, 69, 70, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 84, 85, 0, 85, 86, 0, 92, 93, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 110, 111, 0, 112, 113, 0, 114, 115, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 123, 124, 0, 125, 126, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 136, 137, 0, 141, 142, 0, 142, 143, 0, 148, 149, 0, 151, 152, 0, 152, 153, 0, 155, 156, 0, 157, 158, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 169, 170, 0, 171, 172, 0, 174, 175, 0, 177, 178, 0, 178, 179, 0, 179, 180, 0, 186, 187, 0, 188, 189, 0, 191, 192, 0, 192, 193, 0, 194, 195, 0, 195, 196, 0, 196, 197, 0, 198, 199, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 205, 206, 0, 206, 207, 0, 208, 209, 0, 210, 211, 0, 214, 215, 0, 216, 217, 0, 220, 221, 0, 224, 225, 0, 228, 229, 0, 230, 231, 0, 232, 233, 0, 234, 235, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 241, 242, 0, 243, 244, 0, 244, 245, 0, 247, 248, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 260, 261, 0, 263, 264, 0, 267, 268, 0, 268, 269, 0, 270, 271, 0, 274, 275, 0, 279, 280, 0, 280, 281, 0, 283, 284, 0, 285, 286, 0, 287, 288, 0, 289, 290, 0, 290, 291, 0, 291, 292, 0, 292, 293, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 304, 305, 0, 305, 306, 0, 307, 308, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 328, 329, 0, 329, 330, 0, 333, 334, 0, 336, 337, 0, 337, 338, 0, 340, 341, 0, 341, 342, 0, 347, 348, 0, 352, 353, 0, 353, 354, 0, 355, 356, 0, 356, 357, 0, 358, 359, 0, 359, 360, 0, 363, 364, 0, 364, 365, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 370, 371, 0, 372, 373, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 382, 383, 0, 387, 388, 0, 389, 390, 0, 390, 391, 0, 393, 394, 0, 395, 396, 0, 397, 398, 0, 398, 399, 0, 400, 401, 0, 402, 403, 0, 403, 404, 0, 404, 405, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 411, 412, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 421, 422, 0, 425, 426, 0, 427, 428, 0, 429, 430, 0, 430, 431, 0, 431, 432, 0, 433, 434, 0, 436, 437 }

  112. "()(((())())(((((())()((())))(()(()))((()(((()())())))())))((((((()()()((()()()(()()()(((())()())))(()))(())()(()(()((())()())(()())((()((()))()())()(()())())())()(()))))()())()(()))(()(())(()(()()()())(()))((((())()((()()))(()))(((())(()()))))()()()()(()))))()()()))))()()()()((()(()())((()()()(((((())(()))((()))(((()((())((())(()(()))))))))()(())(((((())))()))())))())))(()()(((()((())(()))(())(()())()())(()((())((((())())))())(((()()()()))())())()()((()(((()(()(()))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 27, 28, 0, 28, 29, 0, 30, 31, 0, 31, 32, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 47, 48, 0, 52, 53, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 65, 66, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 82, 83, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 90, 91, 0, 92, 93, 0, 97, 98, 0, 98, 99, 0, 102, 103, 0, 103, 104, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 119, 120, 0, 121, 122, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 140, 141, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 148, 149, 0, 150, 151, 0, 153, 154, 0, 156, 157, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 168, 169, 0, 170, 171, 0, 173, 174, 0, 175, 176, 0, 176, 177, 0, 180, 181, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 191, 192, 0, 193, 194, 0, 195, 196, 0, 197, 198, 0, 200, 201, 0, 201, 202, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 209, 210, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 218, 219, 0, 222, 223, 0, 223, 224, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 233, 234, 0, 234, 235, 0, 236, 237, 0, 242, 243, 0, 244, 245, 0, 246, 247, 0, 248, 249, 0, 250, 251, 0, 251, 252, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 267, 268, 0, 269, 270, 0, 271, 272, 0, 273, 274, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 279, 280, 0, 280, 281, 0, 282, 283, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 289, 290, 0, 291, 292, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 298, 299, 0, 301, 302, 0, 302, 303, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 312, 313, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 317, 318, 0, 318, 319, 0, 319, 320, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 327, 328, 0, 328, 329, 0, 330, 331, 0, 331, 332, 0, 341, 342, 0, 343, 344, 0, 344, 345, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 357, 358, 0, 361, 362, 0, 366, 367, 0, 371, 372, 0, 372, 373, 0, 374, 375, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 381, 382, 0, 382, 383, 0, 383, 384, 0, 386, 387, 0, 387, 388, 0, 391, 392, 0, 392, 393, 0, 395, 396, 0, 396, 397, 0, 398, 399, 0, 401, 402, 0, 403, 404, 0, 406, 407, 0, 407, 408, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 421, 422, 0, 426, 427, 0, 429, 430, 0, 430, 431, 0, 431, 432, 0, 432, 433, 0, 434, 435, 0, 436, 437, 0, 438, 439, 0, 442, 443, 0, 445, 446, 0, 448, 449, 0, 450, 451, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 461, 462, 0, 462, 463, 0, 464, 465, 0, 465, 466 }

  113. "(())((()((()()()()((()()()())))((()()()(((()))))))))()()()(())(()())()()(((()()())))()()((((()()())()))(()))(())()(())()()()()()()()()(()(()(()((())))()(()())(()))()())()(())(((()(()()()((()())()()(())(((())()))(()((()(()(((())()()))((())(((()((()((()))())))())((((()()))(())()()()(())())())())((()))(()()((())())(()()(()((()))(()()))((())((())(()(())()())(()()))))(()(()()()()()((((())))())())))())))())))()(()))(())())(((())()((()))()()))()))"

    Returns: {0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 36, 37, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 58, 59, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 67, 68, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 78, 79, 0, 83, 84, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 93, 94, 0, 95, 96, 0, 98, 99, 0, 102, 103, 0, 103, 104, 0, 107, 108, 0, 108, 109, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 125, 126, 0, 127, 128, 0, 129, 130, 0, 131, 132, 0, 133, 134, 0, 134, 135, 0, 136, 137, 0, 137, 138, 0, 139, 140, 0, 140, 141, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 149, 150, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 157, 158, 0, 158, 159, 0, 162, 163, 0, 164, 165, 0, 167, 168, 0, 169, 170, 0, 170, 171, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 181, 182, 0, 183, 184, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 192, 193, 0, 194, 195, 0, 196, 197, 0, 197, 198, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 206, 207, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 217, 218, 0, 218, 219, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 226, 227, 0, 228, 229, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 240, 241, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 246, 247, 0, 247, 248, 0, 248, 249, 0, 252, 253, 0, 257, 258, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 266, 267, 0, 270, 271, 0, 271, 272, 0, 274, 275, 0, 276, 277, 0, 278, 279, 0, 280, 281, 0, 281, 282, 0, 284, 285, 0, 287, 288, 0, 290, 291, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 304, 305, 0, 305, 306, 0, 306, 307, 0, 309, 310, 0, 312, 313, 0, 313, 314, 0, 315, 316, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 326, 327, 0, 327, 328, 0, 329, 330, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 338, 339, 0, 339, 340, 0, 340, 341, 0, 343, 344, 0, 344, 345, 0, 346, 347, 0, 347, 348, 0, 350, 351, 0, 352, 353, 0, 355, 356, 0, 356, 357, 0, 358, 359, 0, 364, 365, 0, 365, 366, 0, 367, 368, 0, 368, 369, 0, 370, 371, 0, 372, 373, 0, 374, 375, 0, 376, 377, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 382, 383, 0, 387, 388, 0, 390, 391, 0, 395, 396, 0, 400, 401, 0, 405, 406, 0, 407, 408, 0, 408, 409, 0, 412, 413, 0, 413, 414, 0, 416, 417, 0, 419, 420, 0, 420, 421, 0, 421, 422, 0, 422, 423, 0, 425, 426, 0, 427, 428, 0, 428, 429, 0, 429, 430, 0, 433, 434, 0, 435, 436, 0, 439, 440 }

  114. "(()((())((()((()))(()(((()(())(((()()))()(()()()))))()()(()(((()))(()()))))()()()(()))))))()()((((((()()()())()(())(()())()))()())()(())())())((()))((()))((()())((()(())))())((()))()()(()()()())()()()()(((((())))()))(()(())((()()()())()))()(())(())()(()((()((()(()((()((((((())(())))()(()()()()(())()()())))()((((())()()()))((()(())()(((((()))()((())))))(())))()()(()()()(()(()((())()(((()())()))(()))(()()()(()))(()(()))))(()()()(()))))()(((()(()()))(()))))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 51, 52, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 74, 75, 0, 76, 77, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 103, 104, 0, 105, 106, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 114, 115, 0, 115, 116, 0, 117, 118, 0, 120, 121, 0, 124, 125, 0, 126, 127, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 135, 136, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 157, 158, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 165, 166, 0, 170, 171, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 179, 180, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 186, 187, 0, 188, 189, 0, 190, 191, 0, 193, 194, 0, 195, 196, 0, 197, 198, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 211, 212, 0, 215, 216, 0, 216, 217, 0, 218, 219, 0, 219, 220, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 228, 229, 0, 230, 231, 0, 233, 234, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 243, 244, 0, 244, 245, 0, 247, 248, 0, 249, 250, 0, 250, 251, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 260, 261, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 273, 274, 0, 276, 277, 0, 277, 278, 0, 282, 283, 0, 284, 285, 0, 285, 286, 0, 287, 288, 0, 289, 290, 0, 291, 292, 0, 293, 294, 0, 294, 295, 0, 297, 298, 0, 299, 300, 0, 301, 302, 0, 306, 307, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 315, 316, 0, 317, 318, 0, 319, 320, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 327, 328, 0, 328, 329, 0, 331, 332, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 342, 343, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 353, 354, 0, 354, 355, 0, 359, 360, 0, 361, 362, 0, 363, 364, 0, 364, 365, 0, 366, 367, 0, 368, 369, 0, 370, 371, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 386, 387, 0, 388, 389, 0, 391, 392, 0, 395, 396, 0, 396, 397, 0, 400, 401, 0, 401, 402, 0, 403, 404, 0, 405, 406, 0, 407, 408, 0, 408, 409, 0, 412, 413, 0, 413, 414, 0, 415, 416, 0, 416, 417, 0, 422, 423, 0, 423, 424, 0, 425, 426, 0, 427, 428, 0, 429, 430, 0, 430, 431, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 443, 444, 0, 444, 445, 0, 446, 447, 0, 450, 451, 0, 451, 452 }

  115. "()()(())(((()))()((((()()))())))()((())())((()()()(()()))(((((((())()())((()())(()()))((((()()()))((((()))))))((()((())(())(()))))))((())((())(())))()(()())()((()(()((()()(())()))(())())()()))))))()(()((()())))(((()))(()()())(()))()((()(((())))(())()))()()()()()(((()((())))))(())(())(((()(())()(()()()(())))))(())(((()()(()))))()()()(()(()(())(()(()())())))((()()()))(())((())(())(())()(()())()(()()(((())())())))(()((((()))))(((((()(())()(()((()))())(((()())()(((()()))))(()((((())((())))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 22, 23, 0, 26, 27, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 38, 39, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 66, 67, 0, 68, 69, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 78, 79, 0, 79, 80, 0, 81, 82, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 118, 119, 0, 119, 120, 0, 122, 123, 0, 123, 124, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 170, 171, 0, 171, 172, 0, 174, 175, 0, 178, 179, 0, 179, 180, 0, 182, 183, 0, 185, 186, 0, 187, 188, 0, 195, 196, 0, 197, 198, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 204, 205, 0, 209, 210, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 216, 217, 0, 217, 218, 0, 219, 220, 0, 221, 222, 0, 224, 225, 0, 225, 226, 0, 229, 230, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 243, 244, 0, 244, 245, 0, 247, 248, 0, 251, 252, 0, 253, 254, 0, 255, 256, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 275, 276, 0, 276, 277, 0, 279, 280, 0, 280, 281, 0, 283, 284, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 288, 289, 0, 289, 290, 0, 292, 293, 0, 294, 295, 0, 295, 296, 0, 297, 298, 0, 299, 300, 0, 301, 302, 0, 302, 303, 0, 309, 310, 0, 310, 311, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 327, 328, 0, 329, 330, 0, 331, 332, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 339, 340, 0, 340, 341, 0, 343, 344, 0, 344, 345, 0, 346, 347, 0, 347, 348, 0, 349, 350, 0, 352, 353, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 361, 362, 0, 363, 364, 0, 367, 368, 0, 368, 369, 0, 371, 372, 0, 372, 373, 0, 373, 374, 0, 376, 377, 0, 377, 378, 0, 380, 381, 0, 381, 382, 0, 384, 385, 0, 386, 387, 0, 387, 388, 0, 389, 390, 0, 392, 393, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 402, 403, 0, 405, 406, 0, 408, 409, 0, 413, 414, 0, 414, 415, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 420, 421, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 429, 430, 0, 430, 431, 0, 431, 432, 0, 433, 434, 0, 434, 435, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 442, 443, 0, 443, 444, 0, 444, 445, 0, 448, 449, 0, 451, 452, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 459, 460, 0, 461, 462, 0, 462, 463, 0, 463, 464, 0, 464, 465, 0, 466, 467, 0, 472, 473, 0, 473, 474, 0, 475, 476, 0, 476, 477, 0, 477, 478, 0, 478, 479, 0, 479, 480, 0, 482, 483, 0, 483, 484, 0, 484, 485 }

  116. "(()()())(((()((()())((()(()((()(((()))))()())((((((()()())()()))((()())())()))(()((((((()((()))))(((((())((((())(((()()))()()()))()())()()((())))(((())())())()()()))(((())()())))()())()))((()()()()))(((()))())()())))))()()))))(((()((()))(()))()(()))()()))())(()())()((())())(((((((((()(((((())))(((()((((()()(())))))(()(()()))()((((((((((())()())()(()())))()((()))((()()))((()())()((()(((())))))()()((()((()()())(()))(()())(())((())()())))())))()))))))))))))))))))"

    Returns: {0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 39, 40, 0, 41, 42, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 54, 55, 0, 57, 58, 0, 59, 60, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 67, 68, 0, 70, 71, 0, 73, 74, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 128, 129, 0, 130, 131, 0, 133, 134, 0, 135, 136, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 150, 151, 0, 153, 154, 0, 156, 157, 0, 158, 159, 0, 160, 161, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 170, 171, 0, 172, 173, 0, 177, 178, 0, 179, 180, 0, 182, 183, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 192, 193, 0, 194, 195, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 205, 206, 0, 208, 209, 0, 210, 211, 0, 217, 218, 0, 219, 220, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 228, 229, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 236, 237, 0, 237, 238, 0, 241, 242, 0, 243, 244, 0, 244, 245, 0, 248, 249, 0, 250, 251, 0, 254, 255, 0, 257, 258, 0, 258, 259, 0, 260, 261, 0, 263, 264, 0, 265, 266, 0, 266, 267, 0, 267, 268, 0, 270, 271, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 305, 306, 0, 307, 308, 0, 308, 309, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 319, 320, 0, 321, 322, 0, 325, 326, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 337, 338, 0, 340, 341, 0, 342, 343, 0, 345, 346, 0, 347, 348, 0, 348, 349, 0, 350, 351, 0, 355, 356, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 367, 368, 0, 371, 372, 0, 372, 373, 0, 373, 374, 0, 375, 376, 0, 378, 379, 0, 380, 381, 0, 381, 382, 0, 382, 383, 0, 384, 385, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 394, 395, 0, 396, 397, 0, 398, 399, 0, 399, 400, 0, 400, 401, 0, 402, 403, 0, 403, 404, 0, 404, 405, 0, 406, 407, 0, 408, 409, 0, 411, 412, 0, 412, 413, 0, 416, 417, 0, 417, 418, 0, 419, 420, 0, 422, 423, 0, 423, 424, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 431, 432, 0, 433, 434, 0, 438, 439, 0, 443, 444 }

  117. "()(()())(())()()(((())((())()((((()()(()()))(())(((((())())()()()))(()(())))(((())((())()())(((())())))(((()(()((()))(())())()))(()((((())((())()()(((())))))())()((()()(((())))))()()(())((()))()))())()((()(()()(()())))(((((((()()(((((())())()(()())(((()((((()(()(()()))((((()())(()()()())()))(()()((()))()()()))()()()()((())())))))))))))()(()))()()())((((((()))((())))((())(((())(()())()))))()()))()))((()((()(())(())(())())()))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 62, 63, 0, 66, 67, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 86, 87, 0, 88, 89, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 97, 98, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 116, 117, 0, 117, 118, 0, 120, 121, 0, 123, 124, 0, 127, 128, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 142, 143, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 156, 157, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 165, 166, 0, 167, 168, 0, 168, 169, 0, 169, 170, 0, 170, 171, 0, 177, 178, 0, 179, 180, 0, 181, 182, 0, 182, 183, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 191, 192, 0, 195, 196, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 204, 205, 0, 205, 206, 0, 207, 208, 0, 209, 210, 0, 210, 211, 0, 212, 213, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 236, 237, 0, 239, 240, 0, 241, 242, 0, 242, 243, 0, 244, 245, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 264, 265, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 277, 278, 0, 278, 279, 0, 280, 281, 0, 282, 283, 0, 284, 285, 0, 287, 288, 0, 291, 292, 0, 292, 293, 0, 294, 295, 0, 296, 297, 0, 297, 298, 0, 298, 299, 0, 302, 303, 0, 304, 305, 0, 306, 307, 0, 310, 311, 0, 312, 313, 0, 314, 315, 0, 316, 317, 0, 318, 319, 0, 319, 320, 0, 320, 321, 0, 323, 324, 0, 336, 337, 0, 338, 339, 0, 339, 340, 0, 343, 344, 0, 345, 346, 0, 347, 348, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 356, 357, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 372, 373, 0, 373, 374, 0, 374, 375, 0, 375, 376, 0, 378, 379, 0, 379, 380, 0, 381, 382, 0, 384, 385, 0, 390, 391, 0, 392, 393, 0, 396, 397, 0, 400, 401, 0, 401, 402, 0, 402, 403, 0, 404, 405, 0, 405, 406, 0, 406, 407, 0, 408, 409, 0, 409, 410, 0, 412, 413, 0, 413, 414, 0, 416, 417, 0, 417, 418, 0, 420, 421, 0, 423, 424 }

  118. "((((()()))))()((((()(()())()((())))))()(((()((()(((()()((())))))((()(()((())()))()))()(((())))))())(())((((((((()()())()))))(()(()((()()())(())))))())((((()()(())(((())))((()())())(()(()(()((())()((((())()()()))((()))())()((()())())())(()))(()(()())))(()(()((())))))(()))()))))()()())))((()()))()((()((((()))))))(())()()(()(()(((()())(()(((()))(()))())))(((((())((((()())((()(((())(()(()))()()())()())))()()(((())())))))))))(((()()()()()()()()(()))))))"

    Returns: {0, 5, 6, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 22, 23, 0, 25, 26, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 36, 37, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 75, 76, 0, 79, 80, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 95, 96, 0, 98, 99, 0, 99, 100, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 114, 115, 0, 117, 118, 0, 123, 124, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 133, 134, 0, 135, 136, 0, 138, 139, 0, 139, 140, 0, 146, 147, 0, 149, 150, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 169, 170, 0, 170, 171, 0, 171, 172, 0, 173, 174, 0, 176, 177, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 185, 186, 0, 186, 187, 0, 188, 189, 0, 189, 190, 0, 190, 191, 0, 193, 194, 0, 195, 196, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 202, 203, 0, 204, 205, 0, 206, 207, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 216, 217, 0, 219, 220, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 225, 226, 0, 228, 229, 0, 231, 232, 0, 234, 235, 0, 235, 236, 0, 239, 240, 0, 240, 241, 0, 242, 243, 0, 243, 244, 0, 245, 246, 0, 250, 251, 0, 251, 252, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 265, 266, 0, 266, 267, 0, 270, 271, 0, 276, 277, 0, 278, 279, 0, 280, 281, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 289, 290, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 311, 312, 0, 312, 313, 0, 315, 316, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 322, 323, 0, 323, 324, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 330, 331, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 343, 344, 0, 344, 345, 0, 348, 349, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 358, 359, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 367, 368, 0, 370, 371, 0, 371, 372, 0, 372, 373, 0, 374, 375, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 388, 389, 0, 390, 391, 0, 392, 393, 0, 395, 396, 0, 397, 398, 0, 402, 403, 0, 404, 405, 0, 406, 407, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 412, 413, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 428, 429, 0, 430, 431, 0, 432, 433, 0, 434, 435, 0, 436, 437, 0, 438, 439, 0, 440, 441, 0, 442, 443, 0, 443, 444 }

  119. "(())()((()))()()(())()()(())()()()(()())(())(())((((()((())()()((()))())))))()(()())(()()()()(())((())())((((((()())(())())))()((())()))()))()((()(()()(())(()((())((())()(())())())(()((()())))))))()()(())((()()))()()(()())((()()((()()()(((()(((()()()()())(()(()()(())()()()(((())()()()))((()))()))()((()))())(((()))()(()(((())))(((()()()((())((()))((()((()())(()())(((())(())()((()(()())()()()())))))))))))))))))))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 39, 40, 0, 40, 41, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 88, 89, 0, 90, 91, 0, 92, 93, 0, 93, 94, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 115, 116, 0, 116, 117, 0, 119, 120, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 131, 132, 0, 135, 136, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 148, 149, 0, 150, 151, 0, 151, 152, 0, 154, 155, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 167, 168, 0, 169, 170, 0, 170, 171, 0, 173, 174, 0, 176, 177, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 186, 187, 0, 195, 196, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 207, 208, 0, 211, 212, 0, 213, 214, 0, 215, 216, 0, 216, 217, 0, 218, 219, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 233, 234, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 245, 246, 0, 247, 248, 0, 249, 250, 0, 251, 252, 0, 254, 255, 0, 255, 256, 0, 257, 258, 0, 258, 259, 0, 260, 261, 0, 262, 263, 0, 263, 264, 0, 266, 267, 0, 268, 269, 0, 270, 271, 0, 272, 273, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 278, 279, 0, 280, 281, 0, 282, 283, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 292, 293, 0, 296, 297, 0, 298, 299, 0, 299, 300, 0, 300, 301, 0, 304, 305, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 314, 315, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 332, 333, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 341, 342, 0, 342, 343, 0, 343, 344, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 351, 352, 0, 352, 353, 0, 353, 354, 0, 355, 356, 0, 358, 359, 0, 359, 360, 0, 361, 362, 0, 364, 365, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 370, 371, 0, 371, 372, 0, 374, 375, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 386, 387, 0, 388, 389, 0, 390, 391, 0, 392, 393 }

  120. "()(()())((()()(()((()()())()))(()())))(())(())((((((())(()()(())()()))())()))())()()((((()()())))())()()(()((((((())((()()(()(())())((()(()))(((()((()(()(()()())((((()(()(()))()()()()))(((())(()()))()((())((((()((())()())()()(())((()(((((()()(()))()()(()((())()()(()()())))))(((()))))())))())))()))(((()(())))(()(()()())))())(()())()()))(((())())())((((()(()))((()))))((()))(()(())()))))()()((((())))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 22, 23, 0, 25, 26, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 42, 43, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 63, 64, 0, 65, 66, 0, 69, 70, 0, 72, 73, 0, 76, 77, 0, 79, 80, 0, 81, 82, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 89, 90, 0, 91, 92, 0, 96, 97, 0, 99, 100, 0, 101, 102, 0, 103, 104, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 128, 129, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 135, 136, 0, 136, 137, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 153, 154, 0, 155, 156, 0, 157, 158, 0, 160, 161, 0, 161, 162, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 166, 167, 0, 167, 168, 0, 169, 170, 0, 170, 171, 0, 174, 175, 0, 176, 177, 0, 178, 179, 0, 180, 181, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 190, 191, 0, 191, 192, 0, 193, 194, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 215, 216, 0, 217, 218, 0, 220, 221, 0, 222, 223, 0, 224, 225, 0, 225, 226, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 241, 242, 0, 242, 243, 0, 246, 247, 0, 248, 249, 0, 250, 251, 0, 251, 252, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 258, 259, 0, 260, 261, 0, 262, 263, 0, 263, 264, 0, 265, 266, 0, 267, 268, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 283, 284, 0, 288, 289, 0, 293, 294, 0, 297, 298, 0, 298, 299, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 303, 304, 0, 308, 309, 0, 309, 310, 0, 311, 312, 0, 312, 313, 0, 314, 315, 0, 316, 317, 0, 321, 322, 0, 324, 325, 0, 325, 326, 0, 327, 328, 0, 330, 331, 0, 332, 333, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 342, 343, 0, 345, 346, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 354, 355, 0, 355, 356, 0, 359, 360, 0, 360, 361, 0, 361, 362, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 373, 374, 0, 374, 375, 0, 376, 377, 0, 377, 378, 0, 380, 381, 0, 386, 387, 0, 388, 389, 0, 390, 391, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 394, 395 }

  121. "(()((())())((())(()(())()))((()(((())(((()()(()((())((((()())(())()))(((()()()()()))(()((())()(()))))())()))(()))())))))))()(((())))(((()((((((((())()(((()((()))))())))()()()(())(()(((((()(())()((()(()()(()))())))))((()()(()((()(()((())))())))))()((())))(()(())()))((()(()(()(())((((()))(())))()((()(())()())()())(()()()(()()()))()()))(())())(()(()()(())()(()())((()))))()()())()(()(()))((((((()(()()))()()(())))((()))))((((((()()()((())(((()((()((()())(()(()()()((()())))))))))))())())))))))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 22, 23, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 60, 61, 0, 61, 62, 0, 64, 65, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 75, 76, 0, 77, 78, 0, 79, 80, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 100, 101, 0, 103, 104, 0, 107, 108, 0, 108, 109, 0, 112, 113, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 162, 163, 0, 167, 168, 0, 169, 170, 0, 171, 172, 0, 173, 174, 0, 174, 175, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 187, 188, 0, 188, 189, 0, 191, 192, 0, 193, 194, 0, 194, 195, 0, 195, 196, 0, 197, 198, 0, 198, 199, 0, 200, 201, 0, 202, 203, 0, 203, 204, 0, 207, 208, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 218, 219, 0, 220, 221, 0, 221, 222, 0, 223, 224, 0, 224, 225, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 237, 238, 0, 244, 245, 0, 246, 247, 0, 247, 248, 0, 248, 249, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 260, 261, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 268, 269, 0, 269, 270, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 275, 276, 0, 278, 279, 0, 279, 280, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 286, 287, 0, 287, 288, 0, 292, 293, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 298, 299, 0, 299, 300, 0, 302, 303, 0, 304, 305, 0, 307, 308, 0, 309, 310, 0, 312, 313, 0, 313, 314, 0, 315, 316, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 322, 323, 0, 324, 325, 0, 328, 329, 0, 330, 331, 0, 334, 335, 0, 335, 336, 0, 338, 339, 0, 341, 342, 0, 342, 343, 0, 344, 345, 0, 345, 346, 0, 347, 348, 0, 349, 350, 0, 350, 351, 0, 353, 354, 0, 355, 356, 0, 356, 357, 0, 358, 359, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 369, 370, 0, 371, 372, 0, 373, 374, 0, 376, 377, 0, 378, 379, 0, 379, 380, 0, 381, 382, 0, 382, 383, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 390, 391, 0, 391, 392, 0, 392, 393, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 401, 402, 0, 403, 404, 0, 405, 406, 0, 406, 407, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 419, 420, 0, 420, 421, 0, 421, 422, 0, 422, 423, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 427, 428, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 436, 437, 0, 437, 438, 0, 438, 439, 0, 439, 440, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 445, 446, 0, 446, 447, 0, 447, 448, 0, 449, 450, 0, 452, 453, 0, 453, 454, 0, 455, 456, 0, 456, 457, 0, 458, 459, 0, 460, 461, 0, 462, 463, 0, 463, 464, 0, 464, 465, 0, 466, 467, 0, 479, 480, 0, 482, 483 }

  122. "()()()()()()(()((()(()()((()()((()())()())()()((((())()()(()(()(()(()))))((()((())))(()()))()(()))(())(())())((()())(()))))(((()()()))()))))()((()((()(()()()()(()()(((()()(((())()((((())()()())))))()))()(())))(()))))()())())()((())()()()(()(()))(())()(()(()()())(((()))))(((())(()()())()(((()))()()))(((((()()))()((()((((()()((((())))()()(()((())))(())()())())(())))(()((()()))))()())))))))(()(()((((())())(()))))(()((()(())()(())()(((())(()()(()))((())((((())(())((((()())(((((()))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 33, 34, 0, 36, 37, 0, 38, 39, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 52, 53, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 65, 66, 0, 66, 67, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 90, 91, 0, 92, 93, 0, 93, 94, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 102, 103, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 115, 116, 0, 116, 117, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 129, 130, 0, 133, 134, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 154, 155, 0, 156, 157, 0, 158, 159, 0, 159, 160, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 170, 171, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 182, 183, 0, 185, 186, 0, 187, 188, 0, 189, 190, 0, 196, 197, 0, 200, 201, 0, 202, 203, 0, 203, 204, 0, 208, 209, 0, 209, 210, 0, 215, 216, 0, 217, 218, 0, 220, 221, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 230, 231, 0, 232, 233, 0, 234, 235, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 244, 245, 0, 245, 246, 0, 248, 249, 0, 250, 251, 0, 251, 252, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 258, 259, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 273, 274, 0, 276, 277, 0, 277, 278, 0, 279, 280, 0, 281, 282, 0, 284, 285, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 293, 294, 0, 295, 296, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 306, 307, 0, 310, 311, 0, 312, 313, 0, 313, 314, 0, 314, 315, 0, 316, 317, 0, 317, 318, 0, 318, 319, 0, 319, 320, 0, 320, 321, 0, 322, 323, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 333, 334, 0, 335, 336, 0, 337, 338, 0, 338, 339, 0, 340, 341, 0, 341, 342, 0, 342, 343, 0, 347, 348, 0, 348, 349, 0, 351, 352, 0, 353, 354, 0, 356, 357, 0, 359, 360, 0, 360, 361, 0, 365, 366, 0, 366, 367, 0, 368, 369, 0, 369, 370, 0, 370, 371, 0, 372, 373, 0, 378, 379, 0, 380, 381, 0, 389, 390, 0, 390, 391, 0, 392, 393, 0, 393, 394, 0, 395, 396, 0, 396, 397, 0, 397, 398, 0, 398, 399, 0, 399, 400, 0, 402, 403, 0, 405, 406, 0, 406, 407, 0, 412, 413, 0, 413, 414, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 419, 420, 0, 420, 421, 0, 423, 424, 0, 425, 426, 0, 426, 427, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 437, 438, 0, 438, 439, 0, 440, 441, 0, 442, 443, 0, 443, 444, 0, 447, 448, 0, 448, 449, 0, 449, 450, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 455, 456, 0, 456, 457, 0, 459, 460, 0, 460, 461, 0, 463, 464, 0, 464, 465, 0, 465, 466, 0, 466, 467, 0, 467, 468, 0, 469, 470, 0, 472, 473, 0, 473, 474, 0, 474, 475, 0, 475, 476, 0, 476, 477, 0, 477, 478 }

  123. "()(((()()()()(())())()(())))()()()((())()())(())()((())())((()())())()()((((()))))()()((()()))()(())(())(()(()))((()))()()()()()((())(())(()()))(()((((()((((((())()((()))(()(()())())())()(()()()())((()))())())(()(((()(())))))(()())))))(((())(()()()))((((((((())))())))(())()(())()))()())()(((())))(((()(())))))))()()((()((())()((()((())))()())))())((()()))()()(())((((()(())(())((((())()()(())())(()()()(((()()))(()(()()())()))())(((()()(())()()))((())(())()()()()()(())((()()((((()(())))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 6, 7, 0, 8, 9, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 16, 17, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 38, 39, 0, 40, 41, 0, 43, 44, 0, 44, 45, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 54, 55, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 64, 65, 0, 67, 68, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 81, 82, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 89, 90, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 99, 100, 0, 100, 101, 0, 103, 104, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 125, 126, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 132, 133, 0, 133, 134, 0, 136, 137, 0, 137, 138, 0, 139, 140, 0, 143, 144, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 169, 170, 0, 170, 171, 0, 172, 173, 0, 173, 174, 0, 175, 176, 0, 178, 179, 0, 181, 182, 0, 184, 185, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 191, 192, 0, 193, 194, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 202, 203, 0, 205, 206, 0, 208, 209, 0, 209, 210, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 214, 215, 0, 216, 217, 0, 217, 218, 0, 224, 225, 0, 225, 226, 0, 227, 228, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 240, 241, 0, 241, 242, 0, 243, 244, 0, 245, 246, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 262, 263, 0, 267, 268, 0, 268, 269, 0, 271, 272, 0, 273, 274, 0, 274, 275, 0, 277, 278, 0, 281, 282, 0, 283, 284, 0, 286, 287, 0, 288, 289, 0, 289, 290, 0, 290, 291, 0, 291, 292, 0, 296, 297, 0, 297, 298, 0, 298, 299, 0, 299, 300, 0, 301, 302, 0, 302, 303, 0, 311, 312, 0, 313, 314, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 324, 325, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 337, 338, 0, 339, 340, 0, 344, 345, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 351, 352, 0, 355, 356, 0, 357, 358, 0, 359, 360, 0, 360, 361, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 369, 370, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 384, 385, 0, 386, 387, 0, 388, 389, 0, 389, 390, 0, 392, 393, 0, 395, 396, 0, 396, 397, 0, 398, 399, 0, 400, 401, 0, 402, 403, 0, 403, 404, 0, 404, 405, 0, 405, 406, 0, 407, 408, 0, 411, 412, 0, 412, 413, 0, 414, 415, 0, 415, 416, 0, 417, 418, 0, 419, 420, 0, 422, 423, 0, 426, 427, 0, 429, 430, 0, 430, 431, 0, 431, 432, 0, 432, 433, 0, 434, 435, 0, 436, 437, 0, 437, 438, 0, 440, 441, 0, 442, 443, 0, 446, 447, 0, 447, 448, 0, 448, 449, 0, 451, 452, 0, 452, 453, 0, 455, 456, 0, 457, 458, 0, 459, 460, 0, 461, 462, 0, 463, 464, 0, 465, 466, 0, 466, 467, 0, 469, 470, 0, 470, 471, 0, 471, 472, 0, 473, 474, 0, 475, 476, 0, 476, 477, 0, 477, 478, 0, 478, 479, 0, 479, 480, 0, 481, 482, 0, 482, 483 }

  124. "(((()(()()())))(((()(((()(()))(()())((())(())))()())()))))()()()()()(((())()(())()()()(()()((()()((((()()(())(())))(())()))))())))()()()(((((()()()(())())((())((()((()()))(()))()))))))((((()(()(()(()()((()(())))((())((((()((()()())(())()(()())()()(())(()())()((()())()(())(()(()(()()()))()))(((()(((())(((()()()(()))()))(())))()((())(())(((()(()((()(((()((())()((((()()))((()(((()(())(((())))((()))))()(())))(((((()())))(())())(()())()(((((()(())()))(((((()(()))))))))))))))))))))))))))))))))))))))))"

    Returns: {0, 4, 5, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 40, 41, 0, 41, 42, 0, 46, 47, 0, 48, 49, 0, 51, 52, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 63, 64, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 75, 76, 0, 76, 77, 0, 79, 80, 0, 81, 82, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 114, 115, 0, 115, 116, 0, 118, 119, 0, 124, 125, 0, 129, 130, 0, 131, 132, 0, 133, 134, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 142, 143, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 166, 167, 0, 170, 171, 0, 171, 172, 0, 175, 176, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 192, 193, 0, 193, 194, 0, 195, 196, 0, 196, 197, 0, 198, 199, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 204, 205, 0, 205, 206, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 225, 226, 0, 227, 228, 0, 230, 231, 0, 231, 232, 0, 234, 235, 0, 236, 237, 0, 237, 238, 0, 239, 240, 0, 242, 243, 0, 244, 245, 0, 246, 247, 0, 247, 248, 0, 250, 251, 0, 251, 252, 0, 253, 254, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 262, 263, 0, 265, 266, 0, 267, 268, 0, 268, 269, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 278, 279, 0, 280, 281, 0, 282, 283, 0, 286, 287, 0, 290, 291, 0, 291, 292, 0, 292, 293, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 298, 299, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 306, 307, 0, 308, 309, 0, 310, 311, 0, 311, 312, 0, 315, 316, 0, 319, 320, 0, 320, 321, 0, 325, 326, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 332, 333, 0, 333, 334, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 341, 342, 0, 342, 343, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 351, 352, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 358, 359, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 366, 367, 0, 370, 371, 0, 371, 372, 0, 372, 373, 0, 374, 375, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 379, 380, 0, 380, 381, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 386, 387, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 399, 400, 0, 401, 402, 0, 402, 403, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 412, 413, 0, 414, 415, 0, 419, 420, 0, 420, 421, 0, 423, 424, 0, 426, 427, 0, 427, 428, 0, 429, 430, 0, 432, 433, 0, 434, 435, 0, 435, 436, 0, 436, 437, 0, 437, 438, 0, 438, 439, 0, 439, 440, 0, 441, 442, 0, 442, 443, 0, 445, 446, 0, 449, 450, 0, 450, 451, 0, 451, 452, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 457, 458 }

  125. "()()(())()()(())()()((((((()())())()(()())))))(())((()))((((((((()((((((((((())))((())(())((()))))()((((())()(())((((()((((()))))))(())(())(()))))()()(())))()((()))(())())())(())())))))())))()()))())(()((())()())((()()()((())(((((((()())))(()((())()())()((((()((())())(()()()())()()))()))(())(())((()((((((())(()))()()(()()()((()((()))((((()()(((()((()(()()(()())((()())(())(()(()))()()((()))())))()()()))((((()((()))((()()(((((())))((()()(())())())(()))))(()()(()(())))))))))))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 27, 28, 0, 30, 31, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 38, 39, 0, 45, 46, 0, 46, 47, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 65, 66, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 130, 131, 0, 131, 132, 0, 134, 135, 0, 135, 136, 0, 138, 139, 0, 139, 140, 0, 145, 146, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 163, 164, 0, 164, 165, 0, 167, 168, 0, 170, 171, 0, 173, 174, 0, 174, 175, 0, 177, 178, 0, 184, 185, 0, 189, 190, 0, 191, 192, 0, 195, 196, 0, 198, 199, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 206, 207, 0, 208, 209, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 215, 216, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 233, 234, 0, 238, 239, 0, 239, 240, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 246, 247, 0, 248, 249, 0, 251, 252, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 264, 265, 0, 267, 268, 0, 268, 269, 0, 270, 271, 0, 272, 273, 0, 274, 275, 0, 277, 278, 0, 279, 280, 0, 283, 284, 0, 287, 288, 0, 288, 289, 0, 291, 292, 0, 292, 293, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 305, 306, 0, 308, 309, 0, 309, 310, 0, 313, 314, 0, 315, 316, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 322, 323, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 340, 341, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 351, 352, 0, 352, 353, 0, 354, 355, 0, 356, 357, 0, 357, 358, 0, 359, 360, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 366, 367, 0, 369, 370, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 376, 377, 0, 377, 378, 0, 381, 382, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 391, 392, 0, 396, 397, 0, 398, 399, 0, 400, 401, 0, 404, 405, 0, 405, 406, 0, 406, 407, 0, 407, 408, 0, 408, 409, 0, 410, 411, 0, 411, 412, 0, 412, 413, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 420, 421, 0, 422, 423, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 427, 428, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 442, 443, 0, 445, 446, 0, 448, 449, 0, 449, 450, 0, 455, 456, 0, 456, 457, 0, 458, 459, 0, 460, 461, 0, 461, 462, 0, 463, 464, 0, 464, 465 }

  126. "(())()()(())()((()))()()((((((((())()()(((()((()()((((())((((())))))()()((((()()))(()())((((()))))))(((()((())(()((())())())(())))(((()(()(()()(()(((()))(()((((((())))))(()()((((()(())()))))(((()()())()())))(())(())())()(()))(()()()(((()((()))))))(()())))(()((((((((()(((())(()))())))(()())))()(((()))))()()(((()()()((()(()()()((()()((()))()())))()((())()()))()(((((()))((()((())(((()((()()(()))(()))())()()(())((((())())()))()()()())))()(()())))(()()))(((()(((())))))))))))))))))))))))))))))))))))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 34, 35, 0, 36, 37, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 60, 61, 0, 67, 68, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 81, 82, 0, 82, 83, 0, 84, 85, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 117, 118, 0, 120, 121, 0, 123, 124, 0, 124, 125, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 135, 136, 0, 137, 138, 0, 138, 139, 0, 140, 141, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 152, 153, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 161, 162, 0, 168, 169, 0, 169, 170, 0, 171, 172, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 183, 184, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 192, 193, 0, 194, 195, 0, 196, 197, 0, 199, 200, 0, 201, 202, 0, 206, 207, 0, 207, 208, 0, 210, 211, 0, 211, 212, 0, 214, 215, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 224, 225, 0, 225, 226, 0, 227, 228, 0, 229, 230, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 246, 247, 0, 247, 248, 0, 249, 250, 0, 254, 255, 0, 255, 256, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 273, 274, 0, 274, 275, 0, 278, 279, 0, 283, 284, 0, 284, 285, 0, 286, 287, 0, 291, 292, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 302, 303, 0, 304, 305, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 311, 312, 0, 313, 314, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 322, 323, 0, 324, 325, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 330, 331, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 338, 339, 0, 340, 341, 0, 345, 346, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 352, 353, 0, 354, 355, 0, 358, 359, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 369, 370, 0, 370, 371, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 375, 376, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 387, 388, 0, 389, 390, 0, 390, 391, 0, 394, 395, 0, 395, 396, 0, 399, 400, 0, 402, 403, 0, 404, 405, 0, 406, 407, 0, 407, 408, 0, 410, 411, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 414, 415, 0, 417, 418, 0, 420, 421, 0, 424, 425, 0, 426, 427, 0, 428, 429, 0, 430, 431, 0, 435, 436, 0, 437, 438, 0, 438, 439, 0, 440, 441, 0, 445, 446, 0, 446, 447, 0, 448, 449, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 455, 456, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 460, 461 }

  127. "()()((((())))(()((())()(((())((((()())(()()(()))())(()((())(()((())(()))((())(())((())()(())((()(())))((()))((())(())()))))(((())()()((((())(()))(())(())()(()())))())))(())))((((((((((()))()))))))())(())(()((((())()((((())))(()))))()))()()(())))())(())(()(()))()()()())())(((()((()))))(()))()((())((()(()())))()())()()()((())(((((((())()((()())))(()())()()()()()))))))((()()))(())(((())())(()(())))((((()))))((()))())(()(()(()()())))(()())()((()))(((((()()(()())(()((()((()())())())()())))))())))(())"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 47, 48, 0, 50, 51, 0, 51, 52, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 76, 77, 0, 77, 78, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 87, 88, 0, 88, 89, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 112, 113, 0, 113, 114, 0, 116, 117, 0, 122, 123, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 128, 129, 0, 130, 131, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 139, 140, 0, 140, 141, 0, 144, 145, 0, 145, 146, 0, 148, 149, 0, 149, 150, 0, 152, 153, 0, 154, 155, 0, 155, 156, 0, 157, 158, 0, 162, 163, 0, 167, 168, 0, 168, 169, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 187, 188, 0, 195, 196, 0, 198, 199, 0, 199, 200, 0, 202, 203, 0, 203, 204, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 209, 210, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 223, 224, 0, 224, 225, 0, 230, 231, 0, 234, 235, 0, 236, 237, 0, 238, 239, 0, 239, 240, 0, 244, 245, 0, 247, 248, 0, 248, 249, 0, 251, 252, 0, 252, 253, 0, 254, 255, 0, 255, 256, 0, 259, 260, 0, 261, 262, 0, 263, 264, 0, 265, 266, 0, 268, 269, 0, 271, 272, 0, 272, 273, 0, 273, 274, 0, 274, 275, 0, 276, 277, 0, 277, 278, 0, 278, 279, 0, 284, 285, 0, 285, 286, 0, 289, 290, 0, 291, 292, 0, 292, 293, 0, 293, 294, 0, 296, 297, 0, 297, 298, 0, 298, 299, 0, 300, 301, 0, 301, 302, 0, 303, 304, 0, 308, 309, 0, 310, 311, 0, 313, 314, 0, 315, 316, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 340, 341, 0, 345, 346, 0, 346, 347, 0, 348, 349, 0, 351, 352, 0, 353, 354, 0, 355, 356, 0, 357, 358, 0, 359, 360, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 371, 372, 0, 375, 376, 0, 376, 377, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 382, 383, 0, 385, 386, 0, 388, 389, 0, 389, 390, 0, 391, 392, 0, 392, 393, 0, 397, 398, 0, 398, 399, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 413, 414, 0, 416, 417, 0, 417, 418, 0, 419, 420, 0, 420, 421, 0, 422, 423, 0, 423, 424, 0, 425, 426, 0, 427, 428, 0, 432, 433, 0, 433, 434, 0, 435, 436, 0, 438, 439, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 446, 447, 0, 447, 448, 0, 448, 449, 0, 449, 450, 0, 450, 451, 0, 451, 452, 0, 453, 454, 0, 455, 456, 0, 456, 457, 0, 458, 459, 0, 461, 462, 0, 462, 463, 0, 464, 465, 0, 465, 466, 0, 466, 467, 0, 468, 469, 0, 469, 470, 0, 470, 471, 0, 472, 473, 0, 475, 476, 0, 478, 479, 0, 481, 482, 0, 483, 484, 0, 490, 491, 0, 495, 496, 0, 496, 497 }

  128. "()()(()(())(()()))()(((())((((()()(()(()()((())(((())()))()())((())()))))()((((())()))))((()()((((()((()))))((())()()()(())(()()((((((((((())(((()((((()(()(()))(()(((((()())))()(()()())(()()()((())()((((((((()))(())())(((((((()))((()))(()(((()()()()(())(((()()))(())()()((())))))()))((()))()()(()(()()(()()((()())())))(()((())(())())())))())(())(((())())))(((())())()))))(()(()())((()())))())(())()()()((())))())()((((())(()((()())))((((())((((()))))(()()(()()))))))))))))))))))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 6, 7, 0, 7, 8, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 52, 53, 0, 56, 57, 0, 58, 59, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 66, 67, 0, 72, 73, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 81, 82, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 112, 113, 0, 114, 115, 0, 116, 117, 0, 118, 119, 0, 119, 120, 0, 122, 123, 0, 123, 124, 0, 125, 126, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 155, 156, 0, 159, 160, 0, 160, 161, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 169, 170, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 181, 182, 0, 184, 185, 0, 185, 186, 0, 187, 188, 0, 189, 190, 0, 191, 192, 0, 192, 193, 0, 193, 194, 0, 196, 197, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 210, 211, 0, 211, 212, 0, 214, 215, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 228, 229, 0, 229, 230, 0, 230, 231, 0, 234, 235, 0, 235, 236, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 240, 241, 0, 242, 243, 0, 244, 245, 0, 246, 247, 0, 248, 249, 0, 249, 250, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 257, 258, 0, 261, 262, 0, 262, 263, 0, 265, 266, 0, 267, 268, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 278, 279, 0, 282, 283, 0, 283, 284, 0, 284, 285, 0, 288, 289, 0, 290, 291, 0, 292, 293, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 298, 299, 0, 300, 301, 0, 301, 302, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 309, 310, 0, 312, 313, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 325, 326, 0, 326, 327, 0, 329, 330, 0, 332, 333, 0, 337, 338, 0, 340, 341, 0, 341, 342, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 347, 348, 0, 350, 351, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 358, 359, 0, 361, 362, 0, 364, 365, 0, 370, 371, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 376, 377, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 388, 389, 0, 391, 392, 0, 392, 393, 0, 395, 396, 0, 397, 398, 0, 399, 400, 0, 401, 402, 0, 402, 403, 0, 403, 404, 0, 408, 409, 0, 411, 412, 0, 413, 414, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 420, 421, 0, 421, 422, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 427, 428, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 435, 436, 0, 436, 437, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 449, 450, 0, 450, 451, 0, 452, 453, 0, 454, 455, 0, 455, 456, 0, 457, 458 }

  129. "()()()()()()()()()()((((()()(((())()((()(()())()(()((((()((()((()()())())()))))))))((((((()))))(()))((((((((((((())((()((()()()((())()()(())())()((((()())))(()(()(()()((())()(())))(()((()(((())(())()))))))())))())((()))()((()))))(()())))(())()())((()()(())(()(()))))))()(()(())))))()(()(()()((()(((()(()((())()(((()))))(()((((((((()(()())((())))()()))())((((()()()))))())())(())(()()(()((((()()))))())()(())(())((((()((()())())())()))))))()((()()))((((())()(()(((())))())(()()))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 66, 67, 0, 69, 70, 0, 72, 73, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 94, 95, 0, 95, 96, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 122, 123, 0, 124, 125, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 131, 132, 0, 133, 134, 0, 135, 136, 0, 136, 137, 0, 139, 140, 0, 142, 143, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 150, 151, 0, 155, 156, 0, 156, 157, 0, 158, 159, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 171, 172, 0, 173, 174, 0, 174, 175, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 192, 193, 0, 193, 194, 0, 196, 197, 0, 204, 205, 0, 209, 210, 0, 212, 213, 0, 213, 214, 0, 214, 215, 0, 218, 219, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 236, 237, 0, 237, 238, 0, 240, 241, 0, 242, 243, 0, 245, 246, 0, 246, 247, 0, 247, 248, 0, 249, 250, 0, 251, 252, 0, 252, 253, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 267, 268, 0, 269, 270, 0, 270, 271, 0, 272, 273, 0, 273, 274, 0, 280, 281, 0, 282, 283, 0, 283, 284, 0, 285, 286, 0, 286, 287, 0, 288, 289, 0, 290, 291, 0, 291, 292, 0, 292, 293, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 307, 308, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 318, 319, 0, 319, 320, 0, 321, 322, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 331, 332, 0, 332, 333, 0, 334, 335, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 344, 345, 0, 346, 347, 0, 350, 351, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 359, 360, 0, 361, 362, 0, 367, 368, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 378, 379, 0, 380, 381, 0, 382, 383, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 391, 392, 0, 397, 398, 0, 400, 401, 0, 402, 403, 0, 403, 404, 0, 406, 407, 0, 407, 408, 0, 410, 411, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 414, 415, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 420, 421, 0, 423, 424, 0, 426, 427, 0, 429, 430, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 443, 444, 0, 447, 448, 0, 448, 449, 0, 449, 450, 0, 450, 451, 0, 451, 452, 0, 454, 455, 0, 456, 457, 0, 457, 458, 0, 459, 460, 0, 460, 461, 0, 461, 462, 0, 462, 463, 0, 467, 468, 0, 470, 471, 0, 471, 472, 0, 473, 474 }

  130. "()()(()((((()((()))((((((()))()()))((())))()())()(())(())(()((())()(())(()())()(())))()()()))()))()())()()((())((((()())(()))(()(()((()))(()()()(())())(((()))))()())()))())(()()(((()()(())(()))((())))()((()))(()((((((()(())()())))((())()))(())))())))(())()()(((((())(()))())()((())((())))(())()((()))()(())))()()()(())(()(()(((((()))((()(()))))))())(())()())(()())(()())()()()()()()()((()(()(())())()(())))()((((()(((()())((()))))(()))))()()()(())()())()()((()(())))()(((())))()()()()(((()()((())))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 28, 29, 0, 30, 31, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 41, 42, 0, 43, 44, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 52, 53, 0, 53, 54, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 76, 77, 0, 78, 79, 0, 79, 80, 0, 84, 85, 0, 86, 87, 0, 88, 89, 0, 92, 93, 0, 96, 97, 0, 98, 99, 0, 101, 102, 0, 103, 104, 0, 105, 106, 0, 106, 107, 0, 107, 108, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 119, 120, 0, 120, 121, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 136, 137, 0, 137, 138, 0, 139, 140, 0, 141, 142, 0, 143, 144, 0, 144, 145, 0, 147, 148, 0, 150, 151, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 159, 160, 0, 161, 162, 0, 164, 165, 0, 168, 169, 0, 171, 172, 0, 172, 173, 0, 174, 175, 0, 176, 177, 0, 177, 178, 0, 178, 179, 0, 179, 180, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 187, 188, 0, 188, 189, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 218, 219, 0, 219, 220, 0, 222, 223, 0, 224, 225, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 234, 235, 0, 238, 239, 0, 239, 240, 0, 244, 245, 0, 249, 250, 0, 250, 251, 0, 253, 254, 0, 255, 256, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 265, 266, 0, 266, 267, 0, 270, 271, 0, 273, 274, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 287, 288, 0, 288, 289, 0, 291, 292, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 299, 300, 0, 301, 302, 0, 302, 303, 0, 307, 308, 0, 309, 310, 0, 311, 312, 0, 313, 314, 0, 314, 315, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 345, 346, 0, 348, 349, 0, 349, 350, 0, 352, 353, 0, 354, 355, 0, 357, 358, 0, 358, 359, 0, 360, 361, 0, 363, 364, 0, 364, 365, 0, 366, 367, 0, 369, 370, 0, 371, 372, 0, 373, 374, 0, 375, 376, 0, 377, 378, 0, 379, 380, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 387, 388, 0, 388, 389, 0, 390, 391, 0, 391, 392, 0, 394, 395, 0, 397, 398, 0, 399, 400, 0, 400, 401, 0, 405, 406, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 413, 414, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 418, 419, 0, 421, 422, 0, 422, 423, 0, 423, 424, 0, 429, 430, 0, 430, 431, 0, 436, 437, 0, 438, 439, 0, 440, 441, 0, 442, 443, 0, 443, 444, 0, 446, 447, 0, 448, 449, 0, 451, 452, 0, 453, 454, 0, 455, 456, 0, 456, 457, 0, 457, 458, 0, 459, 460, 0, 460, 461, 0, 465, 466, 0, 467, 468, 0, 468, 469, 0, 469, 470, 0, 470, 471, 0, 475, 476, 0, 477, 478, 0, 479, 480, 0, 481, 482, 0, 483, 484, 0, 484, 485, 0, 485, 486, 0, 486, 487, 0, 488, 489, 0, 490, 491, 0, 491, 492, 0, 492, 493 }

  131. "()((()((()()())((((()()()()((((((()))))))))())()()())))((())))((()))(((())))((()((())((()))))(()(((((())))))))()()()()((((()((())((((()(((((()())())))())(((())()(()(()())()((())())))()(()(()())())()()())((()))()())))()(((())()))(())(()((()))))()()(())((()((()(()))))()))))))((()(((((((()())))((((())))))(((())())(()))(()(()))((((((()((()()()(()())())())(()(()())))())(((()()()((())))(()()()()()((())())))(())))()()(())())(())()))((())((((()((((()((())()))(()(((()))()))))()()())))(()()()))()())))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 14, 15, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 22, 23, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 42, 43, 0, 45, 46, 0, 47, 48, 0, 49, 50, 0, 54, 55, 0, 55, 56, 0, 56, 57, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 92, 93, 0, 93, 94, 0, 95, 96, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 109, 110, 0, 111, 112, 0, 113, 114, 0, 115, 116, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 141, 142, 0, 144, 145, 0, 149, 150, 0, 152, 153, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 158, 159, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 166, 167, 0, 169, 170, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 176, 177, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 192, 193, 0, 195, 196, 0, 197, 198, 0, 199, 200, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 208, 209, 0, 210, 211, 0, 215, 216, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 223, 224, 0, 227, 228, 0, 228, 229, 0, 231, 232, 0, 232, 233, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 242, 243, 0, 244, 245, 0, 246, 247, 0, 247, 248, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 265, 266, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 283, 284, 0, 284, 285, 0, 286, 287, 0, 291, 292, 0, 292, 293, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 305, 306, 0, 308, 309, 0, 311, 312, 0, 312, 313, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 338, 339, 0, 340, 341, 0, 341, 342, 0, 343, 344, 0, 346, 347, 0, 349, 350, 0, 352, 353, 0, 353, 354, 0, 355, 356, 0, 356, 357, 0, 358, 359, 0, 363, 364, 0, 366, 367, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 371, 372, 0, 373, 374, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 382, 383, 0, 383, 384, 0, 385, 386, 0, 387, 388, 0, 389, 390, 0, 391, 392, 0, 393, 394, 0, 394, 395, 0, 395, 396, 0, 398, 399, 0, 403, 404, 0, 404, 405, 0, 409, 410, 0, 411, 412, 0, 413, 414, 0, 414, 415, 0, 417, 418, 0, 420, 421, 0, 421, 422, 0, 424, 425, 0, 428, 429, 0, 429, 430, 0, 430, 431, 0, 433, 434, 0, 434, 435, 0, 435, 436, 0, 436, 437, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 445, 446, 0, 446, 447, 0, 447, 448, 0, 450, 451, 0, 454, 455, 0, 455, 456, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 460, 461, 0, 464, 465, 0, 470, 471, 0, 472, 473, 0, 474, 475, 0, 479, 480, 0, 480, 481, 0, 482, 483, 0, 484, 485, 0, 488, 489, 0, 490, 491 }

  132. "((((())())(((())(())))((((())()())))()((()))(((()))(()))(()(()(((()))())((((((())())))()()((()))()())(((((()(())()())(((((()(((()())(()())()(()()((((())(()())()))))))())))(())())()((((())))))()((())()()((((((()()(()))))))()())()(()))((()(())(((((()))())()())(())())(())())()((((())((())())())()()((()))(())((((())())((())()))())()))((())(((((())))))((()(())())(())())()()(()())())())(())))(())(())))()()()))))(())()())()()(())(()()()()())()((((()))))()((()((((())((()))((())(())((()(())()))())())))))"

    Returns: {0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 15, 16, 0, 16, 17, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 28, 29, 0, 30, 31, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 50, 51, 0, 51, 52, 0, 55, 56, 0, 56, 57, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 80, 81, 0, 85, 86, 0, 87, 88, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 95, 96, 0, 97, 98, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 107, 108, 0, 108, 109, 0, 111, 112, 0, 113, 114, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 137, 138, 0, 139, 140, 0, 140, 141, 0, 142, 143, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 157, 158, 0, 165, 166, 0, 170, 171, 0, 171, 172, 0, 174, 175, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 190, 191, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 197, 198, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 209, 210, 0, 211, 212, 0, 212, 213, 0, 220, 221, 0, 222, 223, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 236, 237, 0, 237, 238, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 249, 250, 0, 252, 253, 0, 254, 255, 0, 257, 258, 0, 258, 259, 0, 261, 262, 0, 264, 265, 0, 265, 266, 0, 268, 269, 0, 271, 272, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 285, 286, 0, 288, 289, 0, 291, 292, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 301, 302, 0, 302, 303, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 312, 313, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 320, 321, 0, 324, 325, 0, 327, 328, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 340, 341, 0, 341, 342, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 352, 353, 0, 353, 354, 0, 356, 357, 0, 359, 360, 0, 360, 361, 0, 363, 364, 0, 366, 367, 0, 368, 369, 0, 370, 371, 0, 371, 372, 0, 373, 374, 0, 376, 377, 0, 379, 380, 0, 382, 383, 0, 383, 384, 0, 388, 389, 0, 389, 390, 0, 392, 393, 0, 393, 394, 0, 398, 399, 0, 400, 401, 0, 402, 403, 0, 408, 409, 0, 409, 410, 0, 412, 413, 0, 414, 415, 0, 417, 418, 0, 419, 420, 0, 421, 422, 0, 422, 423, 0, 425, 426, 0, 426, 427, 0, 428, 429, 0, 430, 431, 0, 432, 433, 0, 434, 435, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 449, 450, 0, 451, 452, 0, 452, 453, 0, 453, 454, 0, 455, 456, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 462, 463, 0, 463, 464, 0, 464, 465, 0, 468, 469, 0, 469, 470, 0, 470, 471, 0, 473, 474, 0, 474, 475, 0, 477, 478, 0, 478, 479, 0, 479, 480, 0, 481, 482, 0, 482, 483, 0, 485, 486, 0, 489, 490, 0, 492, 493 }

  133. "()(())(()(((()(()()((())())()))(()))))()()((()))()(())((()))(()())()(((()))())(()((()(((())))((((()())())))((((())))()(()))())(())))()()()()((()((()())()))()(()()))()(()(()))(())()(()(()))((()))(()())((()((()))))(())()((()))()(())(()(((()))()()()())())((((()(()(((()))()))((())(()()(((())(())()))()()))((()()))((()((((((((()()(())()(((()))(()()(((()))(((((()()))((((()((()((())((()))))))(((((()(()()())()))))))(()())(((((()()((()))(())(((()((()()(())()()())))())()((()()))))))))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 23, 24, 0, 26, 27, 0, 30, 31, 0, 31, 32, 0, 37, 38, 0, 39, 40, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 59, 60, 0, 60, 61, 0, 62, 63, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 74, 75, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 101, 102, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 115, 116, 0, 117, 118, 0, 118, 119, 0, 122, 123, 0, 125, 126, 0, 126, 127, 0, 131, 132, 0, 133, 134, 0, 135, 136, 0, 137, 138, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 147, 148, 0, 150, 151, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 159, 160, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 169, 170, 0, 173, 174, 0, 174, 175, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 193, 194, 0, 194, 195, 0, 196, 197, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 211, 212, 0, 212, 213, 0, 215, 216, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 229, 230, 0, 230, 231, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 239, 240, 0, 241, 242, 0, 243, 244, 0, 245, 246, 0, 248, 249, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 257, 258, 0, 258, 259, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 267, 268, 0, 271, 272, 0, 272, 273, 0, 273, 274, 0, 276, 277, 0, 277, 278, 0, 279, 280, 0, 281, 282, 0, 282, 283, 0, 283, 284, 0, 284, 285, 0, 287, 288, 0, 288, 289, 0, 291, 292, 0, 295, 296, 0, 297, 298, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 305, 306, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 318, 319, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 323, 324, 0, 325, 326, 0, 326, 327, 0, 329, 330, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 338, 339, 0, 339, 340, 0, 341, 342, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 357, 358, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 371, 372, 0, 372, 373, 0, 373, 374, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 390, 391, 0, 391, 392, 0, 393, 394, 0, 394, 395, 0, 396, 397, 0, 398, 399, 0, 401, 402, 0, 409, 410, 0, 410, 411, 0, 412, 413, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 420, 421, 0, 422, 423, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 430, 431, 0, 431, 432, 0, 434, 435, 0, 435, 436, 0, 436, 437, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 443, 444, 0, 445, 446, 0, 446, 447, 0, 449, 450, 0, 451, 452, 0, 453, 454, 0, 458, 459, 0, 461, 462, 0, 463, 464, 0, 464, 465, 0, 465, 466, 0, 467, 468 }

  134. "()(((((()()))(())((((((((()()(()))(((())))())(()(((()))))((())((()))))()((()())))))((()(()())))(()((((()((())(()))())))()))))()()(()()()))))((())())()(())((()))()(()((((()())(()())))()(()))()()()()(()(()((())()))))(())()()()(((()(()))()(())))()((()())())()(()()())((()()(((()((()))()((()()))()((())())))()))(()((((()(()(()))))))()))(()()())()()(()())(())()((()((((()((()())))))()()())(())()))((()()((()(()))(((()(()((()()())(((())))))((())))()())(()()(()(((())())()(()))()))(()))))(()()()(()((())))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 12, 13, 0, 13, 14, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 36, 37, 0, 41, 42, 0, 44, 45, 0, 45, 46, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 61, 62, 0, 62, 63, 0, 63, 64, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 75, 76, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 89, 90, 0, 94, 95, 0, 95, 96, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 108, 109, 0, 109, 110, 0, 113, 114, 0, 118, 119, 0, 124, 125, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 131, 132, 0, 133, 134, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 144, 145, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 170, 171, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 181, 182, 0, 183, 184, 0, 184, 185, 0, 188, 189, 0, 190, 191, 0, 192, 193, 0, 194, 195, 0, 196, 197, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 207, 208, 0, 213, 214, 0, 214, 215, 0, 217, 218, 0, 219, 220, 0, 221, 222, 0, 223, 224, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 233, 234, 0, 235, 236, 0, 236, 237, 0, 241, 242, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 247, 248, 0, 250, 251, 0, 253, 254, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 260, 261, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 267, 268, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 280, 281, 0, 282, 283, 0, 283, 284, 0, 284, 285, 0, 286, 287, 0, 290, 291, 0, 292, 293, 0, 293, 294, 0, 294, 295, 0, 297, 298, 0, 302, 303, 0, 306, 307, 0, 307, 308, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 313, 314, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 319, 320, 0, 327, 328, 0, 331, 332, 0, 332, 333, 0, 334, 335, 0, 336, 337, 0, 339, 340, 0, 341, 342, 0, 343, 344, 0, 344, 345, 0, 346, 347, 0, 349, 350, 0, 350, 351, 0, 353, 354, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 359, 360, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 369, 370, 0, 376, 377, 0, 378, 379, 0, 380, 381, 0, 383, 384, 0, 384, 385, 0, 387, 388, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 395, 396, 0, 397, 398, 0, 398, 399, 0, 399, 400, 0, 401, 402, 0, 402, 403, 0, 406, 407, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 411, 412, 0, 412, 413, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 418, 419, 0, 420, 421, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 433, 434, 0, 434, 435, 0, 435, 436, 0, 440, 441, 0, 442, 443, 0, 445, 446, 0, 446, 447, 0, 448, 449, 0, 450, 451, 0, 451, 452, 0, 453, 454, 0, 454, 455, 0, 455, 456, 0, 456, 457, 0, 459, 460, 0, 462, 463, 0, 464, 465, 0, 465, 466, 0, 469, 470, 0, 473, 474, 0, 474, 475, 0, 480, 481, 0, 481, 482, 0, 483, 484, 0, 485, 486, 0, 487, 488, 0, 488, 489, 0, 490, 491, 0, 491, 492, 0, 492, 493 }

  135. "((((()))()((()))(((())(()(()()())())()((()()(((()((())(()(()())()())())())(()))()))((()(((((())()))()(((())))())())))()))()))())()()(()(())(()()))((()())()()((())()((((()())())()(()()(()(()((())()()))())(())(()))(()())((())())()))()))(())(()())()()((((((())))(()(()((()((()((()()))(())))((()(())()(()()()()))((()((((())())()))(())())((((()())()((()))()))()()(()))))())()))()((()((((()())))()(())()))(()())))(()()()()()(((())(((()(()((()(()(())()))(())()())(())(((((()()(())))(())()(()()))))))))))))))"

    Returns: {0, 7, 8, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 15, 16, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 32, 33, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 59, 60, 0, 62, 63, 0, 64, 65, 0, 67, 68, 0, 70, 71, 0, 73, 74, 0, 74, 75, 0, 78, 79, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 94, 95, 0, 98, 99, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 108, 109, 0, 111, 112, 0, 116, 117, 0, 120, 121, 0, 124, 125, 0, 127, 128, 0, 129, 130, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 135, 136, 0, 138, 139, 0, 139, 140, 0, 141, 142, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 149, 150, 0, 152, 153, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 169, 170, 0, 172, 173, 0, 175, 176, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 185, 186, 0, 186, 187, 0, 188, 189, 0, 189, 190, 0, 190, 191, 0, 193, 194, 0, 195, 196, 0, 199, 200, 0, 202, 203, 0, 203, 204, 0, 206, 207, 0, 207, 208, 0, 211, 212, 0, 212, 213, 0, 214, 215, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 222, 223, 0, 225, 226, 0, 229, 230, 0, 233, 234, 0, 234, 235, 0, 237, 238, 0, 238, 239, 0, 240, 241, 0, 243, 244, 0, 245, 246, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 258, 259, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 272, 273, 0, 273, 274, 0, 274, 275, 0, 276, 277, 0, 280, 281, 0, 281, 282, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 290, 291, 0, 291, 292, 0, 294, 295, 0, 296, 297, 0, 297, 298, 0, 299, 300, 0, 301, 302, 0, 303, 304, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 311, 312, 0, 312, 313, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 318, 319, 0, 321, 322, 0, 325, 326, 0, 326, 327, 0, 329, 330, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 338, 339, 0, 341, 342, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 349, 350, 0, 353, 354, 0, 355, 356, 0, 357, 358, 0, 358, 359, 0, 364, 365, 0, 367, 368, 0, 371, 372, 0, 373, 374, 0, 374, 375, 0, 375, 376, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 388, 389, 0, 390, 391, 0, 391, 392, 0, 394, 395, 0, 398, 399, 0, 399, 400, 0, 401, 402, 0, 406, 407, 0, 407, 408, 0, 409, 410, 0, 411, 412, 0, 413, 414, 0, 415, 416, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 420, 421, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 428, 429, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 435, 436, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 442, 443, 0, 446, 447, 0, 447, 448, 0, 450, 451, 0, 452, 453, 0, 455, 456, 0, 456, 457, 0, 459, 460, 0, 460, 461, 0, 461, 462, 0, 462, 463, 0, 463, 464, 0, 464, 465, 0, 466, 467, 0, 468, 469, 0, 469, 470, 0, 474, 475, 0, 475, 476, 0, 478, 479, 0, 480, 481, 0, 481, 482, 0, 483, 484 }

  136. "(((())((()()((()))))(())()())())()((())((())))(()()(()()))()()(()()(()((()((()()(())))((()())))()(())(((((()))()))()()()()()(())()))))(((()()()))(()()()))(((()()(())(((())())(())()()(())(((()()(()))))()())((()))(()())(((((())))())))))(())((()()()))((((((())())()(((((()))(((((()(()((()()())())()((())))((())()((((())((()((((()()(()()(()(()(()))()))()(()(((()(()((()))()))()(()(())))((())((()()((())))(())))()(((()))()())(())(()((()()()(())((((()(()()))(()()(((((()))))))))))))))))))))))))))))))))))))"

    Returns: {0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 19, 20, 0, 20, 21, 0, 23, 24, 0, 25, 26, 0, 28, 29, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 50, 51, 0, 51, 52, 0, 53, 54, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 89, 90, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 103, 104, 0, 104, 105, 0, 105, 106, 0, 109, 110, 0, 113, 114, 0, 115, 116, 0, 117, 118, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 124, 125, 0, 127, 128, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 138, 139, 0, 140, 141, 0, 144, 145, 0, 145, 146, 0, 147, 148, 0, 149, 150, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 158, 159, 0, 160, 161, 0, 161, 162, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 170, 171, 0, 173, 174, 0, 174, 175, 0, 177, 178, 0, 179, 180, 0, 181, 182, 0, 182, 183, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 188, 189, 0, 190, 191, 0, 192, 193, 0, 193, 194, 0, 199, 200, 0, 201, 202, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 226, 227, 0, 233, 234, 0, 234, 235, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 241, 242, 0, 243, 244, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 256, 257, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 277, 278, 0, 278, 279, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 284, 285, 0, 286, 287, 0, 289, 290, 0, 292, 293, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 306, 307, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 323, 324, 0, 325, 326, 0, 327, 328, 0, 328, 329, 0, 330, 331, 0, 332, 333, 0, 333, 334, 0, 335, 336, 0, 336, 337, 0, 338, 339, 0, 339, 340, 0, 343, 344, 0, 347, 348, 0, 349, 350, 0, 350, 351, 0, 352, 353, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 357, 358, 0, 358, 359, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 366, 367, 0, 370, 371, 0, 372, 373, 0, 373, 374, 0, 375, 376, 0, 376, 377, 0, 381, 382, 0, 382, 383, 0, 383, 384, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 390, 391, 0, 392, 393, 0, 393, 394, 0, 394, 395, 0, 399, 400, 0, 400, 401, 0, 405, 406, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 414, 415, 0, 416, 417, 0, 419, 420, 0, 420, 421, 0, 423, 424, 0, 424, 425, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 430, 431, 0, 432, 433, 0, 434, 435, 0, 435, 436, 0, 438, 439, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 444, 445, 0, 445, 446, 0, 447, 448, 0, 451, 452, 0, 452, 453, 0, 454, 455, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 460, 461, 0, 461, 462 }

  137. "()((()()()())(((()()(((()((((()(((((()())()((()()((()))()((()((()))(())(()(()())((((()((())()()()()())(())()))((()()))())((()((()((()()((())(((()()())())()(()(()))()))()))(()())()((()(())(()(()(((((((()))(())))())(()(((())())))(()(((())))))))))((()()(()(())((())(()()()()()))()((()((()())))))())(()))()(()(())((()())()()((((())))()()))))(())((((()())))()()))()(()))()())(((()))())()())))))()))((((()((())(()))((()(()(((()))((())(())))))))))())())()(((((((()(((()()()(())()(())))))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 19, 20, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 40, 41, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 66, 67, 0, 67, 68, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 76, 77, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 90, 91, 0, 92, 93, 0, 94, 95, 0, 96, 97, 0, 98, 99, 0, 101, 102, 0, 102, 103, 0, 105, 106, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 117, 118, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 132, 133, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 142, 143, 0, 144, 145, 0, 146, 147, 0, 149, 150, 0, 152, 153, 0, 154, 155, 0, 155, 156, 0, 157, 158, 0, 158, 159, 0, 162, 163, 0, 166, 167, 0, 170, 171, 0, 171, 172, 0, 173, 174, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 183, 184, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 195, 196, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 203, 204, 0, 204, 205, 0, 209, 210, 0, 212, 213, 0, 213, 214, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 221, 222, 0, 226, 227, 0, 227, 228, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 247, 248, 0, 249, 250, 0, 250, 251, 0, 252, 253, 0, 253, 254, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 261, 262, 0, 262, 263, 0, 264, 265, 0, 266, 267, 0, 268, 269, 0, 270, 271, 0, 274, 275, 0, 276, 277, 0, 277, 278, 0, 278, 279, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 284, 285, 0, 291, 292, 0, 294, 295, 0, 295, 296, 0, 299, 300, 0, 301, 302, 0, 302, 303, 0, 304, 305, 0, 305, 306, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 312, 313, 0, 315, 316, 0, 317, 318, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 323, 324, 0, 328, 329, 0, 330, 331, 0, 336, 337, 0, 337, 338, 0, 340, 341, 0, 341, 342, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 346, 347, 0, 351, 352, 0, 353, 354, 0, 357, 358, 0, 359, 360, 0, 360, 361, 0, 364, 365, 0, 366, 367, 0, 369, 370, 0, 370, 371, 0, 371, 372, 0, 372, 373, 0, 376, 377, 0, 379, 380, 0, 381, 382, 0, 388, 389, 0, 392, 393, 0, 393, 394, 0, 394, 395, 0, 395, 396, 0, 396, 397, 0, 398, 399, 0, 399, 400, 0, 400, 401, 0, 403, 404, 0, 404, 405, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 412, 413, 0, 413, 414, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 422, 423, 0, 423, 424, 0, 424, 425, 0, 427, 428, 0, 428, 429, 0, 439, 440, 0, 442, 443, 0, 445, 446, 0, 447, 448, 0, 448, 449, 0, 449, 450, 0, 450, 451, 0, 451, 452, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 461, 462, 0, 463, 464, 0, 465, 466, 0, 466, 467, 0, 469, 470, 0, 471, 472, 0, 472, 473 }

  138. "()(((((()()(())))))())(())()()(()(()())())(((())))()(((())))(((()()(())))()())()(())(()())(())(())()(((()((())))(()((((())(()))()))))())()((((())((()())(())))))()()()()(()((())((()(()())))((()())(()()((((((())(())()(((((((())()(()))(()(()())(((()()(((()(())()())()((()))((()(()()())))()()((()))(()())))(())())(()((((()((())))))()(())()()))(())((((()(((()((()(((()))(()(()()))(())())))(())(()()(()))()((())))()))()))(()())((()))()(((())((()(())(((((())((()(())))())))))(()()())()))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 18, 19, 0, 21, 22, 0, 22, 23, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 35, 36, 0, 38, 39, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 44, 45, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 62, 63, 0, 64, 65, 0, 66, 67, 0, 67, 68, 0, 72, 73, 0, 74, 75, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 89, 90, 0, 90, 91, 0, 93, 94, 0, 94, 95, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 111, 112, 0, 112, 113, 0, 114, 115, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 122, 123, 0, 126, 127, 0, 132, 133, 0, 135, 136, 0, 137, 138, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 148, 149, 0, 151, 152, 0, 152, 153, 0, 159, 160, 0, 161, 162, 0, 163, 164, 0, 165, 166, 0, 167, 168, 0, 168, 169, 0, 170, 171, 0, 171, 172, 0, 172, 173, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 191, 192, 0, 194, 195, 0, 195, 196, 0, 197, 198, 0, 199, 200, 0, 200, 201, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 208, 209, 0, 209, 210, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 224, 225, 0, 226, 227, 0, 227, 228, 0, 231, 232, 0, 232, 233, 0, 234, 235, 0, 235, 236, 0, 237, 238, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 245, 246, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 250, 251, 0, 252, 253, 0, 253, 254, 0, 256, 257, 0, 258, 259, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 265, 266, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 273, 274, 0, 274, 275, 0, 276, 277, 0, 278, 279, 0, 283, 284, 0, 285, 286, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 293, 294, 0, 294, 295, 0, 296, 297, 0, 301, 302, 0, 302, 303, 0, 305, 306, 0, 308, 309, 0, 309, 310, 0, 311, 312, 0, 312, 313, 0, 313, 314, 0, 314, 315, 0, 315, 316, 0, 317, 318, 0, 318, 319, 0, 319, 320, 0, 326, 327, 0, 328, 329, 0, 329, 330, 0, 332, 333, 0, 334, 335, 0, 338, 339, 0, 339, 340, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 351, 352, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 360, 361, 0, 364, 365, 0, 365, 366, 0, 367, 368, 0, 368, 369, 0, 370, 371, 0, 374, 375, 0, 375, 376, 0, 378, 379, 0, 383, 384, 0, 384, 385, 0, 387, 388, 0, 388, 389, 0, 390, 391, 0, 392, 393, 0, 393, 394, 0, 397, 398, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 406, 407, 0, 410, 411, 0, 414, 415, 0, 415, 416, 0, 417, 418, 0, 420, 421, 0, 421, 422, 0, 422, 423, 0, 426, 427, 0, 428, 429, 0, 429, 430, 0, 430, 431, 0, 431, 432, 0, 434, 435, 0, 435, 436, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 442, 443, 0, 443, 444, 0, 444, 445, 0, 445, 446, 0, 446, 447, 0, 447, 448, 0, 450, 451, 0, 451, 452, 0, 452, 453, 0, 454, 455, 0, 455, 456, 0, 460, 461, 0, 467, 468, 0, 468, 469, 0, 470, 471, 0, 472, 473, 0, 475, 476 }

  139. "()()()(((((()(((()())()))((((())()))))(())()))(()))())(()())((()(()))((())())(())()((()(()))(((()(()((()())))))()((()(((()(()())(())())(()))(()))())((()(()()(()))(())()(()))((((()((()())))((()())())())()()(()(()())(((((())))))(()())))))(()())())(()())(()))(())((((()((((())()))())()()))((()))))((()))(((())()()))))()(((())())((())((())(((((((())(()())()(())))()))()()(()(()()((()))(()()())())())(()()((()()()()((()((())(()())(())))))()()(()))()(()(()(()()))())(()()))((()(())())))))))(())((())()(()))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 17, 18, 0, 20, 21, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 31, 32, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 45, 46, 0, 46, 47, 0, 50, 51, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 76, 77, 0, 77, 78, 0, 80, 81, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 103, 104, 0, 110, 111, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 121, 122, 0, 122, 123, 0, 124, 125, 0, 127, 128, 0, 128, 129, 0, 131, 132, 0, 134, 135, 0, 135, 136, 0, 139, 140, 0, 140, 141, 0, 144, 145, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 161, 162, 0, 162, 163, 0, 165, 166, 0, 167, 168, 0, 168, 169, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 178, 179, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 191, 192, 0, 194, 195, 0, 197, 198, 0, 200, 201, 0, 202, 203, 0, 204, 205, 0, 205, 206, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 225, 226, 0, 226, 227, 0, 228, 229, 0, 235, 236, 0, 236, 237, 0, 238, 239, 0, 241, 242, 0, 244, 245, 0, 245, 246, 0, 247, 248, 0, 250, 251, 0, 251, 252, 0, 255, 256, 0, 256, 257, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 265, 266, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 272, 273, 0, 276, 277, 0, 279, 280, 0, 281, 282, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 299, 300, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 305, 306, 0, 307, 308, 0, 313, 314, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 318, 319, 0, 321, 322, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 339, 340, 0, 340, 341, 0, 341, 342, 0, 344, 345, 0, 345, 346, 0, 347, 348, 0, 350, 351, 0, 352, 353, 0, 353, 354, 0, 358, 359, 0, 362, 363, 0, 364, 365, 0, 366, 367, 0, 367, 368, 0, 369, 370, 0, 370, 371, 0, 372, 373, 0, 374, 375, 0, 375, 376, 0, 376, 377, 0, 380, 381, 0, 381, 382, 0, 383, 384, 0, 385, 386, 0, 388, 389, 0, 391, 392, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 403, 404, 0, 405, 406, 0, 407, 408, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 413, 414, 0, 414, 415, 0, 415, 416, 0, 418, 419, 0, 419, 420, 0, 421, 422, 0, 424, 425, 0, 425, 426, 0, 432, 433, 0, 434, 435, 0, 436, 437, 0, 437, 438, 0, 441, 442, 0, 443, 444, 0, 444, 445, 0, 446, 447, 0, 447, 448, 0, 449, 450, 0, 450, 451, 0, 452, 453, 0, 456, 457, 0, 459, 460, 0, 460, 461, 0, 462, 463, 0, 466, 467, 0, 467, 468, 0, 468, 469, 0, 470, 471, 0, 471, 472, 0, 474, 475, 0, 483, 484, 0, 484, 485, 0, 487, 488, 0, 488, 489, 0, 489, 490, 0, 492, 493, 0, 494, 495, 0, 495, 496 }

  140. "()()()(()()()((()())))()()(()((()((()(()((()(())))()(((()((()(())()())((()()))(()()))(()))()()((()()))(()))()((()))()(())((()((((()((()((()(((()()))))))())()(()))()()()))))((((((())))))))(()()(()())))))(((((())()))()))()()()()((((())((()())())))((()))(()(()(()((()(()))(((((())(((())))))(())()(()))())((()()()))()(()))))())))))()())()((())())(())()(()((())()()())())((())())()()()((()))((((())(()(()(((())))))(())(((()()))())()((((()())(())())(()))()))))()((()))()(())()((((()))))()()()()()()(()())()"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 49, 50, 0, 51, 52, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 57, 58, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 64, 65, 0, 66, 67, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 73, 74, 0, 77, 78, 0, 78, 79, 0, 80, 81, 0, 84, 85, 0, 85, 86, 0, 89, 90, 0, 91, 92, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 97, 98, 0, 101, 102, 0, 102, 103, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 114, 115, 0, 116, 117, 0, 117, 118, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 141, 142, 0, 143, 144, 0, 151, 152, 0, 154, 155, 0, 156, 157, 0, 157, 158, 0, 161, 162, 0, 163, 164, 0, 165, 166, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 191, 192, 0, 192, 193, 0, 194, 195, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 209, 210, 0, 213, 214, 0, 217, 218, 0, 219, 220, 0, 221, 222, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 236, 237, 0, 239, 240, 0, 244, 245, 0, 245, 246, 0, 246, 247, 0, 250, 251, 0, 251, 252, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 273, 274, 0, 276, 277, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 286, 287, 0, 287, 288, 0, 290, 291, 0, 292, 293, 0, 293, 294, 0, 297, 298, 0, 300, 301, 0, 301, 302, 0, 302, 303, 0, 304, 305, 0, 306, 307, 0, 310, 311, 0, 312, 313, 0, 313, 314, 0, 319, 320, 0, 326, 327, 0, 328, 329, 0, 331, 332, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 338, 339, 0, 341, 342, 0, 342, 343, 0, 345, 346, 0, 347, 348, 0, 348, 349, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 355, 356, 0, 357, 358, 0, 359, 360, 0, 362, 363, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 370, 371, 0, 373, 374, 0, 375, 376, 0, 377, 378, 0, 379, 380, 0, 380, 381, 0, 381, 382, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 392, 393, 0, 393, 394, 0, 395, 396, 0, 396, 397, 0, 398, 399, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 408, 409, 0, 409, 410, 0, 412, 413, 0, 413, 414, 0, 414, 415, 0, 415, 416, 0, 417, 418, 0, 421, 422, 0, 424, 425, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 429, 430, 0, 430, 431, 0, 432, 433, 0, 435, 436, 0, 436, 437, 0, 439, 440, 0, 442, 443, 0, 443, 444, 0, 447, 448, 0, 453, 454, 0, 455, 456, 0, 456, 457, 0, 457, 458, 0, 461, 462, 0, 463, 464, 0, 464, 465, 0, 467, 468, 0, 469, 470, 0, 470, 471, 0, 471, 472, 0, 472, 473, 0, 473, 474, 0, 479, 480, 0, 481, 482, 0, 483, 484, 0, 485, 486, 0, 487, 488, 0, 489, 490, 0, 491, 492, 0, 492, 493, 0, 494, 495, 0, 497, 498 }

  141. "(()((()))()((()()))()(((())(())()))(()((((((()(()((((())))((()(())(()(())())((()()))((()()(((()((()))))))()(())))(((())))())(((()()(((((((())()()))())()((()(((((()(()(())(((())(()))())((())()))))(()))())((((())((()((())()((())())()()((((((()())))()())((((()(((())(()(()()((()()()((()))()()))))))))))(()()()()()()))(()())))((((((((())((()((()())))()())((((((()(()((())(((()()())()()))))()()(())())((((()))))))((())(()(((((()))))((()()))())()((((())())(((()()))())))))))))))))))))))))))))))))))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 8, 9, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 18, 19, 0, 20, 21, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 26, 27, 0, 27, 28, 0, 30, 31, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 43, 44, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 57, 58, 0, 58, 59, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 72, 73, 0, 75, 76, 0, 76, 77, 0, 77, 78, 0, 79, 80, 0, 83, 84, 0, 84, 85, 0, 85, 86, 0, 87, 88, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 115, 116, 0, 120, 121, 0, 123, 124, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 140, 141, 0, 142, 143, 0, 146, 147, 0, 149, 150, 0, 151, 152, 0, 152, 153, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 162, 163, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 169, 170, 0, 170, 171, 0, 171, 172, 0, 172, 173, 0, 175, 176, 0, 176, 177, 0, 180, 181, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 188, 189, 0, 194, 195, 0, 195, 196, 0, 199, 200, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 209, 210, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 218, 219, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 225, 226, 0, 228, 229, 0, 230, 231, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 240, 241, 0, 245, 246, 0, 247, 248, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 262, 263, 0, 263, 264, 0, 265, 266, 0, 266, 267, 0, 268, 269, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 276, 277, 0, 278, 279, 0, 279, 280, 0, 280, 281, 0, 284, 285, 0, 286, 287, 0, 298, 299, 0, 299, 300, 0, 301, 302, 0, 303, 304, 0, 305, 306, 0, 307, 308, 0, 309, 310, 0, 313, 314, 0, 314, 315, 0, 316, 317, 0, 321, 322, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 332, 333, 0, 333, 334, 0, 334, 335, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 340, 341, 0, 345, 346, 0, 347, 348, 0, 350, 351, 0, 351, 352, 0, 352, 353, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 356, 357, 0, 358, 359, 0, 359, 360, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 366, 367, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 371, 372, 0, 373, 374, 0, 376, 377, 0, 378, 379, 0, 384, 385, 0, 386, 387, 0, 388, 389, 0, 389, 390, 0, 392, 393, 0, 395, 396, 0, 396, 397, 0, 397, 398, 0, 398, 399, 0, 399, 400, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 412, 413, 0, 413, 414, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 420, 421, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 430, 431, 0, 434, 435, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 446, 447, 0, 449, 450, 0, 450, 451, 0, 451, 452, 0, 452, 453, 0, 454, 455, 0, 458, 459 }

  142. "((((((((()))()())())())())())())((((()())())))(())()()(()()())()(())((()()(()))())(((()()(()()))()(()((()(()())(()())))(()()))))()(())(()())(())(((()()))())((())(()(()())))(())((()(()))((())()(((()))(())))())(((((())(())(())((())))(((()()(((())(((((()()))))()(((())(()(()((()()))))())((()()()())))))())(())((()()(()((())(((())())))(((()()))(()((((())()))()(()))))()))((())))(())())))(((())(())(((()())(()))))((())))((((((()(()()))()(((()()(()()(()()()()(())))(())())(((()()((((()))()())))))))))))))))"

    Returns: {0, 11, 12, 0, 13, 14, 0, 16, 17, 0, 19, 20, 0, 22, 23, 0, 25, 26, 0, 28, 29, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 40, 41, 0, 45, 46, 0, 46, 47, 0, 49, 50, 0, 51, 52, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 58, 59, 0, 61, 62, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 74, 75, 0, 78, 79, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 91, 92, 0, 95, 96, 0, 97, 98, 0, 98, 99, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 105, 106, 0, 107, 108, 0, 110, 111, 0, 111, 112, 0, 113, 114, 0, 118, 119, 0, 119, 120, 0, 121, 122, 0, 127, 128, 0, 129, 130, 0, 130, 131, 0, 133, 134, 0, 134, 135, 0, 136, 137, 0, 139, 140, 0, 140, 141, 0, 143, 144, 0, 144, 145, 0, 145, 146, 0, 146, 147, 0, 148, 149, 0, 152, 153, 0, 155, 156, 0, 156, 157, 0, 157, 158, 0, 160, 161, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 166, 167, 0, 171, 172, 0, 172, 173, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 189, 190, 0, 191, 192, 0, 192, 193, 0, 193, 194, 0, 194, 195, 0, 198, 199, 0, 199, 200, 0, 204, 205, 0, 207, 208, 0, 208, 209, 0, 209, 210, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 215, 216, 0, 216, 217, 0, 219, 220, 0, 220, 221, 0, 223, 224, 0, 224, 225, 0, 225, 226, 0, 230, 231, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 235, 236, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 240, 241, 0, 243, 244, 0, 244, 245, 0, 245, 246, 0, 246, 247, 0, 247, 248, 0, 248, 249, 0, 250, 251, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 260, 261, 0, 261, 262, 0, 264, 265, 0, 265, 266, 0, 267, 268, 0, 268, 269, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 280, 281, 0, 283, 284, 0, 284, 285, 0, 285, 286, 0, 287, 288, 0, 289, 290, 0, 291, 292, 0, 298, 299, 0, 301, 302, 0, 302, 303, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 309, 310, 0, 311, 312, 0, 312, 313, 0, 314, 315, 0, 315, 316, 0, 316, 317, 0, 319, 320, 0, 320, 321, 0, 321, 322, 0, 322, 323, 0, 325, 326, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 333, 334, 0, 335, 336, 0, 339, 340, 0, 340, 341, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 349, 350, 0, 353, 354, 0, 355, 356, 0, 356, 357, 0, 362, 363, 0, 366, 367, 0, 367, 368, 0, 368, 369, 0, 373, 374, 0, 374, 375, 0, 377, 378, 0, 382, 383, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 388, 389, 0, 389, 390, 0, 392, 393, 0, 393, 394, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 400, 401, 0, 401, 402, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 420, 421, 0, 422, 423, 0, 423, 424, 0, 425, 426, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 441, 442, 0, 443, 444, 0, 444, 445, 0, 446, 447, 0, 448, 449, 0, 450, 451, 0, 452, 453, 0, 453, 454, 0, 458, 459, 0, 459, 460, 0, 462, 463, 0, 465, 466, 0, 466, 467, 0, 467, 468, 0, 468, 469, 0, 470, 471, 0, 472, 473, 0, 473, 474, 0, 474, 475, 0, 475, 476, 0, 476, 477, 0, 480, 481, 0, 482, 483 }

  143. "(((((()(()))(()))(()))()()()))(())()(())()()()(()((()))())()((()()()((())))())()(())(())()(((((()(()(((()))(())(()))()))()))())()())(()()(()))()(())(())()()()()()(())()()()()()(())()()()((()((()(()())()(()))()())))()()()(())(()()())()()()(((()(()))()(()())))()()(())()()((()((()))))(()((((((()()(()(())()(())((((()(()()))))()))((((())(((((())))())(()))()())()())((((()()((((()(((()(())))(())(((((()()()())))))))(((())))()((())(())()((()((()(((())))()))()(()()())))()())))))))))(())())(((())()))))))))"

    Returns: {0, 6, 7, 0, 7, 8, 0, 11, 12, 0, 12, 13, 0, 16, 17, 0, 17, 18, 0, 21, 22, 0, 23, 24, 0, 25, 26, 0, 29, 30, 0, 30, 31, 0, 33, 34, 0, 35, 36, 0, 36, 37, 0, 39, 40, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 46, 47, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 54, 55, 0, 57, 58, 0, 59, 60, 0, 60, 61, 0, 61, 62, 0, 63, 64, 0, 65, 66, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 74, 75, 0, 77, 78, 0, 79, 80, 0, 80, 81, 0, 83, 84, 0, 84, 85, 0, 87, 88, 0, 89, 90, 0, 90, 91, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 99, 100, 0, 100, 101, 0, 101, 102, 0, 102, 103, 0, 106, 107, 0, 107, 108, 0, 110, 111, 0, 111, 112, 0, 115, 116, 0, 119, 120, 0, 123, 124, 0, 126, 127, 0, 128, 129, 0, 131, 132, 0, 132, 133, 0, 134, 135, 0, 136, 137, 0, 137, 138, 0, 141, 142, 0, 143, 144, 0, 144, 145, 0, 147, 148, 0, 148, 149, 0, 151, 152, 0, 153, 154, 0, 155, 156, 0, 157, 158, 0, 159, 160, 0, 161, 162, 0, 162, 163, 0, 165, 166, 0, 167, 168, 0, 169, 170, 0, 171, 172, 0, 173, 174, 0, 175, 176, 0, 176, 177, 0, 179, 180, 0, 181, 182, 0, 183, 184, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 193, 194, 0, 194, 195, 0, 196, 197, 0, 199, 200, 0, 201, 202, 0, 202, 203, 0, 206, 207, 0, 208, 209, 0, 213, 214, 0, 215, 216, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 228, 229, 0, 231, 232, 0, 233, 234, 0, 235, 236, 0, 237, 238, 0, 238, 239, 0, 239, 240, 0, 240, 241, 0, 242, 243, 0, 243, 244, 0, 247, 248, 0, 249, 250, 0, 250, 251, 0, 252, 253, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 265, 266, 0, 267, 268, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 281, 282, 0, 282, 283, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 290, 291, 0, 292, 293, 0, 294, 295, 0, 295, 296, 0, 297, 298, 0, 298, 299, 0, 301, 302, 0, 303, 304, 0, 304, 305, 0, 307, 308, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 313, 314, 0, 314, 315, 0, 316, 317, 0, 322, 323, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 333, 334, 0, 334, 335, 0, 335, 336, 0, 336, 337, 0, 337, 338, 0, 338, 339, 0, 343, 344, 0, 346, 347, 0, 347, 348, 0, 351, 352, 0, 353, 354, 0, 356, 357, 0, 358, 359, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 367, 368, 0, 369, 370, 0, 370, 371, 0, 371, 372, 0, 372, 373, 0, 373, 374, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 378, 379, 0, 380, 381, 0, 381, 382, 0, 386, 387, 0, 387, 388, 0, 390, 391, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 394, 395, 0, 395, 396, 0, 397, 398, 0, 399, 400, 0, 401, 402, 0, 410, 411, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 418, 419, 0, 420, 421, 0, 421, 422, 0, 422, 423, 0, 425, 426, 0, 426, 427, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 435, 436, 0, 436, 437, 0, 437, 438, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 447, 448, 0, 451, 452, 0, 453, 454, 0, 454, 455, 0, 456, 457, 0, 458, 459, 0, 463, 464, 0, 465, 466, 0, 476, 477, 0, 477, 478, 0, 480, 481, 0, 483, 484, 0, 484, 485, 0, 485, 486, 0, 486, 487, 0, 489, 490 }

  144. "(()())()(((((()()))))(()()))()(((((())())(()(())))()()))()()()(())()()(())((()(((()((()))(())()))(())()(()))((()(())))(())())((()())))(((()))()())()((()))((())(()))(()())((()()))(()()()(((()()))(((()((()())))))(((()((())(()())(())((()))(()))((((())))()(()))))()))()((()(()))((((()))(()(()())())(((())()())((())))(())))))()()(((())()))()()(())(()())()(()())()()()()()(())(())(((())))()()()(()()())()(()())((()))()(()()(((())())(((())))(()()()(((()((()())))(()))()))))()(())()((())(())(()))((()()()))()"

    Returns: {0, 2, 3, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 12, 13, 0, 14, 15, 0, 20, 21, 0, 21, 22, 0, 23, 24, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 44, 45, 0, 49, 50, 0, 51, 52, 0, 55, 56, 0, 57, 58, 0, 59, 60, 0, 61, 62, 0, 62, 63, 0, 65, 66, 0, 67, 68, 0, 69, 70, 0, 70, 71, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 88, 89, 0, 89, 90, 0, 92, 93, 0, 96, 97, 0, 97, 98, 0, 100, 101, 0, 102, 103, 0, 103, 104, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 111, 112, 0, 112, 113, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 128, 129, 0, 133, 134, 0, 134, 135, 0, 135, 136, 0, 136, 137, 0, 140, 141, 0, 142, 143, 0, 145, 146, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 153, 154, 0, 154, 155, 0, 155, 156, 0, 158, 159, 0, 159, 160, 0, 163, 164, 0, 164, 165, 0, 166, 167, 0, 169, 170, 0, 170, 171, 0, 171, 172, 0, 173, 174, 0, 177, 178, 0, 178, 179, 0, 180, 181, 0, 182, 183, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 187, 188, 0, 189, 190, 0, 193, 194, 0, 194, 195, 0, 195, 196, 0, 196, 197, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 202, 203, 0, 209, 210, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 219, 220, 0, 220, 221, 0, 222, 223, 0, 225, 226, 0, 226, 227, 0, 229, 230, 0, 230, 231, 0, 231, 232, 0, 235, 236, 0, 236, 237, 0, 240, 241, 0, 241, 242, 0, 242, 243, 0, 243, 244, 0, 244, 245, 0, 249, 250, 0, 251, 252, 0, 252, 253, 0, 258, 259, 0, 262, 263, 0, 264, 265, 0, 265, 266, 0, 266, 267, 0, 268, 269, 0, 269, 270, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 281, 282, 0, 282, 283, 0, 284, 285, 0, 285, 286, 0, 287, 288, 0, 290, 291, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 296, 297, 0, 299, 300, 0, 301, 302, 0, 304, 305, 0, 305, 306, 0, 306, 307, 0, 311, 312, 0, 312, 313, 0, 319, 320, 0, 321, 322, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 329, 330, 0, 333, 334, 0, 335, 336, 0, 337, 338, 0, 338, 339, 0, 341, 342, 0, 342, 343, 0, 344, 345, 0, 347, 348, 0, 349, 350, 0, 350, 351, 0, 352, 353, 0, 355, 356, 0, 357, 358, 0, 359, 360, 0, 361, 362, 0, 363, 364, 0, 365, 366, 0, 366, 367, 0, 369, 370, 0, 370, 371, 0, 373, 374, 0, 374, 375, 0, 375, 376, 0, 376, 377, 0, 381, 382, 0, 383, 384, 0, 385, 386, 0, 387, 388, 0, 388, 389, 0, 390, 391, 0, 392, 393, 0, 395, 396, 0, 397, 398, 0, 398, 399, 0, 400, 401, 0, 403, 404, 0, 404, 405, 0, 405, 406, 0, 409, 410, 0, 411, 412, 0, 412, 413, 0, 414, 415, 0, 416, 417, 0, 417, 418, 0, 418, 419, 0, 419, 420, 0, 422, 423, 0, 425, 426, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 433, 434, 0, 434, 435, 0, 436, 437, 0, 438, 439, 0, 440, 441, 0, 441, 442, 0, 442, 443, 0, 443, 444, 0, 445, 446, 0, 446, 447, 0, 447, 448, 0, 449, 450, 0, 454, 455, 0, 455, 456, 0, 459, 460, 0, 465, 466, 0, 467, 468, 0, 468, 469, 0, 471, 472, 0, 473, 474, 0, 474, 475, 0, 475, 476, 0, 478, 479, 0, 479, 480, 0, 482, 483, 0, 483, 484, 0, 487, 488, 0, 488, 489, 0, 489, 490, 0, 491, 492, 0, 493, 494, 0, 497, 498 }

  145. "()(())()((((()))(()())))(()(((()(((()()))(())()()))()(()()())()()(((((()()()))())))()((())()))(()((()()()()(((((()))()()(((()))((()))))(()()()((())())())))((()()())())())))((()))))(())(((()(())))()()((()((((((()((()((())(())))((())))())(((()())))()(()))((()(()(()))()))(()()(((()(()())(((()())((()()(()()()((()()))))(()()))))()))(((()(())))))())(())())(())))((())()))())())((())))(())()()()(()((()()(()))(()())(()()()))(()(()(()))()))()()()()()()((((()(())()()()()((()())(((()))((())()((()))))))))())"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 10, 11, 0, 11, 12, 0, 15, 16, 0, 16, 17, 0, 18, 19, 0, 23, 24, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 40, 41, 0, 41, 42, 0, 44, 45, 0, 46, 47, 0, 50, 51, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 57, 58, 0, 60, 61, 0, 62, 63, 0, 64, 65, 0, 65, 66, 0, 66, 67, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 71, 72, 0, 73, 74, 0, 77, 78, 0, 82, 83, 0, 84, 85, 0, 85, 86, 0, 86, 87, 0, 89, 90, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 100, 101, 0, 102, 103, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 115, 116, 0, 117, 118, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 122, 123, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 134, 135, 0, 135, 136, 0, 137, 138, 0, 139, 140, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 146, 147, 0, 149, 150, 0, 154, 155, 0, 155, 156, 0, 156, 157, 0, 158, 159, 0, 160, 161, 0, 163, 164, 0, 166, 167, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 179, 180, 0, 180, 181, 0, 183, 184, 0, 184, 185, 0, 185, 186, 0, 186, 187, 0, 188, 189, 0, 189, 190, 0, 194, 195, 0, 196, 197, 0, 198, 199, 0, 199, 200, 0, 200, 201, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 219, 220, 0, 220, 221, 0, 225, 226, 0, 226, 227, 0, 227, 228, 0, 232, 233, 0, 235, 236, 0, 236, 237, 0, 237, 238, 0, 238, 239, 0, 240, 241, 0, 245, 246, 0, 247, 248, 0, 248, 249, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 256, 257, 0, 257, 258, 0, 259, 260, 0, 260, 261, 0, 264, 265, 0, 268, 269, 0, 269, 270, 0, 271, 272, 0, 273, 274, 0, 274, 275, 0, 275, 276, 0, 276, 277, 0, 278, 279, 0, 279, 280, 0, 281, 282, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 287, 288, 0, 289, 290, 0, 292, 293, 0, 293, 294, 0, 294, 295, 0, 296, 297, 0, 298, 299, 0, 299, 300, 0, 301, 302, 0, 303, 304, 0, 305, 306, 0, 306, 307, 0, 307, 308, 0, 309, 310, 0, 315, 316, 0, 316, 317, 0, 318, 319, 0, 324, 325, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 333, 334, 0, 334, 335, 0, 341, 342, 0, 344, 345, 0, 345, 346, 0, 348, 349, 0, 351, 352, 0, 352, 353, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 362, 363, 0, 366, 367, 0, 369, 370, 0, 372, 373, 0, 373, 374, 0, 374, 375, 0, 379, 380, 0, 380, 381, 0, 383, 384, 0, 385, 386, 0, 387, 388, 0, 389, 390, 0, 390, 391, 0, 392, 393, 0, 393, 394, 0, 394, 395, 0, 396, 397, 0, 398, 399, 0, 399, 400, 0, 403, 404, 0, 404, 405, 0, 406, 407, 0, 409, 410, 0, 410, 411, 0, 412, 413, 0, 414, 415, 0, 418, 419, 0, 419, 420, 0, 421, 422, 0, 422, 423, 0, 424, 425, 0, 425, 426, 0, 429, 430, 0, 433, 434, 0, 435, 436, 0, 437, 438, 0, 439, 440, 0, 441, 442, 0, 443, 444, 0, 445, 446, 0, 446, 447, 0, 447, 448, 0, 448, 449, 0, 449, 450, 0, 451, 452, 0, 452, 453, 0, 455, 456, 0, 457, 458, 0, 459, 460, 0, 461, 462, 0, 463, 464, 0, 464, 465, 0, 465, 466, 0, 467, 468, 0, 470, 471, 0, 471, 472, 0, 472, 473, 0, 473, 474, 0, 477, 478, 0, 478, 479, 0, 479, 480, 0, 482, 483, 0, 484, 485, 0, 485, 486, 0, 486, 487, 0, 496, 497 }

  146. "()()(())((()()()))()()((((((((((())(()(())()()()))(((()))()))()((())(()(())))())))(((()(())(()))(()(()(()))(())))((()))(()()())()((((())((())))()())))))(()())()))()()(()())((((())()))())()((()))(((((())((((((())(()((((((()(()(()((()(((())()(()))()(()(((()))()(()(()()((((((()()))())())()))()(()(())))(()()))()((((()(()))))(((((((())))))(()))))()()(((()()))(())(())())))(()))()()())(((((()((((()(())))()))())()())))))())(())()))((()(()(())(((()))(()))(()((()))))((((()(())))(((()))))))))))))))))))))))"

    Returns: {0, 1, 2, 0, 3, 4, 0, 4, 5, 0, 7, 8, 0, 8, 9, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 17, 18, 0, 19, 20, 0, 21, 22, 0, 22, 23, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 29, 30, 0, 30, 31, 0, 31, 32, 0, 34, 35, 0, 35, 36, 0, 37, 38, 0, 38, 39, 0, 41, 42, 0, 43, 44, 0, 45, 46, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 56, 57, 0, 60, 61, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 67, 68, 0, 68, 69, 0, 70, 71, 0, 71, 72, 0, 76, 77, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 86, 87, 0, 87, 88, 0, 90, 91, 0, 91, 92, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 99, 100, 0, 101, 102, 0, 102, 103, 0, 106, 107, 0, 107, 108, 0, 112, 113, 0, 113, 114, 0, 114, 115, 0, 118, 119, 0, 119, 120, 0, 121, 122, 0, 123, 124, 0, 126, 127, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 131, 132, 0, 132, 133, 0, 135, 136, 0, 136, 137, 0, 137, 138, 0, 142, 143, 0, 144, 145, 0, 151, 152, 0, 152, 153, 0, 154, 155, 0, 157, 158, 0, 161, 162, 0, 163, 164, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 171, 172, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 175, 176, 0, 178, 179, 0, 182, 183, 0, 185, 186, 0, 187, 188, 0, 188, 189, 0, 189, 190, 0, 193, 194, 0, 194, 195, 0, 195, 196, 0, 196, 197, 0, 197, 198, 0, 198, 199, 0, 201, 202, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 221, 222, 0, 222, 223, 0, 224, 225, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 232, 233, 0, 233, 234, 0, 234, 235, 0, 237, 238, 0, 239, 240, 0, 240, 241, 0, 244, 245, 0, 246, 247, 0, 247, 248, 0, 249, 250, 0, 250, 251, 0, 251, 252, 0, 252, 253, 0, 256, 257, 0, 258, 259, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 264, 265, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 271, 272, 0, 272, 273, 0, 274, 275, 0, 278, 279, 0, 281, 282, 0, 284, 285, 0, 288, 289, 0, 290, 291, 0, 291, 292, 0, 293, 294, 0, 294, 295, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 306, 307, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 312, 313, 0, 314, 315, 0, 315, 316, 0, 321, 322, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 335, 336, 0, 336, 337, 0, 342, 343, 0, 344, 345, 0, 346, 347, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 351, 352, 0, 355, 356, 0, 356, 357, 0, 359, 360, 0, 360, 361, 0, 363, 364, 0, 368, 369, 0, 369, 370, 0, 373, 374, 0, 375, 376, 0, 377, 378, 0, 380, 381, 0, 381, 382, 0, 382, 383, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 387, 388, 0, 388, 389, 0, 389, 390, 0, 390, 391, 0, 391, 392, 0, 393, 394, 0, 394, 395, 0, 399, 400, 0, 403, 404, 0, 406, 407, 0, 408, 409, 0, 415, 416, 0, 418, 419, 0, 419, 420, 0, 422, 423, 0, 426, 427, 0, 427, 428, 0, 428, 429, 0, 430, 431, 0, 431, 432, 0, 433, 434, 0, 434, 435, 0, 437, 438, 0, 438, 439, 0, 439, 440, 0, 440, 441, 0, 444, 445, 0, 445, 446, 0, 449, 450, 0, 450, 451, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 460, 461, 0, 461, 462, 0, 462, 463, 0, 463, 464, 0, 464, 465, 0, 466, 467, 0, 467, 468, 0, 472, 473, 0, 473, 474, 0, 474, 475, 0, 475, 476 }

  147. "()(())(()())((((())())))()()()()()(())(()((()(((()(((()(())()(()))))((((())))(((())()))()())(((())())))))((()(())())((((((()()())())()())(()))))()((()(()())))()())((())))))(()(()))()(((())))((()))()((()))()((())()())((((((()(()()(()(()(()()()))())())))))()))((())(()))(((()())((()((((()()((()())(()()()))((()(()())())))(())((())()()))))))))()()()()(((()(()))((()()((()))())()(((()()()()(())()())())(()((()())((())()))())()()()()((()(((())(()))))()((())(((((((()))()())((()()))))())))(((((()))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 5, 6, 0, 6, 7, 0, 8, 9, 0, 11, 12, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 15, 16, 0, 18, 19, 0, 23, 24, 0, 25, 26, 0, 27, 28, 0, 29, 30, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 37, 38, 0, 38, 39, 0, 40, 41, 0, 41, 42, 0, 42, 43, 0, 44, 45, 0, 45, 46, 0, 46, 47, 0, 47, 48, 0, 49, 50, 0, 50, 51, 0, 51, 52, 0, 52, 53, 0, 54, 55, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 61, 62, 0, 67, 68, 0, 68, 69, 0, 69, 70, 0, 70, 71, 0, 71, 72, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 82, 83, 0, 86, 87, 0, 88, 89, 0, 91, 92, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 97, 98, 0, 104, 105, 0, 105, 106, 0, 106, 107, 0, 108, 109, 0, 109, 110, 0, 112, 113, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 118, 119, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 123, 124, 0, 125, 126, 0, 128, 129, 0, 131, 132, 0, 133, 134, 0, 136, 137, 0, 137, 138, 0, 143, 144, 0, 145, 146, 0, 146, 147, 0, 147, 148, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 157, 158, 0, 159, 160, 0, 162, 163, 0, 163, 164, 0, 164, 165, 0, 171, 172, 0, 172, 173, 0, 174, 175, 0, 175, 176, 0, 179, 180, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 195, 196, 0, 197, 198, 0, 198, 199, 0, 199, 200, 0, 203, 204, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 210, 211, 0, 212, 213, 0, 215, 216, 0, 216, 217, 0, 217, 218, 0, 218, 219, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 223, 224, 0, 224, 225, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 232, 233, 0, 234, 235, 0, 235, 236, 0, 237, 238, 0, 239, 240, 0, 243, 244, 0, 246, 247, 0, 253, 254, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 262, 263, 0, 263, 264, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 272, 273, 0, 275, 276, 0, 276, 277, 0, 277, 278, 0, 279, 280, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 283, 284, 0, 285, 286, 0, 287, 288, 0, 288, 289, 0, 289, 290, 0, 291, 292, 0, 294, 295, 0, 295, 296, 0, 297, 298, 0, 299, 300, 0, 303, 304, 0, 304, 305, 0, 305, 306, 0, 307, 308, 0, 308, 309, 0, 310, 311, 0, 313, 314, 0, 318, 319, 0, 319, 320, 0, 322, 323, 0, 323, 324, 0, 324, 325, 0, 327, 328, 0, 329, 330, 0, 339, 340, 0, 341, 342, 0, 343, 344, 0, 345, 346, 0, 347, 348, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 352, 353, 0, 353, 354, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 361, 362, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 369, 370, 0, 372, 373, 0, 374, 375, 0, 375, 376, 0, 376, 377, 0, 377, 378, 0, 379, 380, 0, 381, 382, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 389, 390, 0, 391, 392, 0, 394, 395, 0, 397, 398, 0, 398, 399, 0, 400, 401, 0, 401, 402, 0, 402, 403, 0, 404, 405, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 412, 413, 0, 416, 417, 0, 419, 420, 0, 421, 422, 0, 423, 424, 0, 425, 426, 0, 427, 428, 0, 428, 429, 0, 429, 430, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 437, 438, 0, 438, 439, 0, 444, 445, 0, 446, 447, 0, 447, 448, 0, 448, 449, 0, 451, 452, 0, 452, 453, 0, 453, 454, 0, 454, 455, 0, 455, 456, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 462, 463, 0, 464, 465, 0, 467, 468, 0, 468, 469, 0, 469, 470, 0, 471, 472, 0, 477, 478, 0, 482, 483, 0, 483, 484, 0, 484, 485, 0, 485, 486, 0, 486, 487, 0, 487, 488 }

  148. "(())()(())(()((()()())))(()(()(()))(()))((()()))(((()()(())()())())(()()(((()))(()(())((((())((()(((()))))(())))())(()))((())((((())(((()))((()(()()((((()())())())))))((()())))((()(((((())()(()(()()(()()((((((((()(())())(()((((()(())()()))))))()(()()()()()))((()))()))(((()()())())()))()(()))((((())))))()()))(((())))(())))(()(((()((()(()())((((((((()(())(())(()))(()(()())(()()((()))))))()))((())))()))))))((((((((())))))))(((()())((())()(())))())()()()))(((())()(())()()))))((()())))))(()))))))))))"

    Returns: {0, 3, 4, 0, 5, 6, 0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 14, 15, 0, 16, 17, 0, 18, 19, 0, 23, 24, 0, 24, 25, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 30, 31, 0, 34, 35, 0, 35, 36, 0, 39, 40, 0, 40, 41, 0, 41, 42, 0, 43, 44, 0, 47, 48, 0, 48, 49, 0, 49, 50, 0, 50, 51, 0, 52, 53, 0, 54, 55, 0, 55, 56, 0, 58, 59, 0, 60, 61, 0, 63, 64, 0, 66, 67, 0, 67, 68, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 78, 79, 0, 79, 80, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 87, 88, 0, 88, 89, 0, 89, 90, 0, 92, 93, 0, 93, 94, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 105, 106, 0, 106, 107, 0, 111, 112, 0, 114, 115, 0, 115, 116, 0, 119, 120, 0, 120, 121, 0, 121, 122, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 131, 132, 0, 132, 133, 0, 133, 134, 0, 134, 135, 0, 138, 139, 0, 139, 140, 0, 140, 141, 0, 142, 143, 0, 143, 144, 0, 145, 146, 0, 147, 148, 0, 148, 149, 0, 149, 150, 0, 150, 151, 0, 151, 152, 0, 153, 154, 0, 156, 157, 0, 159, 160, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 170, 171, 0, 175, 176, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 180, 181, 0, 181, 182, 0, 182, 183, 0, 183, 184, 0, 184, 185, 0, 187, 188, 0, 189, 190, 0, 190, 191, 0, 192, 193, 0, 193, 194, 0, 195, 196, 0, 197, 198, 0, 198, 199, 0, 200, 201, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 207, 208, 0, 208, 209, 0, 209, 210, 0, 210, 211, 0, 212, 213, 0, 213, 214, 0, 216, 217, 0, 219, 220, 0, 220, 221, 0, 222, 223, 0, 223, 224, 0, 224, 225, 0, 225, 226, 0, 226, 227, 0, 228, 229, 0, 229, 230, 0, 232, 233, 0, 234, 235, 0, 242, 243, 0, 244, 245, 0, 245, 246, 0, 247, 248, 0, 249, 250, 0, 251, 252, 0, 253, 254, 0, 257, 258, 0, 258, 259, 0, 259, 260, 0, 263, 264, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 272, 273, 0, 274, 275, 0, 277, 278, 0, 280, 281, 0, 284, 285, 0, 286, 287, 0, 287, 288, 0, 291, 292, 0, 292, 293, 0, 293, 294, 0, 294, 295, 0, 295, 296, 0, 302, 303, 0, 304, 305, 0, 308, 309, 0, 309, 310, 0, 310, 311, 0, 311, 312, 0, 316, 317, 0, 317, 318, 0, 322, 323, 0, 323, 324, 0, 325, 326, 0, 326, 327, 0, 327, 328, 0, 328, 329, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 334, 335, 0, 335, 336, 0, 337, 338, 0, 340, 341, 0, 341, 342, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 345, 346, 0, 346, 347, 0, 347, 348, 0, 348, 349, 0, 350, 351, 0, 351, 352, 0, 354, 355, 0, 355, 356, 0, 358, 359, 0, 359, 360, 0, 363, 364, 0, 364, 365, 0, 366, 367, 0, 367, 368, 0, 369, 370, 0, 372, 373, 0, 373, 374, 0, 375, 376, 0, 377, 378, 0, 378, 379, 0, 379, 380, 0, 387, 388, 0, 391, 392, 0, 392, 393, 0, 393, 394, 0, 398, 399, 0, 406, 407, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 410, 411, 0, 411, 412, 0, 412, 413, 0, 413, 414, 0, 414, 415, 0, 423, 424, 0, 424, 425, 0, 425, 426, 0, 426, 427, 0, 428, 429, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 436, 437, 0, 438, 439, 0, 439, 440, 0, 444, 445, 0, 447, 448, 0, 449, 450, 0, 451, 452, 0, 455, 456, 0, 456, 457, 0, 457, 458, 0, 458, 459, 0, 461, 462, 0, 463, 464, 0, 464, 465, 0, 467, 468, 0, 469, 470, 0, 475, 476, 0, 476, 477, 0, 477, 478, 0, 479, 480, 0, 486, 487, 0, 487, 488 }

  149. "()((((())))()(())(((()()(((((())()(()(((()())(()))())(((()())())))()))()(((((()((((((())()())(()))(((())))))(((((()())(())())((())(()())()()))(()()((()())()(()(()()))())))((())(()()(()))()))((()))()()))()(())(()(()(())()()()()(())(())()))())))(()()))()))))))()()((())((((())))()())((())))(()()(())()())((((()))))((()())())()(())((((()()))(())))()((()(())()()())()(()))((()))()(())()()(((()))())()(())(((((((()(()))(((()))((())))(((((((()(())))))())))(((())()(()()())(()())(())()(())((((()))))))))))))"

    Returns: {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 19, 20, 0, 21, 22, 0, 23, 24, 0, 24, 25, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 28, 29, 0, 31, 32, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 41, 42, 0, 44, 45, 0, 45, 46, 0, 49, 50, 0, 52, 53, 0, 53, 54, 0, 54, 55, 0, 55, 56, 0, 57, 58, 0, 60, 61, 0, 65, 66, 0, 69, 70, 0, 71, 72, 0, 72, 73, 0, 73, 74, 0, 74, 75, 0, 75, 76, 0, 76, 77, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 81, 82, 0, 82, 83, 0, 83, 84, 0, 84, 85, 0, 87, 88, 0, 89, 90, 0, 92, 93, 0, 93, 94, 0, 97, 98, 0, 98, 99, 0, 99, 100, 0, 100, 101, 0, 107, 108, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 111, 112, 0, 112, 113, 0, 114, 115, 0, 117, 118, 0, 118, 119, 0, 121, 122, 0, 124, 125, 0, 125, 126, 0, 126, 127, 0, 129, 130, 0, 130, 131, 0, 132, 133, 0, 135, 136, 0, 137, 138, 0, 141, 142, 0, 142, 143, 0, 144, 145, 0, 146, 147, 0, 147, 148, 0, 148, 149, 0, 150, 151, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 158, 159, 0, 159, 160, 0, 161, 162, 0, 165, 166, 0, 170, 171, 0, 171, 172, 0, 172, 173, 0, 175, 176, 0, 176, 177, 0, 178, 179, 0, 180, 181, 0, 181, 182, 0, 185, 186, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 195, 196, 0, 197, 198, 0, 201, 202, 0, 203, 204, 0, 204, 205, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 211, 212, 0, 213, 214, 0, 214, 215, 0, 217, 218, 0, 219, 220, 0, 221, 222, 0, 223, 224, 0, 225, 226, 0, 226, 227, 0, 229, 230, 0, 230, 231, 0, 233, 234, 0, 237, 238, 0, 242, 243, 0, 243, 244, 0, 245, 246, 0, 249, 250, 0, 257, 258, 0, 259, 260, 0, 261, 262, 0, 262, 263, 0, 263, 264, 0, 266, 267, 0, 267, 268, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 275, 276, 0, 277, 278, 0, 280, 281, 0, 281, 282, 0, 282, 283, 0, 287, 288, 0, 288, 289, 0, 290, 291, 0, 292, 293, 0, 293, 294, 0, 296, 297, 0, 298, 299, 0, 301, 302, 0, 302, 303, 0, 303, 304, 0, 304, 305, 0, 305, 306, 0, 311, 312, 0, 312, 313, 0, 313, 314, 0, 315, 316, 0, 318, 319, 0, 321, 322, 0, 323, 324, 0, 324, 325, 0, 327, 328, 0, 328, 329, 0, 329, 330, 0, 330, 331, 0, 331, 332, 0, 333, 334, 0, 337, 338, 0, 338, 339, 0, 343, 344, 0, 345, 346, 0, 346, 347, 0, 347, 348, 0, 349, 350, 0, 350, 351, 0, 353, 354, 0, 355, 356, 0, 357, 358, 0, 360, 361, 0, 362, 363, 0, 363, 364, 0, 367, 368, 0, 368, 369, 0, 369, 370, 0, 373, 374, 0, 375, 376, 0, 376, 377, 0, 379, 380, 0, 381, 382, 0, 383, 384, 0, 384, 385, 0, 385, 386, 0, 386, 387, 0, 390, 391, 0, 393, 394, 0, 395, 396, 0, 396, 397, 0, 399, 400, 0, 400, 401, 0, 401, 402, 0, 402, 403, 0, 403, 404, 0, 404, 405, 0, 405, 406, 0, 406, 407, 0, 408, 409, 0, 409, 410, 0, 413, 414, 0, 414, 415, 0, 415, 416, 0, 416, 417, 0, 420, 421, 0, 421, 422, 0, 422, 423, 0, 427, 428, 0, 428, 429, 0, 429, 430, 0, 430, 431, 0, 431, 432, 0, 432, 433, 0, 433, 434, 0, 434, 435, 0, 436, 437, 0, 437, 438, 0, 444, 445, 0, 449, 450, 0, 450, 451, 0, 451, 452, 0, 452, 453, 0, 455, 456, 0, 457, 458, 0, 458, 459, 0, 460, 461, 0, 462, 463, 0, 465, 466, 0, 466, 467, 0, 468, 469, 0, 471, 472, 0, 472, 473, 0, 475, 476, 0, 477, 478, 0, 478, 479, 0, 481, 482, 0, 482, 483, 0, 483, 484, 0, 484, 485, 0, 485, 486 }

  150. "(()(()()))(()(()()))(()(()((()()))(()((((()))))((()()(()((())()()()()(()))())(((()(())(()(()())()((())(()()((()())()((())(())(()(()()))))((())((()))))))()()(())()()(((((()))()))(()()))))()))())())())(())(((()(()(((())(()(()(()()((()()((())))))()(()((()()(((()())()(())())(())()((((()))()()()()(()((()))(())(())))))(())(()(()()(()()))(())()(())((()()((()(((((((()(((((((()((())())(()))()(((()(())()))()()())))((()()((()))))())(())())())(()))((()(((()()))())))((((()))))(())(())))))))))))))))))))))))))"

    Returns: {0, 2, 3, 0, 3, 4, 0, 5, 6, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 13, 14, 0, 15, 16, 0, 19, 20, 0, 20, 21, 0, 22, 23, 0, 23, 24, 0, 25, 26, 0, 26, 27, 0, 27, 28, 0, 29, 30, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 37, 38, 0, 38, 39, 0, 39, 40, 0, 40, 41, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 50, 51, 0, 52, 53, 0, 53, 54, 0, 55, 56, 0, 56, 57, 0, 57, 58, 0, 60, 61, 0, 62, 63, 0, 64, 65, 0, 66, 67, 0, 68, 69, 0, 69, 70, 0, 73, 74, 0, 76, 77, 0, 77, 78, 0, 78, 79, 0, 79, 80, 0, 81, 82, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 89, 90, 0, 91, 92, 0, 94, 95, 0, 96, 97, 0, 97, 98, 0, 98, 99, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 106, 107, 0, 107, 108, 0, 108, 109, 0, 110, 111, 0, 113, 114, 0, 115, 116, 0, 116, 117, 0, 117, 118, 0, 120, 121, 0, 121, 122, 0, 124, 125, 0, 125, 126, 0, 127, 128, 0, 128, 129, 0, 130, 131, 0, 136, 137, 0, 137, 138, 0, 138, 139, 0, 141, 142, 0, 142, 143, 0, 143, 144, 0, 151, 152, 0, 153, 154, 0, 155, 156, 0, 156, 157, 0, 159, 160, 0, 161, 162, 0, 163, 164, 0, 164, 165, 0, 165, 166, 0, 166, 167, 0, 167, 168, 0, 168, 169, 0, 172, 173, 0, 176, 177, 0, 177, 178, 0, 179, 180, 0, 185, 186, 0, 189, 190, 0, 192, 193, 0, 195, 196, 0, 198, 199, 0, 199, 200, 0, 202, 203, 0, 203, 204, 0, 204, 205, 0, 205, 206, 0, 207, 208, 0, 208, 209, 0, 210, 211, 0, 211, 212, 0, 212, 213, 0, 213, 214, 0, 216, 217, 0, 217, 218, 0, 219, 220, 0, 220, 221, 0, 222, 223, 0, 223, 224, 0, 225, 226, 0, 227, 228, 0, 228, 229, 0, 229, 230, 0, 231, 232, 0, 233, 234, 0, 234, 235, 0, 235, 236, 0, 242, 243, 0, 244, 245, 0, 245, 246, 0, 247, 248, 0, 248, 249, 0, 249, 250, 0, 251, 252, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 261, 262, 0, 263, 264, 0, 264, 265, 0, 267, 268, 0, 270, 271, 0, 271, 272, 0, 274, 275, 0, 276, 277, 0, 277, 278, 0, 278, 279, 0, 279, 280, 0, 280, 281, 0, 284, 285, 0, 286, 287, 0, 288, 289, 0, 290, 291, 0, 292, 293, 0, 293, 294, 0, 295, 296, 0, 296, 297, 0, 297, 298, 0, 301, 302, 0, 302, 303, 0, 305, 306, 0, 306, 307, 0, 313, 314, 0, 314, 315, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 321, 322, 0, 323, 324, 0, 325, 326, 0, 326, 327, 0, 328, 329, 0, 332, 333, 0, 333, 334, 0, 336, 337, 0, 338, 339, 0, 339, 340, 0, 342, 343, 0, 343, 344, 0, 344, 345, 0, 346, 347, 0, 348, 349, 0, 349, 350, 0, 350, 351, 0, 352, 353, 0, 353, 354, 0, 354, 355, 0, 355, 356, 0, 356, 357, 0, 357, 358, 0, 358, 359, 0, 359, 360, 0, 361, 362, 0, 362, 363, 0, 363, 364, 0, 364, 365, 0, 365, 366, 0, 366, 367, 0, 367, 368, 0, 368, 369, 0, 370, 371, 0, 371, 372, 0, 372, 373, 0, 375, 376, 0, 378, 379, 0, 379, 380, 0, 383, 384, 0, 385, 386, 0, 386, 387, 0, 387, 388, 0, 388, 389, 0, 390, 391, 0, 391, 392, 0, 394, 395, 0, 398, 399, 0, 400, 401, 0, 402, 403, 0, 407, 408, 0, 408, 409, 0, 409, 410, 0, 411, 412, 0, 413, 414, 0, 414, 415, 0, 415, 416, 0, 421, 422, 0, 424, 425, 0, 425, 426, 0, 428, 429, 0, 431, 432, 0, 434, 435, 0, 435, 436, 0, 439, 440, 0, 440, 441, 0, 441, 442, 0, 443, 444, 0, 444, 445, 0, 445, 446, 0, 446, 447, 0, 448, 449, 0, 452, 453, 0, 457, 458, 0, 458, 459, 0, 459, 460, 0, 460, 461, 0, 461, 462, 0, 467, 468, 0, 468, 469, 0, 471, 472, 0, 472, 473 }

  151. "(())"

    Returns: { }

    Here we can see that S is already lexicographically smallest.

  152. "(()())"

    Returns: {1, 2, 3 }

    Here after performing operation (1, 2, 3), we obtain S = "((()))" which is the lexicographically smallest S we can obtain.

  153. "()()()()"

    Returns: {2, 3, 6, 2, 3, 5, 0, 1, 4 }

    Here after preforming the first operation (2, 3, 6), we obtain S = "()()(())". Now after second operation (2, 3, 5), we obtain S = "()((()))". After third operation (0, 1, 4), we obtain S = "(((())))".

  154. "(()()(()()))"

    Returns: {0, 2, 3, 0, 4, 5, 0, 5, 6, 0, 7, 8 }

  155. "(((((()())(()()))((()())(()())))(((()())(()()))((()())(()()))))((((()())(()()))((()())(()())))(((()())(()()))((()())(()())))))(((((()())(()()))((()())(()())))(((()())(()()))((()())(()()))))((((()())(()()))((()())(()())))(((()())(()()))((()())(()())))))(((((()())(()()))((()())(()())))(((()())(()()))((()())(()()))))((((()())(()()))((()())(()())))(((()())(()()))((()())(()())))))"

    Returns: {0, 6, 7, 0, 9, 10, 0, 10, 11, 0, 12, 13, 0, 16, 17, 0, 17, 18, 0, 18, 19, 0, 20, 21, 0, 23, 24, 0, 24, 25, 0, 26, 27, 0, 31, 32, 0, 32, 33, 0, 33, 34, 0, 34, 35, 0, 36, 37, 0, 39, 40, 0, 40, 41, 0, 42, 43, 0, 46, 47, 0, 47, 48, 0, 48, 49, 0, 50, 51, 0, 53, 54, 0, 54, 55, 0, 56, 57, 0, 62, 63, 0, 63, 64, 0, 64, 65, 0, 65, 66, 0, 66, 67, 0, 68, 69, 0, 71, 72, 0, 72, 73, 0, 74, 75, 0, 78, 79, 0, 79, 80, 0, 80, 81, 0, 82, 83, 0, 85, 86, 0, 86, 87, 0, 88, 89, 0, 93, 94, 0, 94, 95, 0, 95, 96, 0, 96, 97, 0, 98, 99, 0, 101, 102, 0, 102, 103, 0, 104, 105, 0, 108, 109, 0, 109, 110, 0, 110, 111, 0, 112, 113, 0, 115, 116, 0, 116, 117, 0, 118, 119, 0, 125, 126, 0, 126, 127, 0, 127, 128, 0, 128, 129, 0, 129, 130, 0, 130, 131, 0, 132, 133, 0, 135, 136, 0, 136, 137, 0, 138, 139, 0, 142, 143, 0, 143, 144, 0, 144, 145, 0, 146, 147, 0, 149, 150, 0, 150, 151, 0, 152, 153, 0, 157, 158, 0, 158, 159, 0, 159, 160, 0, 160, 161, 0, 162, 163, 0, 165, 166, 0, 166, 167, 0, 168, 169, 0, 172, 173, 0, 173, 174, 0, 174, 175, 0, 176, 177, 0, 179, 180, 0, 180, 181, 0, 182, 183, 0, 188, 189, 0, 189, 190, 0, 190, 191, 0, 191, 192, 0, 192, 193, 0, 194, 195, 0, 197, 198, 0, 198, 199, 0, 200, 201, 0, 204, 205, 0, 205, 206, 0, 206, 207, 0, 208, 209, 0, 211, 212, 0, 212, 213, 0, 214, 215, 0, 219, 220, 0, 220, 221, 0, 221, 222, 0, 222, 223, 0, 224, 225, 0, 227, 228, 0, 228, 229, 0, 230, 231, 0, 234, 235, 0, 235, 236, 0, 236, 237, 0, 238, 239, 0, 241, 242, 0, 242, 243, 0, 244, 245, 0, 251, 252, 0, 252, 253, 0, 253, 254, 0, 254, 255, 0, 255, 256, 0, 256, 257, 0, 258, 259, 0, 261, 262, 0, 262, 263, 0, 264, 265, 0, 268, 269, 0, 269, 270, 0, 270, 271, 0, 272, 273, 0, 275, 276, 0, 276, 277, 0, 278, 279, 0, 283, 284, 0, 284, 285, 0, 285, 286, 0, 286, 287, 0, 288, 289, 0, 291, 292, 0, 292, 293, 0, 294, 295, 0, 298, 299, 0, 299, 300, 0, 300, 301, 0, 302, 303, 0, 305, 306, 0, 306, 307, 0, 308, 309, 0, 314, 315, 0, 315, 316, 0, 316, 317, 0, 317, 318, 0, 318, 319, 0, 320, 321, 0, 323, 324, 0, 324, 325, 0, 326, 327, 0, 330, 331, 0, 331, 332, 0, 332, 333, 0, 334, 335, 0, 337, 338, 0, 338, 339, 0, 340, 341, 0, 345, 346, 0, 346, 347, 0, 347, 348, 0, 348, 349, 0, 350, 351, 0, 353, 354, 0, 354, 355, 0, 356, 357, 0, 360, 361, 0, 361, 362, 0, 362, 363, 0, 364, 365, 0, 367, 368, 0, 368, 369, 0, 370, 371 }

  156. "(())(((()))())"

    Returns: {0, 3, 4, 0, 4, 5, 0, 5, 6, 0, 6, 7, 0, 10, 11 }

  157. "()()()()()()()()()()"

    Returns: {0, 1, 2, 0, 3, 4, 0, 5, 6, 0, 7, 8, 0, 9, 10, 0, 11, 12, 0, 13, 14, 0, 15, 16, 0, 17, 18 }

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