Statistics

Problem Statement for "TwoStamps"

Problem Statement

Alesha has two stamps.

  • One stamp (called the "circle" stamp) is two characters wide and produces an approximation of a circle: "()".
  • The other stamp (called the "eraser" stamp) is one character wide and produces a space. (When used on an area that already contains some characters, both stamps overwrite those old characters completely.)

Alesha has a page. The page is divided into a rectangular grid, with each cell of the grid exactly the dimensions of one character. Initially, the grid was all-white. Alesha then produced a picture by repeatedly using her two stamps. Each stamp was always placed completely inside the page and aligned with the grid. Alesha could have used each stamp arbitrarily many times, and alternate between the two stamps arbitrarily many times.

You are given the contents of a page in the String[] page. Determine whether Alesha could have produced this page. If no, return -1. If yes, return the smallest number of times she had to have used the two-character-wide stamp.

Definition

Class:
TwoStamps
Method:
minCircles
Parameters:
String[]
Returns:
int
Method signature:
int minCircles(String[] page)
(be sure your method is public)

Constraints

  • page will have between 1 and 50 elements, inclusive.
  • Each element of page will have between 1 and 50 characters, inclusive.
  • All elements of page will have the same number of characters.
  • Each character in page will be '(', ')', or ' '.

Examples

  1. {" ", " () ", " "}

    Returns: 1

    This page could have been produced by using the "circle" stamp once, so that is clearly the optimal number of times.

  2. {" ", "(())", " "}

    Returns: 3

    This page could have been produced by using the "circle" stamp three times. One possible way is shown below: +----+ | | | | | | +----+ +----+ | | | ()| | | +----+ +----+ | | |()()| | | +----+ +----+ | | |(())| | | +----+ Note that the third stamp partially overwrote each of the previous two.

  3. {"( ", "( ", "( "}

    Returns: 3

    The optimal way to produce this page is to use the "circle" stamp three times (once in each row, always aligned with the left edge) and then the "eraser" stamp three times (to erase the right half of each of the stamps).

  4. {"( ", ") ", ") "}

    Returns: -1

    It's impossible to produce this page. (Remember that each stamp must always be placed completely inside the page.)

  5. {"( ) ", " ", " "}

    Returns: 2

    These two parentheses cannot be produced by using the "circle" stamp just once, they are too far from each other. It is possible to produce this page by using the "circle" stamp twice and then the "eraser" stamp (at least) once.

  6. {"( ( ( ( ) ) ) )"}

    Returns: 8

    One way to produce this page is to do eight rounds of first using the "circle" stamp and then the "eraser" stamp to remove half of it. There is no way to produce this page in fewer than 8 uses of the "circle" stamp.

  7. {" ", " ", " "}

    Returns: 0

  8. {" "}

    Returns: 0

  9. {"("}

    Returns: -1

  10. {")"}

    Returns: -1

  11. {" "," "," "}

    Returns: 0

  12. {"(("}

    Returns: -1

  13. {"()"}

    Returns: 1

  14. {")("}

    Returns: -1

  15. {"))"}

    Returns: -1

  16. {") ", ") ", "))", " )", ") ", "()"}

    Returns: -1

  17. {")", ")"}

    Returns: -1

  18. {")(( ))(( ", ") ) ) ((", " (()() ) ", ")( ( )() (", ") ) )( )) ", " ()) )) ("}

    Returns: -1

  19. {"() () ", "( (())", "( )))()", " ) "}

    Returns: 12

  20. {"(( ", " ) ", ")()", ")( "}

    Returns: -1

  21. {")(", ")(", "((", " ", ")(", ") ", ") "}

    Returns: -1

  22. {"( )", " ()"}

    Returns: 3

  23. {"( )( ", " ( )"}

    Returns: 5

  24. {"()) ) ", " () ))"}

    Returns: 6

  25. {"(()( ", "())) ", " ( )", " )() )"}

    Returns: 11

  26. {"()) )(( )", " )() () "}

    Returns: 9

  27. {"() (( ))", " )) ) ) ", "()(())) ", "( )) )", "( ) )"}

    Returns: 21

  28. {" )(", " ( ", "( )", "())", " ) ", ") (", " )(", "())"}

    Returns: -1

  29. {" ))", ") (", ") ", ")) ", "())", "(( ", ")) ", " ()", ")()", "() "}

    Returns: -1

  30. {"( ( ", "( ))", "(( ", "( ()", " ())", " ( )", "(( )", " () ", " ()", "((( "}

    Returns: 21

  31. {"( ) ) ", " ) )(() ", " )() (() ", "(()( )) )", "( ((( ( ", " )( ()(( ", "()( () "}

    Returns: 30

  32. {"( ", " ()) ", " )())", "(() )", " ))()", " )(( ", "())()", " ( )"}

    Returns: 20

  33. {"(( ())(( ", "( ) )(() ", "(( ))) ) ", "()))( ))( ", "(( (( ()", "())) ) ()", " ) )) ", " (( ( (( ", " ( ( ) ) "}

    Returns: 46

  34. {"( ))) ", "( )()", " ( ( )", "( ) )", " ())()", " )) ) ", "())) )"}

    Returns: 23

  35. {" ", ")", " ", ")"}

    Returns: -1

  36. {"( () )() )()) ()) ) ( ()))(( ()))()(() ", "( ))() ( (())()((( ( ( ))))(( ))(( ( ) ))", " )) )) (()) ( )))) ( ) ( ((((( ) ) ", "( ) ( ))(( )(()) )) ( ) ))) ( )() ))))(()", " ()(( )()( )) ) ())(( ( ))((() ) ( ( ) ) (()", " )( ) )))) (()(((( ) () () () ())( ", " (( ( ()()(())()( ) ((( ( )) )()( ()() ", "(()() () ((( (() ) ) ) ()(( ))())(( )))) ()()", "( ) )()) ( ) ) ())))())(( )((() ()) ) ()()", "((( ))( ))) )(())( ( )()) ( )(()())() )() ( ", " () ())(( (((())) )()))(()) ( (( ) (( (()", " ( )(())()() (())()() ()()( (() ( )))) )", " ) ( ((() ))) )())( ) ( ) ))(((( ) )() )()", "( (((()(( () ) ( (()) )())( ) )) )()( )", "((())( ( )( ( ()))( ) ( ) () )( ((() ", "( ( )() ) ) ) (( ))( (( (()( ( (())))( () ", "() ))(()))() () ( ()(( (() () ()((( ) ", " )() )(()) ) ( )(() ( (((((((()(( ) ((() ( ", " ((()() ((( ) ()())(()((( ))) )() ) ( )", " ( )()))( () )(( )()) ( ( )) )()) )()( ))(() ", "((()())( ( ( )) ())))(( )() ) ) )()()) )( ( ", " () ))((( ) ( ())()((( ( ( ()))( ) ( ( )", " ) ) ) ))()( )) ) (() ()( ))((( ) ( (()(())", "(() ( )((() ()(( ))(((()) ) )))(((() )( ()", "(( (((( )(( (( ) ))) () )( ( )((()())(( )()())", "() )()( ) ( ( ))(( )( ()() ()(()) ()()(((()", "()( (( ))))))) (() ))))( ()) ()) ()((()", " ) ()()(() (() ( ) )) ) ( (((() )) (( )", " ) )))) () ( ())( )) ) ) ()))) ))", " )) )())( ) ) (( ((() ))(( )()( ()(()((())", " ( () (((((((( () ))( (( ( )() )))()() )", " )) ( ()(( (( ( ) ( ( (( ))( ( ( ))))", " )()))) ( ) )))(( (( ) ) ))) ( ( ()()) ) ) ", "(((((()) )() ) )(() ((()( )((( ((()) (( ( "}

    Returns: 850

  37. {" ))((() ( )(() )(())( ( ))", "() ()) ) ()))) )) ))(( ( )(()( ", " ()()( ) (( (()( ) )())( )() ))", " ))( )(())() ) ) ) ( ( () )", " ( ( ) (( ) ) )))))((()) ", " )))))()( () ))() ))()()(()( )", " ) )))))() )( () ())) ( ) ", "(() ()) )) ( )()))()) ))()( ", " ()(())) () ())))())))() ))( ()", " ( ()())(((() () ) (() )) ", " ))(() (( )) ) ())() )) (( ", "((())(( ()(( )))()) ))(((()(( ))", " ))) ))))( ) ()(( )( ( (( ( ", "())) ))( )) )( )() ) )( ()(( ", "( )() )())) ( ))(( ()()()) ( )", " ) )) ( ( () ( () (( )(( )", "() ) )((((((() (((()))) ))(())))", " () ( )(() (( (( (() () ))", " ())(())( (( ) ) ( ) )) )()( )", " ()()))) )( )((( ))) ( ( ()", "( )) (() )() ((()( ( )( ((( )", "() ( ) )( )))(( () ) (() ((( )", "(()()) )()) (()((((() )()) ) ( ", " )) )( ))()() ((((( ) ) ( (()", "( (()) )) ))))) ( )( ( )( ))", " (( ()( ((( ()( )())()) ))", "((( ( )) )))()() ((())))))) ", " ()(( ) )))))) ()()( )(( ) )) )", " ))) ( )))( )( )( )()))( )", " (( ) ))()()( ( ()))()())() "}

    Returns: 532

  38. {" )(()(()))((()(()(( )( ))()) ))(())( (( ()) ", "((( ))( ) ()()( ()()) ) ) ()((( ))((() ))", "())()(( ))( (()( ( ) )(( )) ) ) ())( ())( )() ", " )) ))( ) ( ) (()) )))( ()()) ()( )(( (((( )( ", " (( )()()((( (( (( )( )( ( ( ()((( )) (())(())", "() (( ( ) ( )()) ( ()) (() (())( )( ) ", " () ) (((()() ( ( (())() ( ( )()( ))())", "((() () )() ( ()() )()()( ( ) )( )((( ( ( ", "((( )))()) ( )( ) (()(( ) () ))()) ()( ))", "( () () ) )())(())(( (() ()))))) ))()())() ", "(()())( ( )((()((( ( ((((() ))) ( ))) )()) ) ", " ))) )) ) ) ())) () )() ) ( ()) ((() ", " ) (( ((( ( ) ((( ()(()() )(( ()( ( )))((()", " () ) (( (( ) (() ( ))(()()) (( )(( )() ", "()(( ))()( (() )))) ())(()) ( )) )(( ) ) ))) )", "(( )()))) (((())( ()) ))((() ) ( ()( ()))(( ", " ((( )(()(( ) )) )) ))) ) ( (( ) (( )( (( )", " ))))()())) ( )))(()() ( )(((( ) ) ((() ) )", "(( (( )(()() ) ( ( ( )(())( ( )())((()) (( )(()", "( ) ())( ())((())))()( ) ) ))(( (((()(() ) ()", " ( ) ( )))) )( )( ( ())( )) )) )((((()( ))", " ( ) ))() )()))) ))() ( )))() (((())(() ", "( () (() ()() ))( ( (( )(( )( ) ()", " (()()()( ) ) ) ()))()( ) () ) )( (()))(( ) ", " ( )()((())((((( (() ())( ( ( (()())))) ( )", "(( ) ( ))) ))() () ( ) ) ) )((( )() (( )) ", "(()() )((()))(( )(( )((( ))) ( )( ()( ))(( ", " (( )())() ( ( ) ( ())))((( ( (( ) () ", "( ))) () ))(() ( (() )() ) ) )) ) ) ))(( ", " ) ) ( ))() )))() () ((( (()(( ( ( (() (( "}

    Returns: 785

  39. {")) ( )(( (())()( ) ))()( (() (()", "((() )(( )) (( ) ()) (( (((()( )", " )( ((( ) ))) )((()()()(() ) )()) )", ")( ( ))(((( (()( ((( ) ) )( ))) () ((", "( ) ) ) ))()))( (((()( )( ( )()", "() ) ( ))( ( ) (()()( ()( ))( (() ", ")))))) ( ( ( ))((())()( () )) ))", " )( (((( )))()(() )())( (()()( (( ", "(( ( ) ) (( ( )() ))) ))) ((()()))(", " ) )) ))()))( ))()( () ))()( )", "( ()() (( ))( )( ( )() ())()( )()", " ((( )) ())))() ( ))( )(((()()))))(", "(( ((((() (( )))((()) ( (( )()))(( (", ")())) ))(( () )))) ( ) ( ))) ()) )(", ") (() (( ( ) ))( ()()) ((( ( ((((", " ()() ))((() ( )((() ) ((() (((", ")(()() ( ((( )) ( ) )) ( ( ( () ", ")) ) ) ( ) ( ) )())(( )))) )(()((( ", "()) ) ((() ( ()((() ( )()( ))(( ((", "())))( ) )((() (()((() )) )())( )", ")((())(() ()()))) )) ()()((() ()(", "() ) ))) () (() ()())(( )) ( () ( )", "() (( ((()) ) ( ) ( )) )) ((((()", ")) (()(()( ) ) ))( ( )))((( )(()) ))", " ((( () ))(() ())( ( ((( (( (( )(", ") ( (() )))( )()) ( ()(() )( ", "( )()))) (( ())) (() )() ( (()) )", "( )() ((( ( ( (( ()())) )( () ())) )(", ")( ()()( ) () ) (((() (( )) ()( )", "( ( (( )())()( ))) ( ( )()(( ( ", ")))( ))) ) )()()())( ) (( )) ) "}

    Returns: -1

  40. {"()( ) (( ( ()())) ())( )(( (() )", " ( ( )( (() )(( () ))()(( () (( ) ", "( )((())()( ) )) )((((( )) ( ) ", " ) )))(((( ( ( ) ( ( )( ( ))()) ", "(( )( ( (()) ()) () ( ( ( )", " (())) (( )()()() (()()( ( ))", " )( ())( (( )))( ()()() () ) )", "()))((( ( ) (() )() ) ) ( ) )", " () (()( ( ( ( ))(( (((())( () ", "()(( )()( ) (())( ) (()((((( )( )", "() ))) ( )))) ))())( ((() )( ) ", " ))((( )(( ( (()) ()( () ( ((()", " ) ((( ( ) ( ( ( )() ))() ", " (( ( ))( ) )( ) )) )))() ( ", " ) () (( ))(( ())()) )) (( () ", " (()()()( )()( )( )))( )) ) ( ", " )()) ( ()) (( (()(( ))() ) ", "(( () ) ((()( ( ) ) )) () ", "()( ()(() ((())))() ( ()) ) (( )", " ) ( )( (( ) ()) (())) ) ( ( )", " )(() (( ( )()))()() (( ( ()()", " ( )()() ( ()) (((( ))(() ))( ", "() )( (( ) ))))( ))( ()() ", " )((((( ) ) ( ( ) )))(( )(()() ", " ))(( ) ) )((( ( )) ) )( ( ", "(( () ()(((( )()) () )()(()))( )", " () ))) ) )(()) ( ( ) ()( (( )", " ) ) () ()()(( ) ( ( )())", " ))()) ))) ()() ((() ))) (( (( ()", "( () ( )( ()() )) ))(() ( (() (() ", " ))((( () (() ) ) ))())(() )(()", " )((()) (() ) ( () ))()))) ", " ))( ( ( ()( ()( )) ( () ( ( ", " ()( )) (( ( ()) ( )(((() ) ", "( )( ) ))()))( ))) ))))) () )", " ) ())( ( (((( ) ( ( )() ( ", " ( )())(((( ((( (()())))(()) ))( ", " ) ) ((()( ) ()(( ( ) ( ))( ", "( ))()(((() (( ) )) ) ) ((( )( ", "( ) ( ) (() ()() ))(( () ())( ", " )( ( ))() )) ( ())( ( ) )", " ))) ) ()(( ( )(( )) ) ()) ) ", " ((() ((((()) ( ) ))( () ()", "(( ( ((((( )(( ( )(( ( ))( ( (( ", " ) ( ) )() ))((())) )(() ((( ", "()) ( ) )(( )))))()( )()( () "}

    Returns: 814

  41. {" )( ( ) (( )((()( ((()", " (( ) ) ()) ( )))())((((( )( ", " )))) )) ( )) (()(() ))", " ()()( ((()) ( () ( ) () ", "( () (()( (( ( ( () ( )( ( ) ", "( (( )((())()(( ( ) )))) ( )", "()( (((( ( ( ( )((( ( ) )( )", " ((())()))( ( ( (()( ( )( )", " )())( ( )(( ( (( )))() )) ", " (( ) ) ( ())( )( (() ( )) )) ", " )() )(())) )( ) )))) ( )( ", "(((()((() )() ( ()) ((((( ))", " () )))) ())) ( ())) ) ( )( ", " (( ))(())()() ((( )()((( ))", " ()( ) ()()))()) )( () )", " ( )() ())( )(())(( ()(((()", " (((( (( ) ()) ( (( ()())()", "((() (( ( (()))() ()) )( ( )))", "((((( )) () ( () ()( ( ) ( ", " )( )())(( ) ) ( ))(() )((()", "()(() (( ) () ) () ) ())) )", "( (())(( (()( )) ( ()()( )( ", "() )) ) ( (( )( ))) (( ( ", " ()(( )(()()( ( ) ())))( ))))", "( (() )) ()() ()) )( (()) ", "( () (())) )())((() () () )) ", "(( ))(())( (( ((()))) ( (() )", " )) ))())( () ) )))( ))", " ((( ((()) )((( )( (( ) ", " )(((( ()(()) (()(((() ( ()(()", "()( ( )) ((( ) (()) ))) (())", "(()())( ( () )))() ) )( ) (()) ", " ()) )(( )(( )) )())( (( ) )", " (( ( )))(()( ()(() ( ) ))", "( )()((( () (( )(((( ))) )", " ( ))())(( ()())((() )()) (( ", " ))) (()())())())(( ( ( ) )( ", " ( ))) ) ( (( ( ()())(()()", " ) ) )())()) )(( )(((( ) )", "( )()) ) () (( )) () ( ", "(( ))) ( )( (( )()( ) )()", " ()) ) ))( ( ( )( ) () ())", "( ( (()(()(( ((( ((( ( )) ", " )(())((()(( ( ) ( )()( ) ( "}

    Returns: 729

  42. {" )) ))) (() )( ) )( )( ()))(() ", "( )( ) )() (() )() )()()() ))) )) )", "( )) )()(( (( ))((( )) ))(( ((() ", "()( ) ( ( ))) ( ) )(() ()) ) ( (( ()", " ) ( () ())( ) ) )) ( ))( (())", " )() () () ))))(()))(() (())( )()() ", "( )(() ( (( ( (())((() (( (( ( ()", " ())) (()( ) ()())( ) ( ( ))) )))))", " ) ((( (() (((( (( ) ()() ()()) ", "()) )( (((()((() ) ( )()() ( ( )) )", "() )(() ) ))))(()) ( ())( () )(( )) )", "( ))((() ()(( ()() ( ))))() )) ()) ", "( ( ( ) )( ( () () () ()))) ) ) (( )", "( ) ((( ((()(( )(( ))(()( )(( )))) )", "( ( () ( ) ) ) (((( ))( ) ()() ", "() )( ()())((((()( )))) )()( (()( )", " ) )( ( ))( ()() ))( (() ) ()))(()", " (( ) () )) ())() )) ))) ( () )", "( (()(() )) ) )) ()((( )( ( () ( ", "(() ( () ( )() )) (( ()) )(((() ()", "((()()) )()) ) ( ))())()( )) ()( )", " )) )(() ( )))))()( ( ) ((( ) ", "( ))(( )())) ( (() ) )( ( ))) ", "( ()()) ) )) )) )))(( (( ))())", "()) ( ( ()(( () (())( ( (()( ()()", " () () )) ) ( )(()( ) )(( )() ))( ", "(()((( ()))))( ((( ())(( )( ))()( )) ", "() ( ) ( (()) )() ))( () (((( )", "()( ( ( ()) ( ()))() ))( (( ( ()))) ", " )(()( (( ( ( ())()) )) ( ( ())))", " (( )) ( ))() )) ( ((()(()(()", "()()( ()(( ) ( (( (((()(()()) () "}

    Returns: 643

  43. {"(()) )()(()(() ( ()) ))( ()() )) )) ))))( ((", ")()(( ()( ( ( ()( ())()(((())())( ( )())))(", " ) )( ())()(())() )()()((((( (()( )))(( )( ( ) ", " ((( ) )()))))( )(() ()(((((()( ( ( ( ))()(((( ", ") ( ( )() ( ))) )( )(( ) ) () ()) )((() () (", " ())) ) )( ) ( )()(( )) (( ))(( ( ( ()) )( )", "(()) ))() ))))()) )(( ( ) ( ) (( ) ( ( )) ()()(", "))) ))( )) ) )))( ) ( (()) ) )()() ( () ) )( (", "((( ) ( ()) ))( )))))(())()) )(())(( () )(((", ")())(( ))))()) ) ()))) )() ) ( ((( ()))))))(((", "())()( ( ()) )() )( (( ))( (())( ())))()", "( ()(())(( ( ()) ) )( ( ) ()))() ) ((() (( )", " )(((()) ) )) ((( ()(( ()()) )((( ((())(( ", "))())(()((( )() ) (() () (((( )()() )) )(( ()((", "(( ))) ())) (( (( ()))( ))))( () ( ))) ()))(", "()()( ())( ( ( () )( ())( )((()))((((((())( (", " (()())( ( (()( ) ( ))((( )) () ((( (( )()( ", ") (((((( ( ) )) ()( () (( ()(() () ))( ) )", " ) )())))( ())( ( ) (( ) ) ) )))) (()((()) ()((", ")(( )) ) (( ((()) (( )(( ) )(( (((()((( ((()) ", ")) ( ) ( ( ) () )( () ()())(()() ) )))( )", ")() )( ()) ) ) ((())()))() ( ()))) ) ) )()() ( ", " ( ( )(( ) ( ) ) )( (() ()()) ))( )( )))(( )", " ()(())() ))))()) )) )()() ) ) )( ()() )", ")((((( )(( ( (()( ) ( (( ) (( ( )) (", ") ) ((( ))( (()((()(() ((())() ( )))() ( )()(( ", "()() ( )()))))( (( )((((() ) () ))(((( () )() ", "()( )))( )()(() ( ) )( ) ()) )) )() )( )(((())(", "(( )) ()(( () )(( (() (())((() ( ) ())()))(( )(", "() ))) ) ( ) ) ))(() (( (()) ))) ( ", "()( ()) ( ( ( )) ))() ( ) ( ( ((()))", "( ()))( ( ())( () ( ) ( ))( )) ((( () )))", " )( ( ()((( ) )) ((())) ))) ( () )(()( ", ") (()( ()(()(() ((() ) ()) ))(()())(() ))( ", " ) ) (( )(( ))())))(() )) (()))(( ) ( ((()(()(", " (( ( ))))) ()) ))(( ( ( () )) )((((())()", ")( ( )(( )(((()) ( (( ( ( )) (() ())( )( ", "((( ))()( (())) ))))((( )((( (( ) ) ( ()) ))", ")( ) )(()(()( ( ) ))( )) ))()() ())) (( ) ( ", ") )()) )( )())() (()( (() ( ) )( ( (() )(", ")( ( ( ( ()))( ))(( ()) (())( ) )()( )()()((( (", "(()()(( ( )()( (() () (( ()(()) ) )( )( () ", " ())())())) )( ( ((()())()(() (( ())() ()( )(", "())) )())()( )( )( ) ) ) )( ) ) ) () ( )", "((( )))() )()) )(( )() ()( )))))( () (()()( ", "((((()()( ())()( () ) )( (( )) ) )(((())( ( "}

    Returns: -1

  44. {" ( ) ( ) ))(((() (()) )() ())", "()))) ))()(((()(()() ( )(( (( ) )((", ")))()( ) ) ) (( ) ( ((())()) )", ")( )((( ) ) ))) ) ()()) )))) )(())", " )))() )(() ( ) ( (()())) () )))", " ) )(( )()( ()( ))())( ( ((()) ", " ))))() ) ( )))) ))((()(( )()(( ", ")( ( ()) ) (())( (( ())(() (()", ") ))(( )()((()( ( ))) ) (( ((()) ((", ")( )( ( ()())( )) ( )) ( ()))(()", " ( ((( (()(( (( (() ) ( ()((", "))) )())(()( (( (()) (( ) ()))( ", "())) ( (()(((() () ) ( )) ) ", "( (() (() () ()((( ( ()(( ( ( ", " ( ) ) ))())) (()()) (()(( ((( ))", "))) )())(()()) () (() )) ))))(( ) )", ")()) )) ())( ( )( ) )((( (((", " ())() ())( )( ((( (() ( ) ( )(( ", ") (()())() ( (( ( (() ()( (() )", "( )))(( (()( ))))()) (( ( () )", "(( ( )) ( ( ()))( )( () ) ))) )()( ", " ) (( (( )( ())((()(() ( )( ()( ))))", ")))) ))(( (())) () ) )))()( ) ()", "(() )()(() ()()( )( ((( ( )) ))", " ()( )( ( )((()() )(())))( ) ", "()) ()(( (( )( ))(( ))())()))()( ", " )()() () ) ()( () )) (( ((()(())()", " (( ) ((((( )() ( ()())(((( ( ))(", "()) )) ((() )( ) (()) ))( ", ") ( () ))()((( )) ) )( )) ( ))", "()( ())(() ( ( (( ( ( ) ) ())(()(", "(())(((( ))())( ) ) ()))( ()) ( ( ", " )) ()() )) ( ()) ))) ) () ) ", "()(( (()) )())(( ()(() ()((( ( ( )( ", ")(( ((() (((())) )) ))) )( ()))(", " ) ) )))((((( ) )((( ((( ))) ) (((", " ( ) )()) )(()) (( ( (()()()))", " )(( )) (() ))(( ((()( ())(() ) ) (", "()) )( ))((( ( ) )( (((()( )))", ")()() ) )) )(( ) )) (((( ))) (()))", ")) )(( ( ))()) ) )(()( ) () )( (", "((( ((( ) (() )(( ( () )( (() )() ", " ()) () ( )) (()))( )( )) () (", " )( ( ) ) ))())( (() ()) )())(( (", ")(()(( ( ) ())() ()( (( )()( ))"}

    Returns: -1

  45. {"())(()) ( ()(( ()())( (()() () ( ", " ( () ) )) ())(() ) ))())(() ", " ()( ( ()))()() )()(( )) ( (()) ", "(()() ()(( ( )) ( (()))))(())() ", "(( ) () ( (() ( )) () )() ", " ))( )(( ( ))( ( ( ))( () ) ) ) ", "(((()) ())))) ()( () )))) ))(()))", "( ( (( ))) )()) (( ) (( ((( ( )() )", "()() ( (( (())( ( ()( ())(( ((( )", "( )(( ))))) ((( ( ))()( ( ( ( ))", " ))( ) ( )))) ()()( ))(( ) ) () ()", " ( ( ( (( ( ()() )(()))))))( ) ", "())( )( )((((()( )))(((( ) ( ", "() ))() ) ) ) )( ( )) (( ) )) ))", " )() )())( ( ( ())( ()) ( ())( )", "( ) ))( ) (( ))( (( () (())(( )", "( ))))( )( ( ( () ()( () (())) ", " ()) () )((( ( ( ( )()() (( () (( ", "((( ))())) ((()( ((())(() ( )) ))", " (( ( ( )(((()() ( )()( (()))) ", "() ) ) ( )(()(() )( ) ( ) )((()", " ((() ())) ) )) () ( () (( ) ", " ))((( ) () ( () )()())) (( ))( ", " ) ( ))( ))())()) ) )) ( () ((( ( ", "(( ))( ()((() ()(( ( )((())())) ( ", "( (( )((( (() ()( )))( ) ((( ()() )", "( ))()) ()) ())) ) ) () ( )) ", "( ()()) () )( )))( ( ((())) )))", " ) ) ( )()()))) ) ) ( (( (( )", " ( (( ())( ()( ) )( (( ) ", " () (()) )(( ( ))(() ( () )( (( ", " )(( () )))) (() )) ))() )(() ", "( ) ))())))( ( ()) ) )(((()( ( (( ", "(( ) ((())()()( ) ( )(()) )() ", "( ( ()() (( ( (()(() ( ) (() ( )", "() ( ())( ( )(())( ) ( (() ) ))", "() )) (( ))() ( (( ) ))(( ) ", " ()() () (()(( ( ( (()( )) )() ()", " )()() )()( ) )(( )))))()()(( ()", " ())())(( ) ))(( )( ( )))( )) ", " )))() () ))( ( )) ( ) ( ((() ", " ()(((((() )( ()(( ())(( ( () )))", " (())()(())() ((( ( ( ( ( ()) ) ", "( ()((( ))()(((( ()() ) (( ()) )", " (()))) )() )) ((() ))) ()(() ", "(((( )(( ( ()()() ) )) (( ) )(( ) "}

    Returns: 869

  46. {" )( ((()())( ( (( ))() ) ) () ))) ) ( )))(", "(() (( (( ( )) )( )( )) )))())( ( (())()(( ", ") ) ((() ( ))(( ()() ()) )))) )() )) () ", "(((()(( ) )) ))(((() (( (()) ()(( )()() ())(", ") ()) ) (() ()(() )))))()( ) )(((( (( ) ) (", ")) ()( ( ) )()( )()) )( () )) (( ( (( ( )((", ")) ())())()) (( (((()()( ()))(()(( ) ( (((", "() (( (()( )())())((( ((( () (( () () ( ))( ", " ()())( (( ((( ( ( ) ) ) )() ) ))))( ) ", ") ) ) ( ())())))())(( () (()() ) )( ) ) ", ")()( ( )) ()) )) ) ())))((( ) ( (() ( ))()))", "( (((( )( ) (( )( ( (( )) )((( ( ( ()(", " ( ( ))()) ( ()()()( )(((() )(()) ()() )( (", ")) ()))) ( (()(())( ))))) ()( (( )(((( ) ))", "() )) ()) ( ( )()())()() )()())(()", "( ))))) ))() )() ()))(((((() ) (( ) ()) ()", " ()((( ) ) ) ( ) )()) ( ((()() )) )))", " ())(( ( ()))(() ((((()))((())( () (((()", "(())( )( ( ) )(() ( )()) ))( )( ))((((( (", "( )( ((()( )(()))))((( ((() )((( (()( (( ( )", "( ) ) )((()(()()((( ) () ( )))(( (()))))) )) ", ") )( (( ( ) ( ( ))(()((() ( () ((()) ", " ))) () () )) () (())() ( (()(()() ) ) ) ( ", "(((( )))) () )) )))(() ()))(((( ( ()( (( ( ", " ())(())) ))))(()( ( ()( (( ))(()( )( (( ", ") ))( )( )) ( ) ())) )()( ) ())( )(( )()((", "( )) ))() )( )( )() ((()(((((( ((())((( (", ")(( ( )( ) ((())((((())))() ))() ( )) ) (( ", ")) ))()() )()))() ) )() )(())(()) ) ) )) ", "())(()(( (()() (( )) (( ()() ( )( ( (())))", " )) () ) ()( ()))( )() ( )() ))()() )()(", ") )) ( )))() )( ) ) ) ((() ))()))))( ))(())", "( ) )()) ()) ))( ) () )()() ))(( )(( )))", ") )) (()))))(( ( )())) ())(( )))) (() ()( )) (", "( )())( ()()( )( (())() ()()( ))) ())))() ", ")((( ))( ( (( )( )( ))())))))))()( ( ))()((((", ")))((( ) (() ) (()( )() )()) ()(() ) () (", "( () () ) ))())) (( () ( )) ) (( ( ))( ()) ", " ((()) ) ( )) )()()(( )() ( ())( ( )) )) )", ") (()( ()))( )) ( ()( ( )()())) )( ( (( (( ", ")) )())(( ) )( ( )))(()(() ()))((( ))( ) ))()", ") )()(( ( )(()(())) ) )() )( ( () ( ()( ", "((())))()( () ((((( ))))) ( )( ())()((()( ( )()", "( ))( )((((()) ) (( () ((( )) ))(( ))))( ( ( ", " ) )) ))() ) ())) ) )()( )((( (() ( ( () (", " )()) ) )(()) ) )()(( ()) ))))()((()()()( "}

    Returns: -1

  47. {" ) ))( )))( )) ) ( ( ))(( () )))( ( )", "((( ) ()() ()((( ))()(() ())(( )) )()))) ", "( ())))((((((( )) () () ( )()(((( ( (()", " ) )() (())()) (()( )))( ) )( )((( )(()(( ", "( ( (((() (((( )(( )(((( (( ) ) ( () ", " (((( )()(( ( ) ( ) (() ) (()( )(( ( ))", " ()( )( (( ))() )())))())()( ( (() )) ", "( (()) (( ))(( (() ) )) ) ()) )( ))( )", "(( () )) (( ))((( ())() )()( ))) ()) ))", " (( ) ()))) ))()(( (() (() ((( )(() ", "() ())))))))(( (() ()) )(( (()) (((( ))", " ) ) ( ( )))( ( ()) ()))) )) (( ( ) )", "( ((( ())( ( ( ) )) (((()( )))) ()( ( )", " ((() ) )) )) )()(( )((((((( )(( ))()) ", "((() ))() ) () ()) ) )( ( ()() ( ))())", "(())) ((((( ()() ( (( ( ())( () ()) ( ", "(( (( )()) (()(((( (( ( )) ( )) ))(((() ", " )()))(()(((((()) (( ) (((( () ) ))))) )", "())() (( ) )) ))() )())()) ) (()) () ) )", "()() () () ( )( () )))))))( () () (() () )", " )( )(( )( ))(()( ) )() ( )) (( )( ()( ", " ) ()) (( )( )( ())( ((()( (())))( ( () ", "( ))() ()) ))()( ))())( ( ())(((( ", "((( ( ( ((() ( ()() )() (( (() ) ()) ( ", "(()(( ) ))() )( (( ) ())( ( )))() )())) ", " ( )) ()))()( (((()) ((() () ((( ( ( )", " ( ) )) ( ) ))) ( ( ))( ()(((()( )( ", " ) )())( ) ( (())(( ))(( ( )))) ( ()((()", "(()())(())) (()) ( )) ()( (()( ))()( ( ", " ( ) )((( ) )((() ( ()) (( ) ((( ) ()) ", " (() ) ) ))) ( ) () ((( ()(( ) () ())", " ( )(()) )))( ( (())) )) ) ((( )()()() )", " ( )( ) ((()( )(())) () ( )() (() )()", " )( ) )))(() )(( ))( ( (()) ) (((((())", " ( ) )( )) )( ( ( )((((( () () ( ", " ) (( ( )( )() ( ()()( () ) ( ) (() ", " ( () ( ())) (() ())(() ))) ((((((()", " ) ))( (( )))( )() ()()) ) (( ))))))) "}

    Returns: 899

  48. {"()(( )))( (()))(( () ))( ( ) )()( ) )((", " ( ( ()( ))()))( ()))))(((() ((())() ) ))", " (() () (( ) ))(()))())(( ( ()((( ( ) ", " )( ((((((()))( ) )())) ( (() )) ( ))", ") )()( )) ) ((())))) ())( ())) ( ( ", " () ((() ( )) ())))( ())) ) )) ())((", " ) ))) ))( )) ()() ) ( ) ( ) (())", " ())((((( (() ) )( (()( ) )(()( ()()(()", " () ))(())( ())(() )((( (() )))) (() )", ") ) )) )(( () ))))()()()( (()))())( (( ", "))()))))) (( ) )( )(( )) ) )) ()) ()) (", " ) )))) ( (()( ((( )((( )()))(())", "()(( ))) (( )) ))) (() ()()(() ()( )", "))) ()) ))) ((( )) ) ((()))))(())()", "( ( )))(( )( ( ) ( ) ) () )) ((( ) ", ")()( (( ))() )(() ( ()() ()(() ()(()) (", "( ) ))) )))()(()))) (( ( () ( (", "()( (( )))) (( (()) ( (()(() ( )(()( (( ", ") ((( ( ) ) () )())) (()( )( )()( () ", "()) ( )((((()))( ( () ) ( ( ))() ) ))()", "( () ()) ()) ()(()) ) ) (( )) )((((()", ")( ) ))( (()) )) ) )()())((( )( )(( ( ", ")(( ()(( (( ()((( (()()))))( ))( ) (( ", ")( ) ))))() ))))(( ))( ( )))) () ) ) ", "(( ()())()() () )((((()(( )() ( (()(", "( ))() )() ) ()((((()( ( ())( (((()( ))", " ))) )) )(() ())) ))) ) ()( ( (()( )", "(()()() ))))(( ((())) )(( )( ) ())( (", "( ()()( )(( () ) (()) ()()))) ())())) )", ") ( )) ( (( )() () )(( ()) )()( ))))", ") ( )(() ())((( ()())(()) ) (( )( ", "( )(() )(() )() ( ( )(( ( )()( ()( ( ", ") ((( ( ) () )))) ))( )) ) (( )()", "( ))(( ( (((( (((( ())() )()(())( ))(", ")))) ( ) )) )((() )( ( )) )) ))(( ( ))", " )())((())(()((( ) ()( ()))) ) (((((", " ()))) )) )( ))) )() ))( ) (( )((( () ", "(( )( ( () )( ( )()( ( ) ()(( )) )(()", " )) ()()((((( ) ()( )) ( )) )))) ()", "( ) ))( ))))) )()((( )) )))()() ( (", ")(() ())()))(( ()))))) )(()()(()) ))( ", ")()( )()(() ()) ) ( (())(((((()( )()( ", ") ()))))()) ) ))) ( ( () ( )) ()()(()", " ) ) )( ( ))) () ()(( ))() )( ( () )", ") ()) (()( ) ))( (( ( ) ) ()( ( () ((", ")) () (())()))(() () )() (((() () () ", ")) ) )( ())( )) ( ))( ) ) ( ()) )", " )(() )) )) () ())())() () ) ( )(()))( ", ")(( ( ())()( (( ( ((( ()( (((( ) ((", " ((( )()) )( )))( (()( ((())(((() (()"}

    Returns: -1

  49. {"(( ) ()( (())()() ))( (()))( ", " )) () (((() )( ( ()( )()( ) ", "(( )( ) ()()()()((() (() ( (()", " () )) (()) () )() ))))) )())", " ) ) ) )( ( )( ( ()() () ) ", "(( ((())) )( )((( ((()() ( ))) ", "( )()( () ) (()( ) ))())) (( ", " ) (( ( ( )() ) )()))))( ( )", "()(()((( ) ( )))( ( )() ) )", " ()())( ( ) )(( (((((())( ()))", " )( ))) ) ( ( )(((( ()) ( ) ", "() ))()( ) )) () ( ))( ) ( )( ", " ))(()(( ) )) ( )( ) ) )))( (( ", " )() ( )((() ) ((())( () )", " ((( )(())(( ( )() (( ))()( ", " ())(( ( ( ( (( ) ))()) )()", "(())( )( )( ))(((( ))()) ))", " ( () ()()()( ( ))( ((( ) ( ", " ))((( )) ((( )( ((() ((( ", " ) ) ()(( ()) ) ) )) (())", "(( ) ((( (( ) )( ( ((()) (() )", " ())))( ( ))() ( ())( (((())()", "( ) )))() ()((( )((() ( (()) ", "( ()())) (( )() ) ) )) )( ( ", "())( (( () ( ) () (( (() ))() )", "( (() ()) )))( (())(((( ( ( ", " () ())()) )( )) ((( ) ( )", " ( ) ( (()() ())((()() ( ))", "( (( () ) ((( () (( )((( )) )()", "( ( ( )) ) ) () ) )() ) (( ", "( (()( ()(( ( (( )))(( ( (()( ", " (() ) ()() () )))) ))()() "}

    Returns: 546

  50. {" ()))) ( ) () (( () (( ) )( (((( )) ", " ()())) ) ( (()( )(( ) )(((((( )( )( () )", " ( ( ( ))) ) ) )() ( ) ((())(( (()))) ", " ))( (()((())( )))(((() )) )( ) ()))( ) ( ) ", "( )( ) () ) )( (( ) ( ())((() ) ((() ", " (( ) ) (( ) )((()(( ))))( )) ((( ) ", " ))) )(()))( ( ))()))((( ())( )(( (( ) ", " )) ))() ) ()(() ) ) )) ( ())())))()))) ", "(() )() ) ))) ))) ())(()( )(( )() ) (( ()", "( ) ) ())) ) ) (())( ( )) ()(())())( ", " ) )( )) ) (()()( ) ((() ())) (()( ", "())))(()) ) )((()( )(( ))(( ()()()( () (( ", "(( )( )))( ()( )( (( (())))(( ( ( ))(( ", "( )( (( ))() ) ) ) ( ))((( ( ))())))", "()) ))( )()))(()((() ( ) )) ) (())() ( ", "()) ) ))( )( ) ) ((( (( ())) ( ) ))) ))))", " )) )()( )( )) ) (((() (() ( )( ( ) ( ) ", " ) ))( ((() ( (( ))(() ) ) ())() )( ", "() (()( ) )((( )( ))) ) )) ) ( ) )) )))))", " (( ( ) ) ((( ) (( ( () ( ( ) ))(( ) ", "( ) ( ( ) ) ( (())( ( ( ) )((( (()( (() ", " )())((( ))( ( )()))( () ))))) ()())", " ( ))())() ) ) ())()) (( )() ) (()) (((()", " ) ()(()) )) () ())))( ()( ))(((()(( () ", "((( ))(()( )() ) ( ) ( )(( )((( ())())))()", " ) ()()) ) (()( ) )()()( ())) )( ) (((((()", "()() )((()) )( ((() ( ((((((( )) )( ( ) )", "(()) )( )(( )) ()))( )) )))(())(())((( ))", "( (( ) (() )( )()()))(( ( ))(( () )() ( ", " ()))(()() )())( ) )( ) ( () ) ( ))(()()))", " (()))( )(() )))))) ())()((((( ( ( )( ( "}

    Returns: 764

  51. {"))) () ()() (( )( )())))) ((", ") )))( ()( ) ))) ( )) ()(() )", ")(( )))(( ) ()) ) () ((( )) )", ")) ( )() )(( ) (( (( ))) )()(", ")(((((()))) ( ()()) ) ))(( ()( ( ", "(( ) ( )( (()( ) ))) ) (()()((( )", " ) (()((( ( )( ) ) ( () )( )()", ")( ) )( ))())( ( ())) ))) ) (()) (", ") ( )( ))))) ( )))())()( () ", "()(( () )( )) ()()( )( ()( ) )( (", "(() (() ((()((( ((( )( () )((((( ", "( )))())))) ( () )) )(( ) ) )) )()", ")(() (( ( ()( ( (( (()()() ( ()", " ))))() ) ( ())( ) ) ) )( )) )) ( ", ") )(( (( ())()(()( (()() ( ((((", "))( (()( ) )( ( )) ()) (())( ((", "(() ( )( )(( ) )(())((( ))) (", ")()(( )()(()() ( ( ))( (( (( () (", " )())()))( ((()))(( )(((( )( ( (", "( )()))((())) ))()(())) ()( ( ()", " ( ( () (()(()) ()))( () )))( )))(", "(( ( ( ))) ()()()) ( )) ((( ", " ) ))) (() )(((( )(( )((( ()() () ", " ) ) ( ((( )( () ) ) ))())( ", ")(( ) ) ( )())( ) )( ) ( ", ") ()))))))() (() (( ) ((((( ))(( )", "))())( )))()() ( ())(( ))( )( ( ) )(", " (())()) (((( ) ))) )( ) )) ) ))(", ") )))() (( ()))() )( ) ())))", " ) ( )( ( ()( () ) )() )( (( )))", ")()) ))(( ) ()() (()(()) ( ) )(", " )(( ) ()( ()( ((( )() ) ))", " ))()(( )))(( ) ( ()())(( ) )))((", " ) )(() (() )( )()( ))( ( )))) ())", " (( ) )( ( (() ))) ((()) ))))) (("}

    Returns: -1

  52. {"((( )( (((( ))) ((() ()))( )) ( (())) ( ", " )()((( )( (()))(())) )(( ()()))())() ( ) ( ", " () ( )()( ((( ( (((( ( ((() ) )) ( ) ", " (((()(())) )(( )(( (((() )() )))() ()()())", "( ( )() () ))()) ( ()())(()(() )( ) )))", "(((() ) (((( ( ) ) ) ())(( ( (()))) (()) (( ", "(()(()()( ) ((()) )))(())) ( ))( ()) )( )()", "( ))(( ) ()() )))))( ))( )()))( )) )()", "((( )) )( ()) )() ) ))((( ( (() ((( )( ", "()) ) ) )(() ) ) ( (( )()() ((((() )()) ( ", " () ((( ( )(( ( ( ())) ) ( (()( ((())()( ", "((()))))))) (( ) (( ) ( ()))( ( )) ()))()", "()() ( ()( )(()) ( ( ) ))( ( ) )(( (( ", "(() ( ( (( ) (( ()) ( )( )) )()( ()) ) ", "() ))(()( ( ) ())() )((()( (( ) )( (())", "(( ))( ) )() )))(() ( )( (())))))( ()", "(( () ) )(( ( )))( )) ) (( )( )) )))( ) ) ", " ((() ())))) ) )( )()((())))( ) ) ))( ))))", " ) ) (( ( ()() ( () ) ) () (( )(( )))) ))", " )))( ( ()) )())(( (( ) ))( ) )()(((()))) ) )", "((( ))))( (( ))) ())))()()( ()) )) ))", "( ))()())())() (( (())()() (((((( () )()()", "((( ()())) ( ( )())()( ))( (()))()) ) ()) ", " ()() ((( () ) )(((( ( ) )))))(( ( ) ) )", " ()(( ( )( (()( () (( ) (( ()( ( ( (() ()", "(())( )() ) )() ) ) ( )((()())()( ( ( ( )", "(((() )((() ((()( )(((( ( (( )(((())) ) )", " ))((()))(((((()( ( ()(()) (())( )(( () ())", " ) ) (() ))(( )( () (((()( (( )())) (( ))", " (()) ))( ))( )() (() ( ((( ())() ", "( ( ))) ( ()((( ( )( (()) )) ) )))))( (( ", " )) ))((())( )) )(( ( ))))( ()( ( )(( ) ))", "(()( ()))()))( (( )))((() ) ) (()() ( ", " )( ())(()(()( ()() )) )) () )( ( (()))", "(()))) )) () ()()( ()()(()))))) ))() )) (((()", " (((( ( (()())(()()( ( )) )( ( ( ( (() ())", " (( )))())) ))() )(()))))) ( ))))) )))", " ( ())() ( ) ))(() ) )( ((()) ) () )))()", "( ))(((()) ) ) ) ))( ( )()(((())))))( ())) ", " ( ) () ( ( () ) )) ()) )(( )) ((( )", " )()))()(() ((( )(() () ( )()) (()(() )", " )( ) )(()())) ) )))) )( () ())) )( ()", "( )() ()(()( ) ( ((() ) ) )()(((() ( ", " ))(()()))( ((() ) )) ( ( ((((() )) (() ) "}

    Returns: 1117

  53. {"( () )(( ) )) ( () ) ) ()) ) )) (()( () ()) )", "()((( ()) ((( ()) ((() (()) ( ()( ) )( ) ", "( (( ())( )) ((()() )()(((() ) ()()()( ))", "() (( ))(((( )( ((()( ) ((((((( )(())( ( ", " ) (( )()() )() ( ()) ())((( ( ) (( )()())", " )(() (( ) )()(())))( ()( (())) ) (( ))( ()) ", " )(()( ) ) ))) (() ()( ) ()) ) ((( (()", "() (((( ( ( ))( )) ))())()() ) ) ) )(()) ) ", " () ( )()(()) ) ) () )( ( )(( )()())( ( ()( ))", " ))(() )())(() )))) ( ((( )))(() ()() (((( )", "())(( )((((( )( ) )()(( )((( )( )( ( ( ()", "(()(( ((( ((((((( )( ())) ) ( ( ((( (())())() ", "()) )() ))( ) ()( ) ()( (() ))) )( (()()( ))", " ( )) ()) () ()( (( ()(( ))) )())(( (( ( )()", "(()())))((( )() )( )( () ( (((( ) )) () ))))", " ) (( (() ()( (() ))(( )( (( ) ) ) ()( )()", "(() )))(( ) ((( ) (( )( ) ()) (((( ( ) ", "( () (()()) ( () ))) )) (() ( (( ( )) ())", " ))) )) () () )()) (() ) ) )) ()((() )))())))) ", "( () ()( (( ()((( )()((())) ()()(() ) ( ))()", "()(( )()) ()))))( ()( ) (()) (()(()))() ))()", "() ()) ((((() (( )()(() (( ))( ) ())(((( ", " ) )(( )) (()) ))( ) ))() ( ()()( ()(( (( ", " ) (( ) () ( )(( (() ()) ())() ) )( ( ", "(( )((() )(()) )() ) ())) )) ())( ) ( (())( ", " (()) ( ( ()())( ((( ) ( )( ( ))(( ( )) () ) ", "( ( ) ((()(() ( ((( )((( (() ) )((())))) ()( ", " ))))(( ( )( (()(( (())( ( ))( )( ) ()) ()))( ", " ))((()((())((( )( )())((( ( )() ) )())) ))(( ( ", "()(((() ) ()( ()) ) )((( ( ()( )()) ) )( ( ", " (((() ( )(( (( ) ) ( )(()( ()() ) (() ", "()() ())((( ()) )) )))())))() )(( )) ( )) )) "}

    Returns: 843

  54. {"() ) ) ( ))((( (( (((()( ) )) )", "( (( ) ))()(((()( )( )(() (() ))", "()) ) ) )) ))()(( ()()(( )))", " ) () ()) ()) )( () ( ) ", " (( ) )) (( )))) )()(()())) ( ", "((() () )() )( ) ((()))()( )) () )", "())((( ())() )))( )) ((()( ()", "(()))) )(( )( )(( ) (() ( ((( ", " ( ((( )( ()(())) ) ))) ( ( (( ", " ) (( )) ))( ) )( () )(() ", " )( ( ( )( (( ( ( )( ( )( ", "( ))() ) )(()) ()) )() ( )(( ( ", " (( )()((()) ))( ( )) ))( ()", "() ) )() ()) )( )(( ( ) ( ) ))()", "() (( (( ( ) ()( () ()()))( ", " )() ) )((() )() ) )))) ))", "( ) ( () )( ( ((((( ( ) )(( ) ) ", "()( ) )( ((( () (( ) )( ( ( ", "(( )()((( )(( ) () ()() ()( ) ))", "()( ) ) ( ) ()) ()()(( (() ", " ( ( )()( ( ) ()( ) )( ( ( () ( ))", " ( (()) )( ) (())(((()(( )(( )( ", "()())(( )(((())( ( ())()()(()( ) ", "( )(( ()() (() )))( ()( )( ))", "(( ((((()( ) )) )( ()()(( )", "() )()) ( ) ))( )) )(() ()(( )", "() ((((((( )) ((( )(( )( (()(( ", " ()) () )( (() ))) ))))))(( )) ", " ()()()())))(( ) ((((( ( ))))() ", "( )()(((()(()( ( ) ) (() )())))", "( )) ( ((() )( )( )) ) ( ) ))", " ( )) )( ()())))( ) ())( ))() ()", "())) )(( ()() ) ( ((((( (( ()) ", "() )(( ) ) (()(()( (((( )(())( ", "(( ) )( (())( )(( ( )( () ((()", "( () () ))))((())))( ) ( )))((( ", " )( ) ( ()) ) ) () )()( ()", " (() (()()))())))( ) ( ))( ( ))) ", " (( ()()() ()())) ) ))( ()", " )( (( ()) ) ( )(( )) ( ( )) ( )", "()(( ))() ()())() )( ( )( )()) ", " )(( ) ) (( )(( (( ()( ()( ", " )(( )()( )(()( ))) ))) ( )() ", "(((( ) (( ) ))(() ( ( ) ) ) )"}

    Returns: 802

  55. {"( )(((() (()())(()) ))() ))())(( ) )) )", " )( (() ())(( )))( (() ((() ( )) )( ()", " (()() )() )((()))(())( )) ) ((())", " (( (()) ()( () ((( ))( )) ( )((((", "))())(( ()())( )(( )()(((() ( )))(( ))", "()())(( (((( ()))) ( ()))))) )))(() (() (", ") (((())(()() () ) (())) ) () )(()(( )", " (((())) ))))))(( )(( ( )() ))( )) ", "(( )( ( ((( ()()) )(()( ))( )(( ( )()(( ", " ( (( () ))(() )) )()()))) (())) (", " ()( )))(( ))()) (( ( )( )) (() ) )( (", ") )((()( ))( ( ()(()))( ))))()( )( ( ))", ")( )))) ())( )) ))( ) )())))(( )() ))", ")) )( ))((() )()(( )(( ((( ( ( ", "))) ))(((() ()))(()) () ))( ( ()() (()(( ", "((()()())() ()) (( ()(((() (( ( )()( )", "( ) )( ()( ( ))()) ) ) ()())()()((()(( (", " ())((() () )())( ) ))) ()() ) )( ((( ) ", ") ) ((()) () )( (( )) ( ( (((( )( )()", ")( )( )))( )( )) ) (() )(( ) ( ()) )(( )( ", " )()()(((( (()) ( (())( ( ) (( ())(())", "(() ))))) ))(( )()(( ((()() ( )(( (()( ", " ) ()()( ) ))))((() ((( ( )))))(())(", " ()()((( ) ())) )( )) ) () (( ( ))( ())", ") ) ((( ( (( ())) )() () )(( ( ( ( ) ", " ) ))((()( (())( ( () ) ( ) ( )) ()((", "( ) ( ))(( ) ( ( ( ()))))) )) ( ) ( ( ", " ) (( )) ())((() ((())) ))( (( ) ", ") )(( ()) ())( )((((((( ( ())( ) (()", "))))( )(( ()( )( (((( )) ) )())) ((", ") () ( ))())( )) )(()))( ) ( ( )(()(( ", ")( (()( ()) ()() )()(((()())( ) ()((( )", "(() ()) ())(((()()())( ((( ( )( ) ( ", " ) )))(()))() ))) ((()))) ((()( ()) ))(((", ")) ( ((( () ) (( (((())(((( (() ()))((", ")) ))(((()(( ) ( ((( (((( )( (()(( ((()", ") ) ( ) (( ) )()())(( ) ( ( )) () ", " ( ()))) ()( () ()((( ))) ))()(((( ()))( ", " ( ((( )( (() )( () (( (((() (( ()()(", "( )() ( ()())) )) )(( )()(()) ()) ))(( )", " () )( () )( ) () (( ( )( (((() ( (( )( ", " (() ( ) ())) )()) ( )() ) )) (((", ")(( (( ) ( ) ((( ) ( ()( ))(((( )( ) ", ") )( )) (((()) ( () ( ( )(((()(() ( (", "))) ( ) (( ())) ((((()))( ) ((() ) )(( )", "( ()( ((( ) ( ) ( ) )))))))( )( ) ( )( ", "()) )) (( )) ( ) ((( ) ) )))())((((((", " )) ()(((( ())(( )(((())( (())( ( ()( (((", " ()) ))(( ) )) )( ( ())) () () )( )((", "( ()() ) ()( )))))) ))((( ) (( () ()("}

    Returns: -1

  56. {" )))( ) () ))(( ( ( )()( ))(() ", " ()(() ))) ) () ((( ))( ()))) )()", "( (( ( )(( (()())))))((() ( )() ", " ))())(() (( ((() (((((()))()( ( ( ) ()( ", "() )( ( ) )) ()))) )(( ))) ) ( () )", "( (( )(())( ( (( )( ) ) ()) ) ))() )) ", " )( ) ( ()())(( ()(( )))( )) )((())()))", " ) ))))()) )))) ( )() (( ) )( ())))() ", "()(()))( ((())) ))) ) ()) ( ) )()() ) ( ", "( ())()) (() ) ( () )(((() )((())()(( ", "() ( ( )() (((( ( ((( )))) )())((( ", "((()( ) (( ()(( (( ((() ) )( )))(()", "(( ) )( ( ()(( () ((()()( )( () )(( )", " )))())( ))())( ) ((() (( ( ( ))(( ) ", "(()()))(( ( (( ) )( ) ) ( ) ))) )() (( ", "() )(( ) )) )))(())(( (()))(( )) ) ) ()", " )) ( ( ()()) )(()))()( )))) ( )(( )()) ", " () ))()()() (() )( ()) ))( ()) ((()", " ))(( ( (() ))()()( (( ()))))((() )(() ", "( ()) ( ( ) ))) () ( )) () ((( )", " (( )) ( ) )(((()(( ()(( ( )(( (()))", "(( ()())) ())((((( ))(( ))) ( ( ) )))", " (()) () ))( ( ( ()( )( )(() ) (( ()))", " (()) ( )) )) ( () )(() ( ))))(()( ()", "())( )))(( ) )() () ))( ((()( )( )) ", "(( ()))())()( ))((( ( ()(( )) )( ( ", " (() ( () () ( ( ())((( ()))( (( )", " (() ( ) )())))))( ( ( ) () ())) ))", "(( ( )) ((()()) ())(()) ) ()( ) ())( (()", "( (() (((( (( )()()( () ))) ( ))( )) ()", "( )))))(() ) ( ) ( (())( (( ) (())() ", "( )())()) )())) ) )( ()()))) (()( (()) ", " (( ( ()( )( )(( (( )) ( ((()) )) ", " ()( ( )) ( ) ))((( ()(()()))() ())() ", " (()(() ()(((( )( )(()( (( ( ", " () ))) ))) ( )))( ) (( ) ))(( ( ( ))", " () )( ))( (( ( )) ())( (((((( (((( ))) ", "(()(())) ( ()) ()) ( () ) ) )( )) )", " ( )( (( ( )))())( )) )))()()) ))()) ", " ((( ())) )) () ()() ( ) )))) ( ()))", "()) ()( ((() ))) )(((( ))) )(()( )( ()))", "( (( ( )( (()))( )) (( )))()(( (((() ())", " ) ) )) ))(( ) ()()()(( () ())(((()", " (( ))( )))) (( ( ) )) (() ))())) ( )))", " (((() ))()(( )))( (( ( (( ) (( ))", " ( )( ( (() )(( )(()()() ( (( () ( )(( )()", "()( )( )( ( (() )(() ( ) ))) ( ) ) ", "( ) ( (() ) )( ) ) ) (( ((()( ) ( ", " ( ()() )( ))((( )( )))))) ((((( ( ) ()) ", " ((()() () )((() ) )())( (((()) )) ))()"}

    Returns: 1147

  57. {" () )(( ())) ) ) () (( (( (())(( ) ())))", "(((( (( )( ( ) ) ())( ( ) ) ))()( ()", "() ) (()())( )()) ( ) ())) ( ()(( () ))", "()()))(( )( )) )(()) )( () (((() ()) ) )", "() ) )((() ) ((() (())(() ( ))) ()) )(( ( ", "( (()( ) )( ) )()( )( ( ) (((( )))( ()) )", "( () ( ())) ) () ) ))( )()(() )))))( (( ", "( ()) ())))( )() )((( ))(()))))))))) )", "( ) )()) )()) )() ()) )) )(()(()(( )))(( ", " )()() ))() )()( ( ( )))()( ((( ) ) )))", " ( ())) () (( ) (( ( ( )(( () )(( (( )", " ( ( )()() )(())))()( ) ) )))()()( ))) )", "())()( ( ))(( ( ) )))))) (( (( )) ( () ( ", "((() ()(( )(( )( ())) ) ( ))(( )( )))( ", " ( )( ( (()) ((( ((((() () ()) ( )( ( ", "(((( ) ()(( )( )))( () ) )()) ())))))", "(()))((())()) ()( )))) () )( ))) (()(( ", " ))( ))) ( ((((((())( ))(() )()( ( )( ()( ", " ( ()) ((((((( ) ))() ) ((()(()))( )) ())", " )) (()(()()) ) (() )( () )))) ) ) ()) (( ", " )(())() (( ( )()()))( )( ) ))(()((( )) ", "( )(( ( ((( )( )()() ((() ( ())( ))) ()", "() (((() ) ( ))))())())( ( ))(() ( ))", "(((( ( )( (( )( (())()(())()) ))) )( ))", " ( ) (()( )( ) ( ( ))))()()( ) ()((( )", " )()) ( )(((((( ((( ) ))( ))( ) (( ()))( ", "()))() ( ( (( ))))( )))))))) )( ( ((( ()))", " )( )(() ))) ( )( (( ( () )()()() ( )", " )))( ((( )( ( ) () (()( ( )))()) ))( ", "( )) ((()(( ()))) ) (((()(( ( )(())( ))", " ))( ( ())))) ))()()) ()))((( (()(())((( ", "((()(()(( )))(() ( )() )(( ((( )(()))()", "()))((( ( ())())) ) (( )(() () () )", "(( (()( ()(( (((()( ))) ( )(( ( ()()( ", " )) ) )(((())) (( ( ))()) )()))))())() ( ) ", " ))()() )))() ))))( ( ((()) )) ", " )))( ((()( )) ) () ))) ( )(())) ( ( "}

    Returns: 922

  58. {")(()()()()) ( ( ( ))) ))( ( ( ) ))() ()()", "() ) )() ((( ))))))(((( ))(( ) (())( )() (", "()(((( )()() ((()))) ( ) () )() )(() ))( ", "()))()() ()))(()())())) )(() ) ))) ( ))", "((((() (( ) )())(() ) (()) (((() ( ( ))))) ", ")(() )() )( ()((()(())() (( )()))() ))", "((( )) ( ()) ))()( ()) )))() ())) ())()", "(( ( () ) )))) ( ) )) ()(())( (() ( )", " )() ( (( ))(( () )( )) ((( )())() ))", "() ( )) ( ( (( ()))) ( ( ) )( ) (", ") ) ))))) ( )) )) ( ))(())()() ( ())) ( ) ", "() )()( )()))))) ())( )( ((() ))()) ))) ", " ) () ( )()(( )()( (()()((( ))) )(( )) )(", " () ())( () ()) )) (( ()() )(()()))( ))))", " ))( ) ((((()(((((( )( ) )))) ) (( )()( ", ") )) (( )()(( ) ( ) (( ( (())()()( ( ", "))( ) )( () (( ) ) ())))) ) ) ((()(( ) ", "( )() )((( )(((()) )(( ))( ())((( )", "( )()()( )(( )( )()))() ))) )))()()) ()()(", "(((()()())()() ) )( ))( ( ) )) )) )))", " (( ))()( ) )( )))) )) )( )) (( ))) ", " )( ) ))( ((()()( )( )( ()((()())())))))) ", " ( ((()())()) (()( )() ( ((( ) ( ( ) ( () ", ")))( ( ()) )) ( ) ( )((() )()(( (( ))()(", "( ) ( )())(( )) )))))) )(())) ()( ( ) ", ")(((( ))))(( ( ) ) )) )((( (( )))) ) ( ) )", "((()))())) ))() (()() )) (((( ( ( ((", "(((( )() ) ) ( (( (( )()( ))) ) )() ) (", " (() ) ()) )(( )) )()() (( ))(( ()(( )", " ( ) ) ((()( ) )) )() ( )()( )( ((( ((", " () (( )(( ()() )) )( ) (( (())) ((()(", "( ()()) ) )))( ( )())())())( )((( )))) )", "))(( ((() ()( ()) )( ((( )() )()(( (( ( ", " ) )(()())( (()) )()) )())) ) (( )(())( )"}

    Returns: -1

  59. {"(( ()) () ())) )()((( )((() ()", ") ) )( (((( )(()(( ( ()( (", " )( ()(((() ) ()( )((() ())() ", " )())) )( ( )(()()) () )(((", "((( ()))) (( ) ((( (()() )))", "(() ) ) ))( )()()(((((( )((", " (((() )))) ) ) () ) ( ))", ") )(( () )((( ) )(( ) ((() ", " )))()( ) ) ))( )((() ( ) ()", "( ()(( ) ( ( )( ( ((( ( (((", ") )((( ) ( ( )((() ))( (() ", ")( )() ( )( ( ) ) (()( ) )", ") ))() ((()( )()()( )( ())) ", ")))(( ))((())) ))))()())(()", "(()()((( ))))( )) ))) )() ", ")) (( ())) ) ( (() )() ()(", " )()) ))(()() )(() ) )) )) )", "(()() (( ( () (( ))( )( (", " (( ))(( ) )()))) ((() ) (((", "( ( ( (( ))) ) ) () ()) ((", " )()(( ) )(())) ( ( ) ) )", " () ( )((( )())))) ())((( )( ", " )) (())( (( ) ) )(( ))) )(", " () ( ))) ) )() ()(( )(", ")() ( ) ( )( ((())() ())", " )( (( (()( )( )() )) ) ( () ", ") ) )) )( ) )( )))( ())( )(", "(( ) )(( ()() )())) () )(", ")))(() ) ) )))(( ( ) ( (( ", "((())) ()))) () ()) ))())((()", "( )()) ))((((()))((()) )( (()", "(((( )()) (() ) )))) )( (( )(", "()(( (() ( () ) () ( (", " (()) ()( ())) (( ) ( ) ( ", " ( ))( )))) (() ()(())(())", "()()()))) ) ( ( () )( )(( ((", " ( )) () ) ()((()))))( ()) (", ") ))((())( )( ) ) ()))))(((", " ( )((() )) () ( (((())((( ", "))()))( )() ))(( ()( ( ))))()", ") ( ())(((( (( )))))((( ((((", " (( ((()( )()( ()( ) )))("}

    Returns: -1

  60. {"()()() ()(()( ( ()() ((())) () (((((() ", " ) ())())( ( (( ( ()) ))())) ( ))()", "(()( (((( () ( ( )))(( () ((( ((()((( ()", " )( ( ( ) ) ) ) ))( )) ) )( ) ))( ) ", " ()) ))( ( (()( ( )(( ( ( ((( ( )() ", " ( )) )) ( ( )( (( )()) ) ))) )((())", "() )) )) )))((())(() ())( () ()() (()", "(((( (()( )() () ) (()) ))))( ()))() ) ) ", "()((( )) ( ) ))) ) ((( )()) )() ) (( ", "((( )(( ))) () ) ( ) (()((()))(() )", "()(() )()))())())()) ) () ))) ())) ) ", " ( ( () )) ( ) )( (() (( (( (((( ) ( ", " ) ) ) )) () ()())())) ))) (((( ) (( () ", "(( ((()()( ) )(()() (( () (() ) ( () ", " ( ))) ) ) )( ()( ) ()(() ))(( )(( )( ", "( ) ( ()( ( ( () ) () (()( ( ", "() ()) ()( (( (()))(()( ( ) ())()))(( )( ", "()()(() ( )(())))( ) ( (())) ( ()) ) )", "( ( ) )()( ))(()(( )))() ((((() ( ) ) ", " ( ) )() ))(((( () ( ) ) ) ))( () ) ", " ))( (( ) (( (())) )() )))) )( (() ()", "( )( ( ) ( )) )( )))()((( ) ))))( ) ", "()) () ((())(( (()(() () ( () ( ) ( ", " ())(((() ) )(( ) (()()(( ( ( () )()", "( )))) ( ( ()) ( ()( () ) )( ) )) ))( )", "()()))) () ))())) ())()) ((() ((( ))() )( ", " )( ) )(( ) ) )))( ( ))( ((((( )( ))))", "()()( )))( )((((())) ()) ((()() () ) ( ", " )((( ))))) ) ()() ((()( (()() ()) )))( )", " ( ()(() )() )) (( () ))) )()( )((( ( ", "( ( ()() ((()( ) )()()() () )( ) )))", " () ) ))( () ( ()( ( )()( )))) ) (()() ", " ( )( ( (() ( )()) ())(()))( ()())( ( ))", "( ) ()(() (()(( ) )() )))(((())(((((( ", "( (()( )( (()( )() (()) ))()) )))( ( )", " ()) (()))( ( () ))(())(()( ))(( () ", " ((()() (( ))) ) ()() ) )( ) )()) ))( ", "(() () (( )( ) )( ( ( ()() ))) )()(( ()))", "( ( ) (()(( ( ( ( ( ()) ) (((()) ( )", " ) ()) )( ) ) ))( ( ))) (()())) ) ) ", " )) ) ( ((( )())))(( ) ( (((()( ( (())"}

    Returns: 927

  61. {" )())(( () (((()) )) ( ( )) ())(( )( ", " ) ) ) )( ) (() )())(( )(()( ( ( ( )", " ) ) )))(( (((( ) )(( ( ( (((() )) )", " ))(())) )) ) ((()() ( )())())((((( ", " ( ()())(( (()()) (()))((( ) )) )", " ))) ( (() ))(( ()( (((( ) )))( (((( ", "( )((( ) ) ) ) )( ( (()) () )((( ))", " )()(( ( ))((() ) ( ((( ()(((() ))) ", "(( ))() ) () )((( ) )()())( ( ())(( )", " (( ()())) )( ) )())()()()) () ( )( )", "())(( (( () ) ) )))() ( ()() ) ))(( ) ( ", "(( ) ())(()) (( ))( (( ( )(()()(())", "(())()())() ))((()((( ) )))) ) )) ))(( ", " )()()()))()) ( )()( () ) ) )(() )()", "( ) ) (( ()( )()) () ) ( ( )", " ( ( (() (( )(((()) ()) )( (( ) ", "((()((()( () )(( ) ()( ) ( ) )) ", "(( ( ( ()( )) )))))( )() () ( )) ", "((( )()(((((( ))()))) ) ) ) )( ( ", " )((((( )() ( ) ))((() )( )))) (() ", "(()() ( (((((( ()( )( ) ( ) (((( ", "( ( (((( ) )() ()((( ) ((( ( ))(() ", "( ( ( )()())) ()()( )()(( ( (()( )() ()", " (( ) ( (()) () ))))(()))( (())) (()", "()() (( )))) )(( ()()) ()( ())", "( )(())()) ()()))(()))() ))()(() ) (())", " () ()))())()( ( )) ( ((()((() )()))", " ((() )(( )( ( ( ) ((() ()() (()( ", "( ) ( ( ())())() ) ))( () ( ) )( ", " )()) )( ( )) ))(( )()) ) (( ()(()", "())() ( () )()) )))) ( ( )))) )( ( ()))", "( ) )())) ) ()( ()))) )()) ( )) (( ", "( ) ( )() )((( )( ) )(() )() )( (() ", " )) ) )(( (( )( ()((( )() ))(()) )))(()", "((( ((() )))())())((( () ))(( )) () )", " )())()( )(((()()((( )( (( ) )(())() ", " ((( )) (( ( ( ())) ( ( ))()( )())", " (((()() ()(( (( ( )))()(() ) ( ()", "()) ) () ())(()(( ( ) ((( (( ( )(( ", " )))( )))()()))()(( ) ))() ()(( ( ()", " ) ) )())( ( () )(( ()() ) ()() ((() ) ", "( ( ))() ) (() )))()( ) )() () )) ", "() ( )() ) )(())(()) ) )( )( ))( ) ) ", "(( ( )() )() ( ( (( ) )((((() () ))", "()) ( ((()()))( )( ( )() )) (()( ((( ) ", " (( )((() ) ( )()((()() ( (( () ()) ) ", "(() ) )( ( (( ( )( )( ) ( (( ()( ", "( )( () )) ) )) ) ( () ))() )))))"}

    Returns: 1042

  62. {") () )() ()(( )) ) (((( ) ) ) )) ()(() ", "(( ( ((()))()( ) ) (( ()( ())()( )(( ( )(", " ) ))( ( ))( () ))() ) () )) ()) ((", " ( )( (())) )() ( ())()(() ( (() ))()(( ))", "))() ) )( ((()))))) )))()()(() ))) ()) )(", "( ) ()( ()()((()( ) (( () )) )() ()()( )( ()", " ) ( ) ) )) )() (( )( ( ( ( ((() ) )) (( ", " )((()() ) ) )())( ) () ))))))() )(() )) (", " )()) ))()))(( ( )((((() ( ( )(() ) () ( ", " ((()(() ))) )))) ())()))( (( (() ) ) ( )(", "(( )(( ) )() ( ((( (()( )) ( ) ()() ()(", " ((() )(( ( ((( )) )) () ) ()( ((()))((", ") (((( (( )() (())( ())( ) ) ) ((( ( ((() ))", " ) ) ())()( ((() ) (( ) ( )((()() (( ", " )) )))()) )(()( )( (( (((( (( ))))( )()", " )) ))()))) ( (( (())( ( )( )((( )", "))()() ( ) ( )) )) )(( ((( () )((( (() ) ", ") )( ) )))(()) ()))() )) ()( )( ) ( ))))()(()", " ))()( ))((()()(( (( )( ))( ( ))()) ) (( )", " ) ) ()( )) ) ((((( ) ( ))))(( (( (", "()))(( )( () )) ) ) (()(( (((( )(", ")) ) ()( ) ( ( )( ()( ())))())) (( ( (", ") (()( ((()( () )()(( (()) (((( ()( ())", "() ( (( ( ())) )((()))( ) ))()( ) ( )(( ", "()((( (() (( ( ((( ) ))(( ) )() )() ", "(() )))() )) () ( ) ) () ) ( (( ) (", ") ( ) ())( () ))(() ( () ))) ) ()() (()))", ")(() ((()( ) ((()()) )( )) ( (() )( ) )", ")( ( ) (()))())( ()()) ) )( (( ) )()))(", "()(( (( ) )) (( ) ) ( ) )) ()))(( ) ) )))((", "( )) (( )() ((( )( )( ))) )))((( () ( ())))(", "(())) )() (((( ()( ()))))) ( ) ( ())) ( ) (", " ))) ( )( ( () ))) ())( (( ))(( )((( ()", " )( )( (( ))()) ))((()(()(( ) ( ( )( )(", "))()()( ) ))() ( ) )))((( (() )) ) ()) )))(", "()())())))))) (()) )))(( )(((((() ()) () ("}

    Returns: -1

  63. {" ()())(() ) )(( ) ) ( (( ) )))( ) )", "())) ( )( ()() ) ( ( )((( )()", "())) (()( )( (() ))()()))( ) ))(())", "()( ((()((()(())()) ( ) ()(( ())( )))", "((()()(() ())) ))( ()((()(( )(( () ()()", " ((( ()( (( ( () ( () ) ()( ) )() ( ", " (())( ((( (() ) ) ) ( () ( ())())", " )((()))( )(()) ( ) (())( ) ( ()( ", "( ( (() ( ((((() )( (( (( ) (()()", " ((()))) ( )))())(( (()) ) (( (()) ", " ) (( ) ) ()( ))( ()()( ))( ", " )((()(( ( (() )( )(()(((() )( ( )( )", " ( )))( ) () (((()((()( )()) ( (()", " () ())))()( ( (()( )) )(((((( ))( ", " (( ( ()( ()))( (( () ) ) )( ( )(( ", " ( )( ))))( () ( (( ()(())( ( (()()", " ))(((()))(() )))) ((()( ((( ()) (() ", "( (( ((( ) ) )) (() ) )))) ) )()) ", "()( ( ()()( )))( ( ) ) (((( ())( ", " ( () ))( ))))() ( )((( ) )( ()( ", " )( ( ) (()) )) () )(( )))(( ( )() ()", "() ( ((()( ( ) )()) ) ( )))( ()", "((( )()) ( )) )(( ( ((())) )( ) ))() ", " ))() ( ( )))() ) ((()) ( ) )((()(())", "( ( ( ((( (())) () ( ( )))( (() (( ( ", " ))) )(()())(()(( ((() )( (()) )))() )", " ) )) ))( ) )(( ( (()((( (())()) ", "( ))() ))(( ( ) () ))(( (( (((()()) ", "( ))())()()( )( ( ) ( )) )()(()() ", " )(() ((()(()) )( ) ) ()())((((() )", " ))( ((((() ( )))) ((() ( (( ) ( )))", " (( () )())) () ()( )(( ) ( (((( ()", "(( ) (())())(()(( )( ()))(( ( ()()() ", "(((()( ) ()( ( ) ( (( )( )( ()( ) (()", " )() ( () ( ()( )( ()() ()((())(( (()", "() ()(())( ) )) )))))) ) () )()()) )", "(())(((( )) ) (( ()) )(( ((() (( ) ) ", "(( )) (( ( ((()( ) ) ())( )(() (()", "( (()() ( (((() )))( () )) ( ((() )", " ))( ))())) )))((( ))(())())) () )( )", " ))( ) () ( (( ((( ) ))()())( ) )", " ) )()) ( ( () )) (()(( ( ))))())() )", "(( ( )()() )) ( ( ( ( )))) )) ) )()( "}

    Returns: 928

  64. {"( (()( ) ) )( (())(( )( ))", "(( ( (()((( )() )) )( ) (()", "()) ) () () )) ()()())()) ", " ((() (( )(() (()() )(( )) ) ", "()(( ))( (( ) (((((( ((( )((()", " ) ( (((()( )() ) )( ( ((()", "()()() )(( )) ( ( )( ) )) )", "(( ( ) ) ()())()) ))(( (() ))", "() )((( )()( ( ))) ) )( ( ", " )(( ) (()) (() ((( ()(())) ", " )(()) )() (( ) )(() (((()", " ( )) (()(( )(((() )(( ( ", " )(((()) )))()(( )) ))((() ", " )())))( ((() ( )) (())(()))", "( ( ())))()( ) ()( ( ()) ))", " ((( (( () (())( ) ) ()()))", "() ))(() ( )(() ))()((() (()", " ( (( ( ((( ( ) ( ) ", "(( (((() ))()) )( (( () () )", " )()( ( ( ())(((((( )(((( ( ", "((())) ( ( ()((() ( ( (( )", "( ())) ) () )(()) )( )() ()))", "(( ()) )()) (()() (( )) () ()", " )() ))( ()) ( )))( ) ) ))", " )(()() ))(() ) ( ) (( ( )", "()) ( ())) ) )( )) )() () )", "( ()()() ) ) ))) ))))( )(( ", "( (((( (() ) )(() ( ( ()", " ((()) )((()( ()(((()( ( )", " ( ()((())(((( ())( ())))))))", "()() (()) ( ()()) )(()(( )))", " ) () ) ()((() ( (( ( ))", " ) ())( ( () () )() ) () ", " ))) )()() ( ) (()() ( ()( )", "(( (( ) (()( )))( () )) (() )", " ) ( )))(()() ()((()) ()) ", "())()())()( )((( ()() ))))() ", "())( )(((( )) (()() ( )))( ", " ())) (()( ( (( ( (( ( ))", " (())) ( ) (( )( )) )( (( ", "( ( )(( )) ))) ))(()())) ", "(( (( ) )( ())( ))( ))( ) )", "( )( )((( )(( ( )()(()() ) ", "( )() )))(()(())()() ( ) "}

    Returns: 722

  65. {"()) (( ( ())))) (( ()()) ( ) ((((()(())) ) ))", "( ())))( ))( )()( ( ( ) ) )) ) ( )()()))", "(( )()()((()) ( ) ) ) ))()) )))( ((()) ((( () )", " ()()) ))) )( ) () ) (( ))) ()(((( (() )()()))", " )) ( (( )(()(() ) ) ))(() ( ()) )()))())", " (( ( )()( )( )(((()() ( ))((( ()( ) ) ())", " ( )))()() ( (())() ) ( ( ( ( )( ()(((()()", "(( (())( (( )(( ))(( ( ()()(((( ) )() ()(( ( () ", "( ) ( )( ( )) ( )( ) ( )) ))()()( ))) ))))", "(())) ) ))) ( ( (( ()( ()((( )() )( )(( )", "( )(((( ) )( )) ) () ()(( ) ()( ()( ( ( )) () ", " () ) ( (( ( () (((( ()( () (( )(( ))() ) ( )", "(( )(( )(( )( ) (() ) )(()( ((((() )((((( ", " ) ())((()) ) (( (() (( )() ) )( )()( ( )) ) ", "()) ())(( ()()())) ))( ()) ( )((( )()( ) ) ) )", "(() ()()) ( (( )) )() (())) ))())) (((( ()) ( ", "( ( )) )))()(( ( () )( )()) ((( )(( ) ( ) ( ( ", "(( ) )))())( ((( (( ((()()( )) ( (()( ( ( )", "(( ))) ))()( ((((()) ) )( ( ()) ) (((())() ", "(()( )) (((( (((()() (( )()(( ((()((() ))( )) ( ", " )(((( ((() ()( ()((((( ))))( )(( )( ( )) ", " ()) )())( ()( ) (( ()( ) (( ) (((( ( ())))(( ", " ()( ))) ) ()( )(( ) (((() )((() ()()) ()))( ", "( )))(( () ))(() )()()))((((() ( ( ( ) ) )))", "((() () ) ) ((() ))) ( )( (( )) ( )((()) (((()", "()(( ( ()) )) )(( ))())((() (((( ( ) (())) ))) ", " ( (( ( ) (( ( ( )( () ((((( ( )( ( ", "( ((((()) ))) )))() () (( ()))() ))()))(((()", "(()()(( )( () ()( ) )) )()) (()()(()))(( (( () )", " ) )( ()) )( ) ( )(())(( )())) ) ( (() ", " () ( ()( ) )( )( ( ) )) ) ( )))( (( ( (( (( ))", " ( ( )) ))) ) ) )()))) )(()())(( ( ( )) ())) ", "(())) )())((())))) )) ()) )) ))) )) )()( (()))( ", " () )( )())) ( ))()) ))) )))() ( () )() ) ()) ", "(( ()((( ((( (()()( ) ) ( ))) )())(( ))()))", "((( ( ))(() )( )()(( ))) ( ( )( ) ) ) ()((())) ", " )()) )) ( () ((( ((()(((( ()() )() ( ( (()", "()) )(( ((())( ())(( )) ( () ))() (()))) ( ()", " ) )( ( ) ) ( (( ()) () ))()() ) ( ())(((( ", "(() (((( ))()))) ( )()(() )) ( (()( ( ()( ", " ) ) (((())() ) )())((( ) (())() )(()) )((( ", " ) ())(( () )) ) )) ())))((( ()(())))( ()() ", "((((()(( (() ) ) ((() )) ( ) (()) ( () ", "() () ) ))(() (((() ))( ))()) ) ()(( )) ((()( ( "}

    Returns: 1208

  66. {" ", " (" }

    Returns: -1

  67. {"( ( ( ( ) ) ) )" }

    Returns: 8

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