TopCoder Statistics - Problem Statement

Problem Statement

Correct parentheses sequences can be defined recursively as follows:

The empty string "" is a correct sequence.
If "X" and "Y" are correct sequences, then "XY" (the concatenation of X and Y) is a correct sequence.
If "X" is a correct sequence, then "(X)" is a correct sequence.
Each correct parentheses sequence can be derived using the above rules.

Examples of correct parentheses sequences include "", "()", "()()()", "(()())", and "(((())))".

You are given a String s. You are also given int[]s L and R, each with the same number of elements. These encode a set of conditions. For each valid i, you have to satisfy the following condition: the substring of s that begins at the 0-based index L[i] and ends at the 0-based index R[i] must be a correct parentheses sequence.

You can only modify s in one way: in each step you can choose two characters of s and swap them. Return the minimal number of swaps needed to produce a string that satisfies all the given conditions. If it is impossible, return -1 instead.

Definition

Class:: ParenthesesDiv1Medium
Method:: minSwaps
Parameters:: String, int[], int[]
Returns:: int
Method signature:: int minSwaps(String s, int[] L, int[] R)
(be sure your method is public)

Constraints

s will contain between 1 and 2,000 characters, inclusive.
Each character in s will be '(' or ')'.
L will contain between 1 and 2,000 elements, inclusive.
L and R will contain the same number of elements.
For each valid i, 0 <= L[i] <= R[i] < |s|.

Examples

")("

{0,0,0,0}

{1,1,1,1}

Returns: 1

We have four identical conditions. Each of them tells us that the substring that begins at index 0 and ends at index 1 must be a correct parentheses sequence. We can satisfy all conditions by swapping s[0] with s[1]. This swap produces the string "()".
"(())"

{0,2}

{1,3}

Returns: 1

The only way to satisfy both conditions is to change s into "()()". This can be done in 1 swap: by swapping s[1] with s[2].
"(((())"

{0,2}

{1,3}

Returns: 2

This time we do swap(s[1],s[4]) and swap(s[3],s[5]).
"((((((((("

{0,2}

{1,3}

Returns: -1
"()()()()"

{0,0,0,0,2,2,2,4,4,6}

{1,3,5,7,3,5,7,5,7,7}

Returns: 0
")()(()()((())()()()()()()))(()())()()()("

{3,5,17,25,35}

{12,10,30,30,38}

Returns: 3
"((()())())"

{1, 4, 3, 2, 0}

{8, 5, 6, 7, 9}

Returns: 1
"()))()(()("

{0, 0, 8, 0, 6}

{5, 3, 9, 7, 9}

Returns: 2
"(()())))(("

{4, 6, 0, 2, 2}

{7, 9, 3, 5, 9}

Returns: 3
"((()()))()"

{3, 4, 2, 0, 1}

{6, 5, 7, 9, 8}

Returns: 1
"(()))(())("

{0, 2, 6, 2, 2}

{9, 7, 7, 5, 3}

Returns: 2
"((())))(()"

{7, 2, 0, 4, 5}

{8, 3, 9, 9, 6}

Returns: 2
"))()())((("

{0, 4, 0, 4, 6}

{3, 7, 7, 9, 7}

Returns: 2
"()()()(())"

{2, 0, 0, 5, 4}

{9, 1, 9, 6, 7}

Returns: 2
"())((()())"

{4, 4, 0, 0, 8}

{9, 5, 7, 9, 9}

Returns: 3
"()()))(()("

{2, 2, 0, 4, 6}

{9, 3, 9, 9, 7}

Returns: 2
"))(("

{0,1}

{3,2}

Returns: 2
"((()())()(())())))))))((()()()((()())(()()()((())))())))())((()())(((()(())(()((()(()))(()(())))()(()())((()()((()()(((((((()((())(((()(()))((())))))(())())()()))(((((((()(())((()()(())())))))(()((()(()))()()(())()(()))()((((()(()((((((()))()())(((()(())())((()())())))()((()()(((((())))((()))(()((()()(())))(()))()()))))(()()())))))(()()()())()))((()()))((())())))))))))(()()()(())))()())))()))(())()(()()))))(()((()(())(())())()((())))))()(()())()(()))())())())((())))((()())(())))(()())()((()()))())(()()()((())()))))((()()()()((()))()())))(()((()(()()()()()()()(())))((()))(()()()()(()))()())))()((((()()((((()()))))))())())(()((((()())))()()))))())))())()()))())((()(())((((()(()(()(()(()))()())((((((()())(()()((()(()(()())()(())())())((()((((()((())()()())()()())(()((()()))()()()(()(())((()))))))()()()(()))()()()()((((()))()()))()((())(()((()()))(()()(())()((()(()((((())())())())(()())))))())((()(())(()))(()(())((((()(())))((())()()())(())()(())))))))()((())((()((()()(()))())()(()))(())))((()((()(()))()())))))(())(()(())))(()()())()))(((((()))()))(())())()(()((()())))))()))()(()(())))))((((((()))((()())))((((((())((()(())))))))))()()))())((()))(())))))())(((()()((())))))()(())()))())()((()))))()))))((()(((())()()))))))))(())())))((()()()))))((((()))))())(()(()(()))())()(()(((((())()(())))(()(())(((()((()()))((())()()(())()((())((()())))())))(((((()()))))())()(()())))((()((()(()(()))((((()(()())()())((()))())))))()))(((()))()))(((((()(((((((()(((()()))())((((((()(())())))()())))(())(((((()(((()()(()(((()()()(((())()(()(((()))()()((()((())())()(()((((()))()(())((()(((()))))(())())(((((((()())))((())))((())(())((((()))(())()()(()())))()(()())((((()))))))()((((((()(())()()()))))))())))))))(())))(((())(())()())(()())(((()(())((()((())((()))())))))((((((()))))))()()))(((())(((((((())(()(()))((())(()((()())()()(())))()())((()()((()(())(()))()(()))(((((()())()()))((())())())((()((((()()(()((()())))()((((())()()((())())())(())()(())()()())(())))))(()))))(()()(()()(())()(()((((("

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Returns: 456
"(())()())())((()(())())))))(()())))((())))()()(()))))))(((())()))()())(())))))()))()()((((()()(()))))((((((()))))(()((()(()))))))(()()()())))(()(()))((()((())())(())())())()(()()(()))(((()(()))))))()))()))()()(((()((())())))()))))()((()()(()((()(()()))()))())()()())))()((((()(())()(())((()(((()((()))((()()((()())))(()())))(()()((())(((()((()(())))()()())))())(()()()()())()(())((()((()))(()))(()(()()(((())(())))))()(()))(((((()()((()(()(())(())()()((((()())(()(((()))((())((()(())(()()((()(()(()(()((())))(()(())(()))()((((((((())))())(()())))()(((())(())(())(((())))(()(((()((()))(((())())()((()))))))())))(((()((()((((()))((()()()())))())))()(((())))))()()))(())())))(()(()()()))())((()(()()))))(())))(((()()))()))(((((((()))())(())((((()(((()()()(()))))(()))()()(()))))))())()((()((((())()()))((()((()())(((()())(()(((()((((()))(()()))())))())(())())))(()((())))()(((()(()(())(((())((()((()))())))())(()))(())())())()()(()()))()(()))())()())))(())(()()(()))(())((())((()(()())())))))()))())()()()()(()()(()))(()())((()))()(((((())))))(())((())))((())))))())))()()(())))())((((((((((()()()()()((((()())()(()())()()))(()()))()()(()(()((()(((()())(((()())())))((((())()))))))()))()(()(())))()))))(())))((()(()(((()))(())()())))(()(((()))())((()())))()(()((()())))()))(()())()))))))(())(()())))())))(()())())(()(()(())((()(((()())())(()(())((()((()(((((((((((((()()))())(())()(()(())))(()((((())())((()))((()())(()((()((((((()())))))((()())())(())()((()())()))()(())()(()(()))()))()))(()(())))))()())(((()))())))()((()(()))(())))()()(())()))(())()(()))()()())))(()()((()))(()((()((())((()((())(((())()))(((()()(()())()(()))(((()((()(()))))()())))))((())))()))()(()()(()))((()))(()()))(((()(()(((())))(()((((()((((()(((()))))(((()()(((()))()))())()()((()))())))())(()(((()((()()(()())((()())))))))()(()(()((()((())(()(())()()(((()()()))()))()(((()(((((())(((()))))))()))()(((((()()()(((()(((((()(()))())))()())))()()())))(())(()())())()((())())((()((()()((()((())()())(()()))))())())((()()()))))((()"

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614, 442, 1726, 1791, 1874, 1368, 1056, 422, 738, 770, 1404, 1477, 679, 341, 246, 1793, 1707, 1711, 1634, 310, 1590, 788, 1751, 1036, 1787, 388, 602, 1354, 547, 1751, 1209, 1671, 697, 1310, 422, 654, 1217, 1665, 665, 13, 1900, 898, 1493, 1787, 744, 1357, 240, 886, 647, 625, 1393, 59, 1040, 959, 1253, 288, 1154, 1247, 1769, 917, 1644, 693, 42, 204, 19, 910, 226, 994, 1879, 1100, 849, 232, 225, 948, 89, 1172, 1176, 1971, 202, 898, 1775, 1630, 1751, 394, 1054, 1184, 628, 1864, 1743, 1669, 1696, 946, 896, 265, 430, 1874, 1775, 683, 1743, 299, 1875, 1295, 1461, 878, 1084, 1981, 510, 1541, 826, 392, 1327, 1513, 727, 1097, 134, 947, 1209, 732, 1128, 679, 1321, 1627, 1877, 1612, 1397, 238, 6, 1618, 1775, 609, 93, 1765, 1709, 369, 76, 446, 1712, 1071, 61, 1364, 1198, 1422, 429, 240, 1750, 1986, 152, 1102, 683, 683, 489, 548, 612, 1570, 1518, 73, 1642, 1440, 1471, 699, 1058, 103, 1331, 1089, 1390, 1335, 646, 1787, 622, 1926, 479, 1120, 1019, 1532, 1998, 687, 1410, 1546, 1789, 1398, 1506, 87, 1773, 1856, 1827, 142, 969, 1999, 1314, 254, 1290, 1557, 1150, 1604, 47, 663, 864, 47, 1936, 85, 614, 675, 1234, 1775, 1327, 1199, 1294, 1333, 1670, 1741, 1737, 935, 1978, 930, 1351, 76, 685, 1045, 1793, 956, 1797, 103, 576, 1677, 1743, 1999, 85, 371, 849, 1150, 1430, 1152, 1438, 702, 1893, 70, 99, 699, 1785, 1741, 1379, 1493, 246, 1335, 742, 1376, 1175, 184, 1591, 820, 356, 1153, 63, 317, 1637, 1517, 1791, 1081, 1941, 1939, 558, 1088, 791, 233, 581, 1797, 1530, 594, 1058, 18, 1771, 1630, 91, 1775, 1995, 413, 377, 1789, 289, 1504, 1664, 1693, 1319, 1456, 446, 991, 992, 895, 1200, 415, 1872, 1999, 147, 1297, 128, 1331, 197, 1962, 1267, 59, 950, 1338, 238, 877, 1293, 1325, 1325, 1948, 1694, 1789, 1169, 849, 852, 600, 99, 1787, 933, 664, 297, 1210, 1748, 1890, 508, 1293, 1333, 105, 1791, 1404, 63, 1640, 1036, 705, 868, 1787, 456, 1067, 1928, 1858, 1797, 128, 731, 1091, 1693, 1338, 1381, 329, 182, 746, 1690, 105, 1704, 1123, 1467, 1743, 1412, 352, 1504, 1010, 1946, 63, 1620, 1561, 1793, 1500, 1633, 101, 1763, 1883, 264, 1639, 719, 1333, 557, 227, 97, 1577, 879, 693, 179, 1789, 1826, 910, 1615, 1789, 793, 369, 878, 843, 1787, 87, 921, 948, 1121, 1757, 1797, 1945, 184, 73, 582, 1298, 934, 1785, 1695, 1352, 1276, 422, 1524, 91, 390, 1412, 652, 685, 85, 1545, 1237, 1517, 757, 1113, 151, 1265, 1045, 49, 149, 652, 1791, 1123, 1673, 1791, 484, 1751, 894, 1736, 1190, 798, 1086, 885, 821, 171, 1392, 1086, 1330, 1207, 378, 1991, 1677, 907, 101, 1245, 167, 1999, 464, 184, 565, 1335, 1183, 1356, 997, 1048, 1785, 79, 1874, 198, 993, 260, 755, 1994, 93, 794, 528, 1741, 330, 59, 1787, 202, 1640, 1628, 1883, 1154, 1797, 1327, 807, 1064, 1591, 510, 1045, 562, 186, 1637, 46, 775, 59, 97, 291, 99, 896, 1685, 640, 1791, 628, 242, 834, 1722, 1791, 1408, 317, 948, 101, 1805, 1773, 103, 877, 1620, 1871, 999, 99, 1640, 1999, 1695, 1826, 1743, 1990, 1976, 387, 1205, 1198, 1094, 327, 1736, 105, 607, 1544, 1239, 681, 1065, 749, 938, 342, 1594, 565, 1711, 358, 611, 1152, 1333, 1945, 1544}

Returns: 488
")(()()()(())(())((()))(())())(()(())())()((()))(((()()((((()(())()))())(((()))()))()))()()))()(((()))()(())()))))))())())()())()()()))(((((()))((()(()))(()(((()))()()))((()((((())())))(())()()()))(((((())((())(()(((()()))(((()(()))(()((((()))()(())()((((()(())())()(((()))(())()()(())))()))((()))())(())()())((()())))(())(((())()()()((()())))((())))())))((()(((((())))((())()))((()()))))((())((())())))()((()(()())))()))(())()((())(()(())()(())(())()((()(((()))())(()()((())()))((())(())(()))))()(()))())())(((((()((())((()(())(((((()()((())(()((()()()()())()))())))(()()()()()())))()((())))(()))((((()))))))()(()())()(())))))))(()()))((((((()()(())))())()()))))))()()()))))(())()(())(()))))()))(()())())()((())())))()(()))((((()()()()())))()(())()((()((()))()))()()(())((()()))(((()(()))))))(())((((()()(())()())(((()()(()()())))((())(()())(()(()))((())))()(((()((()()))()()))(())())())())()())()()()))()(()()))(((((()(((((((()((((()))()(())))()(()()())((()()(()(()(()()())))(())(()()((()()()(()))())))))())(()())(((((((()())())))())(())())()))(())(())))))))())()()))(((()()(((()))()))(()()))())())())()()))(((()(()(()()(()()(())()(((()(())()))())()()())()(((()())))(()))())())(((()()))))()(()()(((())()))()))()()())(((())))())())()(())()())((())((((((()))))()(()))))((())(()))()()((())())))()(((()(((()))()(((()))())())()(((()((()())())(()()((()))())()())))))((((()(()(()()(())(()())((((()(()))((()()())()()))(()(()(()()(())(()())))))))())(()))((()())(())((())()))())())(()()(()(()())(()()))((((((((()((((()())(()(()((()())()(())()))()))(())))((((()))(()()()(())())()(())())()))(())((()(()(()()())()))()(())(())(()(()))()(()()())()())())())(())()())(()))())))())()()))())))()((()))((())))()()())(())))()))(((()))(((()())((((())((()())()((()(((())(()())(((((((())((()((()(()()((()()()((()))()))))())((()(())(()())())(()(()((()()())()(((())()())(()(((()()()(((()((()()((((()))(()(((((()()()))))(()(())()())()(((()()(()))(())(((())())))))(()()(((()((())()(())()))())(())())()((())((((())(()())(()((()("

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272, 799, 527, 145, 1418, 1924, 509, 1420, 426, 489, 1753, 487, 1945, 155, 237, 1081, 531, 1816, 83, 1836, 23, 1663, 1651, 147, 1752, 1432, 72, 509, 54, 507, 1999, 646, 483, 1422, 506, 650, 1702, 487, 1252, 1999, 1681, 255, 885, 1961, 1721, 1959, 1339, 529, 1392, 509, 523, 155, 1466, 1442, 268, 485, 1985, 523, 529, 1652, 549, 1258, 155, 1643, 1985, 89, 527, 982, 321, 1094, 507, 910, 83, 914, 306, 1374, 1283, 1891, 493, 876, 1454, 1366, 1456, 350, 234, 1872, 507, 1957, 495, 1604, 473, 1761, 1494, 489, 1201, 529, 1371, 1110, 1461, 531, 1709, 85, 783, 23, 89, 1999, 1423, 1577, 1124, 89, 824, 9, 1259, 1534, 932, 638, 1147, 1529, 1863, 1709, 552, 61, 1904, 1561, 966, 319, 1570, 527, 529, 531, 1425, 166, 628}

Returns: 489
")()(()))))())())(())((((()(()))(())(())((((())()(())(((())())))()(()(()()))(((())())()(()((()())))))()(())((()()(((((())())()))))()())((()(())()()((())))((((())))(()(((()))(()()((()))(((((()()(((((()((()()((())))((()))())))(()()))()))()()((())()(()))(()))()))())())())))))((()())()((()))))()))))(((()))))(()()()((())))())))()(()()()(()())())))))())())))))(((())(()(((()))((())))()()))))(())(((()))()())())(()))))()(()()(()()(())(())(()())()()))((((()))))()()))((()()()()))())(())()(()(()(((((()()(()()))()))()(((()))((())(()))(())(()))(()(())(())((()()())(()))(()))()()()))()()(()(((()(()()(()((()))())()(())))(()(()((()()(((((()(()(((()))(()))()((((()()((((()(()()()))))()(()())))))))((()()(()))))(())()()(()(())()())))))())()(((((())()(((()))((())(()()()(((((())))()(())))(()(()()))))((()()()())(())()))(()))()((((((((())(((()()))((()()(()((((()()))(((())(()()(()(()(((())(((()(((()()(((()))())())))))()((()(())))))(((())(()))()()))(()(())((()()(()()())()))(())))))))(((()(()()))())(()()(()((())())()()))((()())((((())))((((())()((((())()()))()()((())()())))(()()()()))))()(()((())(())(()((()()(((())()))((()((()((((((())))(()((((((((())()))(((((()())))(())()((()))((())))))()(())(()((()(()(((())())))((((((()(((())())((())((()(())(((()))()))((()()(())(()())((((()())()))(((()))(()())())())(()(()()))))))))((()))(())((()))(())()((()(()))((()()()))()(())())()(())(())(((()((()))())))(()))()))()))())())())()()()()()))(((())))))((((()))())())((((((()(())((((())(((()))((())())(()))(()()()(()()(()(((((()))(()())))())(((()))(()((((()(((())(()(()()())(()(())((()((()())())))()())())))((()(())())))((())))()(())(())()())(())))(()))())(()))()(()()())))()(()))()()(((((())())(()))))())())))(((()())()(()()))(()())((()()()((((())(()()())(()))))()()(())))((())())))())(())()))(((()((((()())))))(()(())())((((()()((()))()(((()))()))(()()()))())())(()))()())))(((()(()())(()()(())()))))()())()())(((())(()(()())))((()((())(())))()(((())((()()()())()((()()(())))())(()))()()))((((()))()(()()))))((()))))()))))("

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1167, 1968, 1181, 1347, 1365, 1359, 1345, 1359, 94, 733, 1399, 1919, 925, 1665, 531, 237, 941, 1321, 919, 1353, 1399, 917, 1353, 1343, 927, 1347, 1992, 1329, 1361, 364, 1134, 1999, 903, 1359, 1347, 1345, 1317, 1399, 1321, 1181, 919, 1345, 1399, 1397, 1395, 1470, 1351, 1319, 941, 1317, 129, 701, 1189, 1867, 1349, 1179, 1395, 1205, 1351, 1321, 1349, 1958, 1321, 1022, 1321, 1365, 809, 1881, 105, 1171, 1095, 1663, 1090, 1189, 1540, 615, 1306, 889, 1048, 1231, 1359, 207, 1203, 378, 1433, 371, 1999, 825, 945, 1866, 1189, 1395, 713, 83, 1347, 1766, 1395, 331, 877, 1865, 577, 1205, 1361, 1379, 1377, 923, 917, 1323, 1171, 369, 1976, 891, 1427, 891, 1586, 708, 1292, 1977, 1329, 1343, 941, 1311, 927, 1351, 1976, 1999, 915, 1321, 1179, 1999, 1361, 1377, 1766, 1379, 1171, 1166, 927, 1347, 945, 1365, 282, 1809, 1999, 1095, 1343, 1399, 277, 297, 1205, 1299, 1113, 1183, 1614, 757, 1405, 945, 753, 1203, 1553, 619, 939, 577, 491, 424, 1669, 1416, 1311, 822, 1435, 1310, 1327, 972, 1203, 759, 1365, 457, 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1866, 561, 1327, 823, 1496, 759, 1064, 1936, 619, 1181, 756, 945, 945, 1203, 474, 917, 493, 1345, 1311, 1751, 1205, 110, 1399, 1367, 1259, 1315, 1431, 1435, 941, 611, 1177, 889, 1948, 1433, 1512, 1728, 545, 1575, 1501, 414, 1361, 767, 1715, 939, 1967, 280, 1399, 1313, 1367, 539, 1583, 1329, 1361, 907, 1315, 427, 1317, 945, 1359, 1095, 57, 917, 1329, 1329, 1379, 1361, 110, 1999, 1527, 1183, 1351, 1313, 1205, 734, 1339, 1724, 1433, 907, 1359, 310, 1313, 1937, 939, 1804, 108, 1308, 1999, 1810, 1285, 887, 1365, 1431, 416, 530, 1347, 1095, 708, 1435, 1828, 1339, 157, 250, 682, 1175, 1394, 286, 1377, 1869, 1179, 1657, 1734, 1905, 93, 1319, 1343, 1734, 1359, 1395, 859, 941, 1377, 1353, 1397, 1329, 1177, 1201, 1427, 1095, 1223, 147, 1177, 556, 1377, 1353, 927, 750, 1663, 903, 1999, 1397, 1351, 1325, 1347, 1095, 1327, 919, 1156, 1361, 107, 1999, 1395, 917, 1367, 1397, 1830, 889, 1299, 938, 1433, 1609, 1351, 1179, 1181, 1345, 375, 1435, 516, 221, 1177, 1999, 945, 923, 132, 340, 1345, 1321, 1167, 915, 1353, 545, 1351, 1315, 57, 944, 1315, 1367, 1758, 1169, 1175, 1205, 1177, 1329, 335, 1183, 1179, 648, 1965, 1628, 939, 1359, 1349, 1169, 47, 1315, 1361, 776, 930, 1183, 1311, 458, 1274, 1169, 1343, 1313, 1359, 917, 1317, 1095, 354, 1179, 1749, 1351, 1162, 505, 1921, 1456, 816, 1797, 903, 765, 939, 404, 1612, 1335, 423, 1349, 447, 1136, 1389, 1720, 1167, 1321, 1325, 1445, 1365, 1377, 1014, 1189, 245, 1325, 1723, 53, 1721, 1317, 941, 698, 14, 911, 1367, 1070, 1315, 1897, 1901, 1379, 1645, 1359, 1205, 1367, 1461, 1676, 1903, 1347, 1175, 1189, 1179, 945, 1325, 1183, 414, 887, 340, 1929, 1433, 1738, 1343, 38, 1347, 35, 707, 1365, 714, 1323, 1397, 197, 945, 941, 1347, 335, 1351, 1377, 1321, 915, 1365, 1008, 250, 265, 1319, 1435, 1821, 1347, 1315, 1313, 527, 927, 143, 1379, 1365, 1399, 1359, 1046, 1999, 1347, 83, 1179, 66, 923, 1399, 231, 42, 351, 1347, 889, 1261, 1339, 919, 116, 1189, 1329, 1075, 1397, 1570, 1339, 1353, 1205, 563, 99, 135, 767, 1347, 1365, 1397, 1349, 1175, 1300, 1315, 1145, 457, 1131, 1313, 180, 911, 1325, 1379, 1359, 1377, 1024, 1347, 1395, 1095, 1329, 473, 222, 1327, 1361, 1327, 1615, 927, 271, 1351, 459, 53, 851, 1323, 1139, 939, 686, 1999, 263, 1205, 1379, 287, 403, 1188, 1166, 857, 1181, 1327, 945, 1936, 915, 875, 907, 945, 1029, 1059, 795, 1956, 1191, 1629, 1977, 1397, 1058, 1999, 1171, 486, 1349, 1379, 1137, 1433, 556, 1349, 945, 104, 1351, 1189, 1351, 1315, 903, 941, 437, 155, 577, 1167, 149, 1203, 1147, 1359, 1183, 1435, 1999, 1377, 923, 910, 1359, 1755, 1585, 1177, 1375, 568, 1710, 1365, 1095, 1191, 1339, 1203, 1339, 1310, 798, 1075, 1379, 1323, 1319, 1329, 1317, 615, 1179, 1435, 917, 1200, 1175, 903, 1433, 1169, 1041, 1325, 383, 1175, 1395, 1399, 457, 1359, 1347, 1397, 1095, 1379, 1395, 1035, 1325, 1399, 818, 1435, 1349, 1189, 1177, 721, 1862, 911, 1367, 1321, 1408, 683, 1293, 907, 1343, 14, 1399, 1339, 1169, 1942, 1256, 1753, 1345, 889, 1901, 1311, 907, 1183, 1315, 919, 1484, 765, 1311, 1349, 1999, 915, 214, 1397, 1367, 1353, 1603, 1650, 1367, 307, 1189, 1323, 1308, 875, 1189, 1494, 368, 1377, 1339, 1487, 1327, 1310, 1435, 1353, 714, 1189, 531, 539, 1167, 891, 1327, 1377, 1359, 1345, 1073, 337, 1377, 1319, 1073, 1729, 1164, 1007, 1757, 1433, 941, 1259, 1630, 1175, 1323, 1189, 398, 1140, 1349, 1804, 310, 1361, 1379, 1677, 421, 1435, 1359, 1133, 1423, 1762}

Returns: 426
")))())())(((())))(()))())()())()))(()()()(((()((()((()(((())())())((())))))))((()()))))()(((())))))()()(()((()((((((((((((()))))()())))())))))()()))())(()(())())))(()(((()()(()(())()(()()((())))()(()()((()))(()))))))(((())())((()(((())))())()(((((()((()())((((((()))()))((((((()()(()))()()()))))())()()))((()()(()())(()))))))())()(((()))())))(()())()))))())))))()(())()))()()(()()((())))))())((((()())()(()()())())(()()(())()))()))(()((((())()())()()()))()))))))(((()()()())((()()()((())(())(()((())()(()()())(((()((()())))((()))))()()())(())(()))()()))(()((())))(((())(()(())(((()(()()))((((((()((()(()(((()(()(()())(()))))(())()())(())))(()))))((()()))()((()))()(((((())))))()()()())())(()((()())))())())(())())())())()()((()))(()(()()))())))()())()())())()))())()(()))))())))())))(())())(()))))())()((())(((()()()(((()((((((((()(()(()())))(()((((((()))()()((((()(((()(()))))()())()(((()()()))()())((((()()()())))()(()((()(((((()))())())(())))))((()(()())()()(()))))())(()()((((()))))(((()(((()))((())))()((((((()))(())((()))((()())()((())(((())(()(()(()()))())(((((()(()())()())(((()(()()())())))(((()))(()()())(()()((()(((((((()())())()))(((()))()()((()(((()))())()()((()())((()))))))((()()))(()())())))(()()(())(())(()))))(((((((((())(()))((())()((()))())(())(((((()))())())(()))))((())())(())(())()))(()))))()(()((())(((())()(()()((((((())))(()))(((()))()()()()(()((())))()()()())((()(((())((((((((()()())))())(()))()(()()()(()))((())))())(()))())())()))(((()()))(()())()()))(()()()())))())()()((((())((())(())))()()()((()))((()(()()())()()))))()()())))))))())()()))())(()(()(((((((((()(((((()))()(()())))()((()((())()((()())((())))()()()(()(()))(()()(((((())(()()())(()()(()()()()()())((((())(((((()((((((((()()((())()((()))()(())))())))(()((()())(()())(())()((()(()((((((()()())(()))))())()(()((()))()))()())(()())((())((()))()(()(((())((())))(((()()))))()))())))(())())))))()))())))(()((()()()))(()())())(((()))()((()()()()(((((())))))())()(())))()()())())()())((()()())(())))()))(((())))())"

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1433, 198, 648}

Returns: 492
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591, 1681}

Returns: 462
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1987, 934, 304, 695, 401, 335, 1672, 514, 188, 1189, 399, 278, 199, 1482, 863, 1858, 1042, 390, 1167, 1583, 295, 1528, 566, 1895, 65, 1999, 1167, 1572, 1926, 401, 1558, 149, 1164, 1261, 1245, 1637, 915, 1245, 1009, 1668, 1671, 1166, 1169, 269, 1245, 1245, 1982, 809, 1010, 1927, 1169, 309, 305, 309, 1169, 1999, 1100, 1145, 1058, 1755, 394, 538, 344, 1811, 1883, 465, 279, 1953, 19, 290, 1479, 180, 1153, 1644, 616, 1575, 1676, 63, 1972, 595, 694, 212, 335, 601, 529, 1999, 1245, 1830, 53, 1672, 715, 328, 923, 393, 1056, 1245, 1660, 233, 311, 1189, 298, 699, 1811, 1317, 970, 1008, 1588, 996, 298, 23, 309, 1169, 279, 401, 1946, 1306, 970, 324, 1561, 945, 1317, 1331, 1448, 638, 67, 717, 1181, 1084, 1984, 67, 328, 1331, 813, 790, 63, 1539, 27, 884, 1261, 1083, 228, 1270, 923, 1189, 1637, 595, 1367, 267, 1741, 593, 25, 411, 1778, 1099, 1372, 63, 595, 335, 1374, 1700, 1977, 1505, 155, 1654, 443, 188, 1513, 1029, 485, 1261, 395, 1145, 309, 1999, 1084, 653, 1564, 472, 63, 1604, 1222, 1113, 1736, 311, 426, 880, 1145, 339, 266, 1129, 558, 407, 610, 127, 1788, 1674, 399, 469, 401, 233, 1751, 304, 42, 1261, 1964, 1401, 1999, 1169, 27, 399, 1036, 1588, 469, 1484, 1673, 556, 681, 267, 393, 1189, 867, 1337, 859, 481, 269, 1456, 279, 520, 665, 593, 480, 481, 1278, 674, 128, 933, 1807, 1111, 931, 1879, 1169, 1951, 564, 300, 335, 1814, 1336, 160, 1144, 17, 717, 1188, 852, 923, 1988, 279, 1679, 1118, 964, 65, 375, 1913, 481, 1258, 781, 885, 1169, 1261, 1221, 612, 1040, 1889, 1999, 1445, 253, 691, 198, 546, 1966, 1167, 1909, 1245, 1201, 1999, 586, 1562, 1999, 305, 364, 1972, 1945, 1838, 946, 873, 1167, 1261, 311, 967, 1354, 566, 300, 1145, 1189, 1261, 1261, 1486, 1003, 1016, 1539, 926, 696, 1351, 1999, 1919, 178, 329, 1507, 1999, 1367, 1169, 291, 593, 1962, 558, 395, 1931, 1306, 804, 1967, 251, 857, 592, 67, 1509, 1677, 224, 821, 1460}

Returns: 460
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803, 1553, 289, 1186, 1399, 1010, 1133, 1221, 1168, 1152, 1217, 1543, 756, 1221}

Returns: 474
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1293, 1232, 1965, 1661, 1293, 1245, 1995, 1034, 157, 829, 1130, 758, 1111, 291, 1899, 1326, 1291, 1279, 966, 712, 915, 1853, 710, 1277, 1283, 858, 1203, 1853, 1851, 1266, 1559, 1281, 271, 1041, 1062, 477, 1303, 1853, 615, 1957, 119, 1998, 1174, 1845, 1095, 1262, 1301, 808, 1748}

Returns: 467
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1145, 960, 1197, 1607, 1521, 14, 458, 145, 1999, 826, 15, 177, 1515, 1048, 1427, 1213, 1207, 1983, 342, 1307, 1695, 1711, 897, 183, 1205, 81, 93, 1832, 1398, 1607, 1921, 1421, 333, 352, 911, 1587, 360, 1877, 303, 1362, 163, 497, 1425, 113, 868, 843, 925, 910, 1267, 592, 1425, 1331, 743, 1616, 209, 1883, 1046, 803, 1048, 1145, 699, 1045, 170, 1139, 1427, 1777, 1705, 1692, 785, 813, 455, 946, 1402, 739, 102, 1155, 1405, 121, 1957, 91, 296, 1005, 1427, 1721, 1571, 1692, 765, 410, 1577, 344, 641, 183, 1360, 1515, 1823, 119, 733, 1353, 276, 66, 1361, 1045, 619, 828, 756, 1303, 46, 198, 398, 1331, 452, 711, 964, 314, 741, 1982, 1980, 1211, 1853, 1941, 36, 1453, 749, 786, 1234, 19, 596, 777, 1058, 1864, 1953, 1470, 1323, 1604, 1423, 181, 1766, 1999, 706, 515, 1145, 998, 897, 460, 1071, 779, 280, 1975, 1957, 306, 1596, 98, 44, 1337, 1413, 1421, 1996, 1103, 1022, 985, 1787, 942, 481, 428, 1106, 1560, 1582, 878, 336, 899, 1143, 1413, 597, 942, 182, 1267, 1849, 1050, 691, 643, 1074, 1427, 1729, 1247, 856, 427, 1288, 1805, 1691, 521, 1983, 1030, 1090, 189, 1440, 1429, 1970, 813, 314, 858, 698, 1957, 1425, 75, 1205, 431, 836, 48, 1295, 374, 395, 780, 562, 136, 1192, 1577, 354, 736, 450, 1103, 777, 173, 1515, 1999, 81, 1284, 911, 1648, 427, 1427, 746, 1647, 130, 49, 96, 1956, 978, 958, 125, 1051, 271, 990, 732, 1322, 753, 19, 1814, 403, 1983, 460, 191, 14, 1085, 462, 191, 209, 830, 1805, 795, 1398, 1181, 173, 791, 189, 1203, 1957, 237, 1421, 719, 1552, 1427, 1812, 1972, 1064, 1150, 1427, 1879, 1101, 305, 154, 1902, 1844, 973, 719, 1398, 832, 239, 882, 1738, 501, 1691, 777, 753, 882, 1305, 211, 596, 142, 563, 1190, 1423, 1607, 1092, 876, 1730, 1427, 1677, 1050, 1629, 757, 785, 19, 789, 17, 409, 1782, 172, 191, 428, 887, 115, 1981, 1879, 1048, 1382, 1429, 125, 1423, 1444, 1407, 1128, 1263, 460, 960, 489, 355, 623, 1015, 952, 1425, 701, 1141, 49, 1714, 843, 123, 101, 693, 913, 1576, 501, 1953, 903, 1413, 738}

Returns: 492
")()()))()())(()((())(()(()(())(((())))()))))(())(((())(())()(()((())()(((()))((()(())))(((()))()()()())())((()(((()()()(())())((()()(()))())(()))()))()))))(()()()()))()())))(()(()))()))())(()))((()))())()(())((((())())()))()(()())(((())))(())))((()()()((((()))(()))()(()))))))))(((()(((())(()())(((((()((()()()()())()))((())(()(()))()()(()()())))(()((()))()((())(())(((())))(()())))())(()))((((()(()())))))()(())(((((())))()((()(()()(((()())))()()()())(()(((())((()()()(()()())))))((()(())()()()(()((())(()())())()(((()(()(()))((()())()(()())(()()())()(())))())))((((()()))())()()(())()))()(())())((()()())())()(())())))(())(((((())()())(())(()()()((()())))()))))(()(()(((())))())()(())((()(()))))((())(()()()))()((((()())()((()(()))(((()())(()(())))((()))()((())(())(()()))()())(((()))((())()()(((()(()()()()(()())))()((((())(())()))))()())())((()()((((()((((((())(((((()()(()(((()(((())((((()()))))))(())())((()))()(())))(()))()))))()())(())()()(((())))(((()())))()))))()(()())((()((((()())())()()(()()))())()(()())())())))())))()))((())))(((()()(((((()((())((()(()(((()))))(()()))((())(())))()(()((()())))(())()())((()(()())())(()()(())())(())()()())))((()()(((()((()))(((((())((()((())(())))(()(()(()(((()()))())(()((()()))(((((()))))()(()))())((((((()()))((()()))((()(()(()()))(())((()()((())()))())))()())(())())()())(((()))))))()))()))())))())))(())))(()))))()(())()))))()()()())))())(())()()()())(((((())()())((()(())((((())()((()(()()()))()()))(())()))()()()()()()(())))(()()()((((()((()()(()(())((()))())(()())())((())(()()(())))))()(()((((())()((()()))(()(((()()(())(((()))())))(((())(((((()(()()())()()))))))))(()()(((()())))()))(()()(((())()))()(()())()))()))))))))))()((((()())()()))()))(()(()))))()(()(()((()(((()))(()()((((())))))(((()(()))(((()(((())()())))()(())(()(()())()()))(()(((())))()()()())((()))(((())()(()))())(())((((())))))(()()())(((()))(()((())))((())((())()()(()()()))()))))))(()))))(((()((((((()))())())()(()())()((()()(()((())(())())((()(((()))(((()(())())((())(()(("

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582, 1501, 492, 853, 1984, 736, 390, 40, 114, 114, 11, 1731, 1758, 234, 1622}

Returns: 501
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969, 1446, 1364, 1964, 1835, 529, 1851, 391, 1759, 239, 1140, 126, 1463, 1855, 1324, 1472, 1438, 364, 665, 925, 1589, 944, 213, 287, 274, 837, 259, 1974, 775, 1741, 645, 954, 1827, 886, 413, 451, 1392, 1855, 908, 1392, 835, 1234, 631, 1779, 1084, 1636, 1736, 1441, 1999, 491, 710, 252, 1180, 1797, 1154, 1845, 854, 1444, 1851, 318, 1769, 1879, 1226, 251, 114, 1879, 503, 187, 1799, 1120, 1799, 1783, 555, 1117, 947, 1767, 1134, 1783, 584, 1455, 553, 738, 1338, 938, 1829, 585, 1163, 1453, 391, 371, 215, 1999, 1797, 1327, 1038, 413, 12, 1689, 1799, 637, 610, 768, 1163, 1382, 1199, 1861, 1779, 1299, 1219, 989, 1455, 1783, 1142, 1611, 1016, 844, 440, 1139, 1992, 1685, 818, 1857, 1585, 1453, 1994, 1407, 1857, 1273, 1621, 553, 669, 1392, 1989, 1583, 265, 1981, 1983, 292, 1378, 1436, 168, 109, 1761, 1448, 318, 273, 1453, 1404, 1861, 1879, 1779, 804, 47, 1845, 1668, 1889, 1263, 1234, 677, 1999, 1857, 1204, 1033, 1857, 390, 430, 1061, 1463, 308, 1599, 1847, 430, 397, 1398, 1218, 1855, 1861, 880, 818, 1161, 955, 1149, 770, 1851, 469, 1773, 126, 1398, 1845, 1186, 1851, 127, 194, 1606, 1847, 20, 1497, 1236, 1047, 738, 1589, 760, 1767, 415, 1479, 1168, 873, 276, 1283, 555, 411, 1514, 950, 1131, 27, 1769, 27, 1503, 949, 88, 1185, 743, 1783, 1985, 739, 1751, 397, 1999, 1977, 1999, 265, 1845, 1152, 1567, 891, 966, 795, 1861, 1879, 1186, 200, 975, 762, 626, 1797, 362, 968, 444, 1260, 961, 1550, 1310, 933, 1585, 1465, 639, 1847, 1748, 262, 1170, 1696, 1972, 1849, 1879, 1799, 339, 1855, 1851, 1463, 1446, 1605, 1847, 333, 552, 1165, 1855, 501, 1088, 249, 1451, 1703, 1763, 622, 1924, 640, 1845, 1373, 170, 558, 1845, 1417, 1876, 821, 863, 486, 1427, 1675, 1767, 1937, 1174, 1623, 955, 1638, 1261, 1224, 1155, 1136, 684, 1999, 878, 363, 1080, 1759, 1783, 1771, 610, 1847, 1494, 87, 891, 1504, 1730, 1749, 849, 1570, 763, 1413, 1110, 811, 110, 1702, 317, 1062, 1444, 1940, 1226, 415, 1767, 1016, 533, 1152, 563, 1819, 555, 366, 1134, 1984, 1698, 1855, 1997, 564, 1579, 1857, 1857, 12, 1088, 321, 882, 1761, 1861, 1612, 1212, 1097, 1845, 168, 1689, 1779, 1531, 1150, 1759, 1910, 1757, 1857, 1129, 1365, 1879, 555, 1799, 769, 379, 1429, 1728, 1845, 665, 860, 51, 48, 1849, 889, 1769, 1404, 537, 488, 49, 1226, 1332, 92, 1372, 925, 1067, 1196, 1628, 1855, 339, 1108, 1610, 812, 265, 569, 342, 1857, 1857, 1532, 1515, 247, 1195, 1382, 157, 1849, 1855, 1342, 771, 1861, 249, 1783, 1569, 1682, 310, 1861, 1996, 969, 314, 1771, 878, 512, 1769, 540, 1503, 1758, 1845, 1200, 1569, 727, 1763, 1861, 431, 436, 1324, 1855, 1465, 1020, 30, 818, 1204, 1726, 251, 1029, 1381, 1766, 1455, 234, 1779, 25, 867, 833, 1855, 684, 1799, 1569, 551, 1855, 1730, 932, 14, 1829, 1376, 1729, 785, 942, 1016, 944, 854, 1069, 1181, 1855, 366, 821, 1659, 1747, 241, 1585, 1329, 1224, 1022, 1724, 569, 969, 1855, 669, 1453, 553, 942, 1564, 670, 663, 771, 1112, 686, 950, 1020, 1914, 739, 1471, 581, 888, 1533, 1851, 669, 1448, 1455, 361, 1847, 97, 1816, 556, 30, 1405, 740, 1843, 1706, 1152, 1675, 802, 1783, 112, 1328, 945, 1738, 99, 1999, 969, 1267, 1714, 1999, 1448, 331, 1849, 1773, 1534, 1419, 636, 1999, 460, 428, 394, 1799, 1419, 1144, 1989, 1330, 506, 1860, 1796, 1061, 1161, 1771, 1593, 1299, 634, 1763, 413, 1835, 1763, 1747, 1861, 486, 112, 1779, 1847, 949, 1362, 312, 1771, 340, 360, 176, 415, 1857, 1755, 940, 931, 1847, 70, 30, 359, 911, 1436, 351, 680, 1073, 648, 1761, 615, 28, 1763, 1995, 224, 453, 1851, 1767, 1857, 1861, 1138, 936, 935, 940, 1799, 1401, 1843, 1738, 1741, 1517, 1448, 202, 925, 1025, 1799, 1740, 907, 1071, 1773, 884, 1295, 442, 1146, 933, 1722, 1634, 1847, 1783, 1315, 1773, 278, 1879, 1367, 1417, 1300, 1855, 266, 940, 402, 1625, 241, 1999, 1480, 672, 1656, 1999, 996, 837, 627, 1779, 166, 1773, 1845, 1142, 1112, 1988, 968, 442, 756, 256, 287, 884, 51, 1589, 886, 739, 526, 1120, 1236, 1726, 756, 920, 1073, 1078, 686, 851, 1222, 884, 169, 1448, 1282, 1728, 120, 776, 1589, 108, 1851, 1779, 1737, 1975, 1797, 1771, 1455, 447, 415, 1419, 1080, 1861, 647, 1855, 187, 317, 1617, 703, 924, 1763, 1159, 57, 1769, 1799, 1827, 1168, 1049, 385, 1603, 1202, 606, 346, 1825, 1297, 647, 1851, 1779, 1849, 1122, 1871, 1559, 1857, 1212, 1799, 955, 162, 1838, 1999, 1410, 1937, 1756, 505, 318, 1508, 1740, 1724, 1999, 1797, 1617, 1587, 986, 489, 720, 1587, 479, 957, 471, 837, 1656, 51, 1594, 1654, 940, 1726, 820, 320, 616, 950, 1851, 251, 1174, 1212, 1740, 1405, 189, 1623, 1639, 87, 1779, 1449, 383, 637, 1154, 1463, 1761, 1795, 54, 1175, 302, 709, 1589, 261, 1843, 1767, 1977, 1404, 1419, 1677, 1204, 1250, 1561, 1704, 1818, 335, 1698, 1728, 551, 612, 1845, 1405, 42, 1771, 99, 1871, 1465, 1404, 1517, 1058, 709, 1979, 1403, 541, 731, 1086, 1658, 1297, 518, 1942, 1771, 1799, 898, 1847, 1849, 1386, 1861, 705, 504, 639, 835, 627, 1155, 1999, 234, 799, 1743, 1012, 710, 1981, 215, 1469, 1419, 792, 708, 799, 1088, 631, 1783, 1771, 686, 1741, 1350, 1783, 315, 1759, 1845, 318, 1773, 1747, 837, 1855, 1658, 1807, 278, 276, 1999, 1561, 631, 695, 1786, 1453, 1105, 1851, 1142, 986, 1165, 1845, 1398, 1857, 1819, 1378, 1750, 1763, 1434, 543, 287, 640, 1038, 1861, 1471, 616, 1446, 1200, 1133, 1990, 640, 1861, 1451, 951, 1224, 1426, 1202, 58, 605, 1448, 147, 1855, 1847, 491, 1857, 515}

Returns: 462
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Returns: 472
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484, 177, 288, 1618, 1011, 1709, 480, 1462, 733, 160, 283, 1972, 125, 31, 1440, 1463, 1688, 932, 527, 1802, 420, 1273, 1542, 813, 1444, 1721, 1215, 151, 1280, 379, 1565, 920, 1542, 727, 1565, 1999, 1666, 1248, 1348, 46, 487, 523, 164, 1396, 1983, 182, 350, 204, 467, 1783, 338, 1562, 373, 1952, 1862, 1565, 1437, 1525, 1657, 358, 701, 1668, 537, 1289, 1084, 1563, 398, 1395, 265, 1888, 1163, 1342, 1458, 123, 1163, 325, 598, 1157, 1127, 1633, 1517, 1169, 1307, 1814, 537, 1708, 1565, 1118, 1628, 1668, 1614, 983, 1709, 441, 933, 1668, 1925, 308, 1934, 1546, 1280, 1335, 865, 42, 1348, 1593, 1038, 1701, 362, 267, 1872, 1288, 247, 445, 151, 216, 1530, 1565, 606, 1978, 22, 1404, 1626, 1699, 1973, 1563, 439, 360, 153, 1481, 1461, 22, 1697, 1101, 1428, 153, 443, 1671, 60, 135, 1515, 529, 1501, 219, 1961, 304, 72, 1333, 694, 443, 784, 832, 815, 153, 1285, 1628, 1696, 441, 1537, 1701, 1998, 1909, 648, 204, 1333, 589, 1181, 1699, 1947, 151, 425, 1163, 156, 1770, 1808, 49, 1235, 1346, 736, 1360, 857, 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1911, 1054, 213, 1071, 1905, 811, 1224}

Returns: 485
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Returns: 461
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Returns: 495
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Returns: 485
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179, 1565, 1308, 261, 1520, 279, 237, 1820, 1356, 1536, 1353, 1359, 368, 1078}

Returns: 505
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191, 1952, 835, 1149, 1213, 601, 382, 1621, 276, 1983, 1999, 1739, 1823, 1791, 919, 835, 1791, 859, 1525, 1805, 1573, 1581, 1765, 1739, 1733, 675, 1821, 1525, 835, 1823, 1737, 1625, 1821, 207, 1837, 651, 1821, 1581, 1729, 1813, 593, 80, 1573, 1735, 1805, 129, 1735, 1625, 1753, 1757, 695, 1753, 191, 1165, 1543, 1765, 859, 1817, 843, 1509, 1735, 1903}

Returns: 386
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Returns: 473
"((()()())))((())())()()()()(((())())()))((()(((())(()())())()((()(()))((())())(()()())))(())((((()(()(())()))((((()((()))(())))(((())())(())((((())()())(((())()))(((())((())()()())())(())()())((((((())))((()((()()()))(())(()(())))((())(()())))((()(()))()())()))()))())()))))()))))()(((()())()())))(()))))()())()(()))(((()())))()())(((()(((((()()))((())()((()))(()()((()()))())))))))(()))()())()))((()()))))()()))()()(()((((())())))((()(((((())()))))()()(((()()())((()))((()((()()))()()(((((((()))((((((()))())(()(((())(())))())(((()))))()((())(())))((()))))(())))))())()())((((()))))))((())())(((()))()((()())(())((())))(()))()()())(())((()(()(((())))(((((((())))()(()(()()))((()())(()((()(((()(())(())))()(())(()()(()))((()))((((())(()()(()((()))(())()()()(()((()()()((())((((()))((())(())()()))())((()(()))))))()())()()(()()(()(((())()(()(()))((((()))))())()))))))))(()))(())(())()((()))()))()(((()()()()((()(((((()()(()))((()()()((((((())()))))(())(())((()()()(()(((()()())())(((()))(())(((()()))(()()())(((((((()()()()(())()(((())())()(()))()())()()(()))))))()())((((()()(()))())()())()))((()(()())(()))()(((((()((((()())()()(()))())))()()))))())))))()((((()(()(()((()()))((()(()(()((())()((())((((()()())(()(()))())))()())())(()()(())))())()()((())(()((()())())))((()())()())(()()()))))((())(()((((()))(()((())))()))((()))()()((((()()))(())))))))()(())((())(())(()(()()(()()()((()))(((()(())((())((((((())()))()()))))(((((())())))()(()())))))(()()))))())()))()())())((()((((())((()()(())())()(())))()())()))(((((()((())((()((())(()())))(((()(())()()(()(((((()()()(())()))()(())))))((()(())))()())))()((()(()))()(()(()))()()()))()))(((()))((()()(((()((((()()))((())((())))())(()(((()()()()()()())()()()))()()()))()(()((())((()((()()()))(()))))()(())()())))(()()(()())()(()()()(()(()()())))(())())())))))))(()()))()()))(((((())((()())()(()()))))((())))()((()))(())((()())))()())()(()()(()((()()())())))())(((((()((())()())))))(()))(())())((())())(())()(()(()()()))()))()))()()()))(((((()))(((())))"

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714, 1202, 736, 716, 1728, 1315, 733, 76, 1150, 1294, 144, 1460, 994, 1515, 498, 986, 1278, 1460, 1118, 502, 948, 161, 146, 1212, 498, 1510, 72, 504, 1212, 982, 1330, 430, 144, 512, 496, 1954, 952, 76, 440, 72, 986, 1052, 1950, 722, 1784, 494, 948, 144, 1613, 156, 78, 900, 1052, 104, 76, 72, 76, 1258, 1304, 72, 442, 105, 78, 894, 1330, 440, 950, 1476, 718, 1270, 547, 176, 1272, 990, 1202, 1854, 144, 496, 146, 1220, 1769, 1222, 894, 426, 1354, 948, 1206, 498, 1360, 144, 1282, 952, 1024, 176, 948, 946, 512, 1274, 1912, 894, 1288, 1270, 1198, 996, 686, 1962, 1236, 554, 494, 1304, 1270, 504, 272, 78, 144, 146, 954, 144, 500, 1627, 1340, 1512, 508}

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Returns: 336
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1451, 938, 1625, 157, 546, 1793, 1822, 1581, 1789, 1863, 1171, 587, 1759, 461, 1635, 966, 34, 147, 1849, 1793, 932, 592, 936, 1839, 1618, 1781, 1753, 1376, 1797, 1739, 1851, 1490, 1237, 1651, 1894, 1879, 680, 1645, 1897, 666, 1651, 804, 1823, 451, 439, 1651, 402, 1831, 327, 1771, 1863, 439, 1865, 1797, 1879, 1881, 1647, 1769, 1453, 1793, 191, 1170, 979, 111, 1767}

Returns: 441
"(()()))(()(((()()(()(()())()))()))()())())()))(())())()()()(())(((()((())))()))())())(()(())(((()(((((()()))))(((((()))(()))(()(((()(())))()())(()))()())())))((((((())(()())()()))())()()(()(()((()((()))()()()))))()()()))())))()()(()(()(())(()())))))))(())))()())(((()()))()(())()(((((((()()((())))()())(((()())(()(((())(((())(()((())))())()()()))(()()()((()(())(()((())())(()()((((((((((())(()()(()(()(((()))(()()()(()(())))((()(((((())((())(()))))))((()(())(()())((())()()()(((())())))())())()))))()((())))()(()(()((()())))()()))((()()()))()()()))()())(()((((()(((((((())(())())))(((())(((((((()((()(()))))()()(((((()()())))))))(()())((()())()))))()((((((((()()(()((()))()))())()))((())()())()(()())(())))))))(()()()()(())()()(((())))((((()()(())()()(())))(((()())(((()))))()(())()()()))))(((())))))()((()()(())()(()))(((()()()(())))(()()(()))))((()()())))(((()))(()())()()()())((())))(()()))))))))((()))()())(())((((()(())))())))(())(((((()()))))))())((((()((()))))((()(()())))))())))(((()()())))(()(((())(())))())()(()))(())))()()))))())((())())(()))()))))))(())))()))()()((())())))()(()((((())(((()()()()))((())(())()(())()((((()(()()))()()()()())(((()(()))())(()))())((((()(())(())))())(())))(())())(())))))()))(((())()())))()))()())(())())))(())))())(()))))(()())(()))()))((()()((()()())(()())))())(()())))(()()(((())(()))()((()))))()(()()((((()()(())))))()(((()(()))()((()()))())(()())))))())()()))(()(()())((()(((()()))(())()(())))()((())()())())()()(()))()())(()(()())()())(()))))(((((()(()))))()())((()(((()))(((((()())((()(((()(()(()()())()()((()(((((())(()()))))()()((((((()(((()()((())))())()((()(())))((()(()())((((())()()()(())(((((()())(()(())))()))(())))())()((((()(())()(((((())(((())()()(()()(())(()))()))(())(((()(()(()(()()()(()(()(((()()()))))(()()()(()(()()()())((()()())())(((((()))))()((()()))))(()))()(()))(())()(()((()))(()(())))())((((())())(((())))(())))()()))))((()(()()))))((())()(())()()()(()(()))(())))()()()(((()))(((()((((((((())()()()(((())(()((()(((((())()())()))"

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Returns: 495
"((())(()(()))(()))))()())((())(()))())((()))())))(()))())())(())((((()()(()))((((())))))()())()))))((((((())))())()(((())((()(())()((()(((()((())((())((())(())(())(()()()((((()()))))()((()((((()((()))))))))((()))((())(())((()(())()(((())()(((())((()))()))()()())()(()(())))(()())))(())())()((((())((()()())(()()(()()()((((((()))((()()()())())(()))(())(())())))))())))))())(())))((((())((()(())())()(())))()())())()))())))))(()()((()))())(((())(()))(()))(())()(()))(()((()))((((()(((()))((((((()))())((()()(((())))(()(()()())((()((()))))()(()))))(()))(((()())()(()()(()(()))))(((()()()()(()))((()))(()()(())))())())))()((((())(()()()))())()))(())(((()))((()(()(()())))()))())()(()(())())))(()))(((()))))()())())()()(((((((())())(()((((())(()()()(()())()()(((()))()()))()(()((()))()()))())))(()(())(())((()))((()(()))((()(((()()()(((()())(())))())))((())((()(()((((((())())(()()()(((()))()))(()()()(())))((()))()(()))()(()()(()((((()())(()(((())))())))))((()(()())))(()((()(((((())((())(((((()))((()(((())(()(()))((()())(()))((((())))((()((()(((()))))(()(((()(()(()()(((())(())()(()(()(((())))(()(()))((((()))((()()))())))())))(()))(())(()((()(()())()((())()(()()()((()((()))(()(()()()))))())))((((()(()(())())()))())))())))())(()())()))(((()))())(()(()()()()))))(()()))()((()())))(((())(()())(()(())))))()()()))((())())))))()))((((((()(((()())(()))())(()(((())(())()))())((()((()()()()))()(())))())(())())())(()(()(()(()()()()((())))()))((()())))()((()))())))(((())(())())))(())(())())((()()((()())())(()()(()))())()()())(()()())()))))((())))))()(((()(()(()(())(())())(()()())((()(()()))))()((()())(()(()))())(()(())())(())))((())(()))()())())()())()(())(())()(()()()(()()(((()))))())()()((()))()(()((((((((()()())((((()))()()(()())()()))))(())())))(((((())(()(()()(()())(((()())()(()))))()))())((()(()())())()()()))((()())((()))())())(()))()(((((()(((((()()((((())))((()()()())())())(()))()))()(()()()())())))()())))((()((()))))(()()((()))(())())((())))))))(()))((()()()(((()(()()(())(()(()))()))))(("

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1781, 627, 1811, 723, 1722, 1739, 1906, 1681, 1420, 570, 1401, 1723, 1683, 478, 1259, 656, 1486, 1855, 1683, 213, 206, 631, 1449, 631, 599, 1711, 809, 1573, 723, 465, 1378, 1506, 574, 1737, 191, 1817, 1635, 399, 689, 752, 609, 1731, 1999, 1786, 1723, 627, 1741, 939, 922, 681, 1729, 933, 1729, 90, 1378, 1577, 755, 1168, 725, 1729, 939, 941, 262, 1486, 939, 303, 1745, 236, 1741, 1918, 1128, 1571, 1768, 941, 1681, 939, 934, 1577, 532, 57, 1737, 1533, 1968, 1669, 436, 781, 1999, 599, 621, 35, 1015, 1739, 1745, 1999, 263, 757, 1541, 769, 1394, 1832, 1638, 1731, 1741, 941, 952, 159, 693, 966, 939, 393, 1681, 1681, 1681, 1657, 1743, 545, 1747, 286, 1017, 1279, 723, 1188, 1322, 759, 1134, 1743, 941, 1729, 1115, 1224, 1683, 1051, 1677, 389, 444, 1840, 1769, 1743, 299, 887, 543, 633, 1575, 1328, 1571, 1571, 838, 1577, 231, 1743, 1747, 1743, 1729, 941, 1722, 446, 1743, 383, 710, 689, 1183, 1769, 633, 1743, 1149, 1344, 45, 1999, 597, 755, 1729, 621, 1734, 1393, 1723, 1747, 1745, 1999, 1741, 1999, 1737, 1743, 1743, 693, 1999, 489, 1545, 941, 1443, 1681, 852, 1743, 1577, 1771, 922, 1999, 1910, 1729, 1610, 1348, 374, 299, 721, 385, 689, 681, 862, 1910, 1743, 1716, 1524, 1743, 430, 782, 759, 757, 1723, 599, 191, 512, 1449, 399, 1741, 753, 1772, 1948, 1811, 1166, 1907, 1893, 1961, 1891, 1999, 1676, 1729, 485, 383, 755, 1741, 1648, 1505, 1948, 1999, 693, 757, 1860, 1741, 1151, 757, 568, 493, 21, 1370, 1988, 941, 1741, 755, 297, 1588, 1225, 1737, 1597, 970, 1398, 270, 467, 939, 227, 1253, 1542, 1009, 153, 1667, 1452, 1741, 1999, 1138, 1338, 691, 1275, 52, 1180, 1079, 629, 515, 576, 1999, 1743, 753, 629, 992, 941, 1009, 461, 207, 723, 878, 721, 491, 1729, 251, 1138, 1731, 1074, 570, 914, 769, 1745, 1739, 1063, 1544, 1731, 755, 213, 212, 1832, 1999, 446, 1731, 1747, 1177, 878, 535, 769, 1320, 927, 1451, 331, 112, 1702, 629, 799, 816, 626, 570, 606, 753, 1151, 1638, 1741, 1577, 1980, 757, 293, 976, 62, 1946, 1577, 744, 1884, 1737, 1731, 311, 1683, 1471, 1607, 1331, 299, 769, 1723, 688, 275, 681, 515, 689, 285, 759, 759, 1784, 755, 115, 1117, 1747, 941, 1259, 1743, 1747, 583, 1998, 927, 721, 1683, 1165, 1745, 755, 1739, 922, 759, 287, 1585, 1619, 681, 721, 759, 734, 1239, 768, 1747, 1723, 721, 1092, 582, 118, 104, 755, 759, 583, 1912, 599, 759, 753, 1884, 1577, 1575, 809, 627, 1747, 1723, 1556, 1729, 1729, 1573, 1891, 769, 1120, 341, 679, 46, 1188, 45, 1175, 599, 739, 689, 1681, 1683, 263, 911, 1546, 273, 104, 485, 1781, 956, 679, 939, 1571, 119, 1737, 725, 1745, 1153, 1166, 1368, 1681, 929, 215, 493, 32, 550, 1723, 1679, 298, 1681, 599, 1012, 1447, 693, 597, 1729, 1656, 393, 1347, 1928, 611, 922, 1745, 753, 1155, 631, 679, 1745, 1359, 1255, 446, 1585, 568, 299, 1745, 1956, 1996, 603, 137, 1575, 28, 1739, 574, 1225, 691, 721, 168, 1771, 1737, 493, 1219, 721, 1021, 1038, 1831, 691, 472, 1683, 1726, 1523, 1747, 723, 809, 1577, 1729, 769, 895, 759, 623, 1592, 576, 1268, 755, 648, 1279, 1631, 373, 125, 1520, 1511, 757, 1575, 755, 1890, 1272}

Returns: 452
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609, 755, 1032, 585, 893, 747, 1631, 1999, 1167, 751, 1054, 793, 897, 546, 1010, 809, 749, 453, 582, 779, 741, 1385, 749, 741, 1735, 1625, 1902, 779, 1705, 1694, 1735, 1844, 1508, 1737, 1374, 231, 589, 753, 1621, 1919, 807, 359, 1625, 1793, 777, 809, 1627, 1159, 1046, 745, 1996, 575, 1886, 136, 498, 747, 1711, 148, 231, 1625, 607, 429, 1739, 1739, 755, 787, 721, 1793, 546, 1621, 1999, 1080, 1143, 1739, 1178, 142, 753, 1499, 236, 895, 1521, 163, 1288, 1711, 1999, 713, 611, 1498, 1999, 797, 779, 1737, 611, 910, 1737, 733, 1739, 597, 1926, 1739, 459, 1999, 1999, 1840, 1711, 1024, 105, 1833, 20, 381, 1153, 1529, 132, 589, 1017, 1524, 777, 1254, 1735, 1268, 183, 611, 1793, 1573, 809, 1579, 1621, 1273, 1326, 619, 603, 1619, 1617, 747, 1153, 1615, 1621, 150, 1932, 793, 1793, 1753, 807, 1793, 1787, 1230, 1159, 755, 1619, 1621, 1978, 1055, 950, 787, 791, 793, 77, 741, 1753, 1944, 797, 1906, 148, 1858, 797, 1441, 1981, 809, 1554, 1566, 1822, 1627, 1786, 741, 228, 331, 619, 968, 1735, 799, 1617, 323, 1720, 797, 1787, 1711, 1793, 1693, 733, 1547, 220, 755, 472, 222, 755, 1230, 793, 1723, 560, 1056, 666, 793, 304, 1009, 779, 564, 749, 1237, 138, 799, 1723, 733, 755, 587, 831, 1330, 1844, 809, 1723, 1142, 1737, 1627, 1572, 1723, 751, 1540, 1115, 1615, 799, 1631, 1548, 1077, 551, 1617, 1855, 791, 632, 1210, 1039, 753, 680, 741, 619, 336, 1113, 240, 222, 488, 619, 1080, 126, 912, 607, 1723, 1619, 787, 311, 1188, 1603, 1138, 947, 1711, 137, 779, 583, 1735, 787, 1630, 749, 1116, 1627, 1243, 609, 1617, 1753, 575, 603, 1625, 1723, 1142, 897, 1846, 1723, 1986, 1381, 1548, 809, 932, 154, 309, 813, 733, 779, 1793, 1461, 1621, 135, 1737, 1842, 1329, 1631, 1822, 621, 122, 1617, 1615, 390, 799, 1981, 707, 51, 1598, 1188, 1610, 1753, 912, 378, 1735, 578, 1449, 1666, 336, 787, 1523, 705, 1313, 753, 809, 1615, 799, 1631, 791, 337, 1508, 1999, 797, 749, 490, 382, 793, 1615, 232, 751, 1631, 850, 1142, 1986, 809, 1032, 1735, 1753, 1142, 1957, 587, 1739, 741, 111, 1793, 897, 587, 473, 1621, 751, 1735}

Returns: 462
"(()()(((()))(())((()(()((()())(()((()((()()(((((())))())()()(((((())))))()())(())(((((()((()()()(()()(((()())))(())))(())()()(((()))(((()(((()(((())()()((())))(((((()))()())(())()()(()((())(((())()()())))(()))()(()()()(()())((()))()((((()()()(()(())((())()(())(()(()(())))())()((()((((()(())())))((()()))(((()()()(()()()))()())(((()))())()(())((())())(())))))(((()((()))()()((((())(()))(((())))))))))))()())())((())(((()())(())((())((()())))()())()))(())(()((()(()()))()))))))(((((()(())())((((((((()))(())())(((()))())))))())())))()(()((((((())()(()(()(())()))(()))))((()()(()))(())(()())())))))))))()(()(()())((()()())(()))(((())(()())()))())((()((())))(((()()((()())(()(((()))()(()((())()(()()((((((())())()()((()))()())(((()())())((((((())(())((((())()((()()(()()((()(()((())()()((())())(()(()))())()()))(())()()()()))())()()))(())()))()))(())((())))))()))))((((()(((()())))))))(()()((((()(()()((((())()((()()(()))(()((())()(())((((((()))))()()((((()()((()))))))())((())()(((()()()())(())())())())((()()())(()()))))()))())())))((((((()()))(())())))((()())((((()(()()((()(()))())(()())(()((((()(())()((()(()(()()()())))(((()())))())()(()))))(((())(()()()(((()()()((()((())))()))((()()))))))(()((()())(((()(()))()((()()(()(())())))()()())()))))))()((((((()()()()))))))(())())())()(()))(((((()((()))(((((((()(()))())(()))())(()(((()((((()()(())()())))((((()())((())()))(())(()))()))(()((())))())((()(())))())(())((()(((()())(())()))()()))()((()()(((()())()()))(()())()))()(()))((())(())())))(()()))()())))())())))(()))))((((()((((((((())))()())()))())(()((())()()))()(())()))()))(())(()))((()(()((((()(()((()))())))))))))()(()))))))))))))(((((()())))))()(((())()()()((((())))))))((())())())(()(()(())(()()()()()(())))))))())((()(()(())()())))((())())()()())()))((()))(())(())())))((()(())))))(()((()()())))()())()((())))(())(())())((((()()())((()()()()))())()((()))()))())))((()(()))((())))))((()(((((()(((()(((()(())))(())))()()()()(())))))()()))(((()((()))()))()))()()(()))(())()())()(()((()))()))"

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762, 345, 1764, 90, 1544, 398, 262, 1737, 95, 548, 286}

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Returns: 464
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444, 341, 1600, 1219, 325, 315, 231, 351, 1533, 666, 39, 125, 902, 238, 321, 1497, 1124, 866, 1903, 598, 717, 1713, 337, 1591, 1982, 264, 120, 1025, 1732, 291, 345, 637, 351, 28, 1659, 644, 1271, 1584, 1147, 55, 319, 857, 315, 1241, 305, 239, 1998, 1436, 1100, 904, 1975, 312, 1954, 1059, 1, 341, 224, 1099, 325, 239, 333, 1852, 1375, 1377, 404, 1519, 317, 1502, 1212, 53, 1790, 513, 668, 351, 267, 1950, 998, 249, 1282, 249, 1341, 333, 1535, 1313, 818, 317, 633, 562, 351, 887, 39, 648, 1397, 251, 1334, 333, 95, 345, 1584, 234, 951, 1667, 1799, 861, 1173, 267, 1672, 7, 890, 650, 345, 1574, 831, 1515, 1580, 1059, 1964, 51, 337, 1565, 1578, 53, 1495, 787, 1937, 895, 1550, 510, 1144, 535, 12, 315, 1601, 403, 325, 490, 390, 321, 436, 315, 870, 1936, 419, 28, 1057, 124, 1584, 1991, 1710, 842, 245, 191, 703, 325, 1082, 1157, 321, 245, 1945, 431, 1415, 1901, 1587, 351, 341, 1094, 239, 345, 995, 89, 285, 578, 59, 1044, 1999, 337, 1636, 849, 713, 935, 1816, 1786, 1767, 337, 1072, 34, 1165, 845, 443, 1110, 1487, 245, 124, 1173, 599, 1262, 508, 315, 122, 349, 166, 1933, 263, 717, 1812, 319, 485, 349, 1444, 635, 745, 1182, 1056, 1077, 343, 1827, 1955, 1538, 317, 1596, 1171, 265, 1071, 1212, 1714, 761, 748, 1003, 1689, 251, 75, 239, 319, 1599, 51, 581, 1404, 1478, 267, 321, 761, 1135, 1117, 1244, 613, 1668, 1839, 1508, 668, 1695, 315, 341, 217, 321, 289, 1238, 319, 887, 245, 299, 1600, 1254, 524, 505, 349, 1250, 773, 1124, 249, 1173, 906, 1507, 1417, 267, 158, 1935, 835, 343, 948, 265, 1177, 886, 289, 1078, 1288, 1809, 1341, 1179, 1011, 349, 325, 437, 1990, 255, 113, 1032, 631, 1548, 125, 1343, 285, 927, 1208, 1301, 345, 1547, 1958, 289, 39, 1903, 1674, 171, 1942, 37, 265, 923, 341, 341, 142, 97, 321, 1212}

Returns: 482
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Returns: 493
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1859, 815, 1130, 1721, 1341, 1156, 543, 862, 176, 896, 623, 172, 835, 1064, 1292, 354, 593, 540, 1905, 1985, 1512, 269, 1214, 222, 711, 647, 111, 1445, 417, 917, 861, 1937, 1913, 182, 1943, 713, 1087, 1391, 1240, 1057, 1959, 49, 1439, 1122, 1367, 335, 1153, 1409, 741, 675, 210, 97, 851, 1325, 1386, 1472, 401, 1258, 1472, 90, 1644, 181, 95, 678, 1360, 504, 667, 1257, 362, 1875, 715, 221, 268, 168, 542, 1321, 101, 250, 1020, 1355, 1199, 1283, 1972, 1105, 743, 292, 791, 643, 831, 371, 580, 680, 556, 1931, 1907, 307, 1104, 819, 656, 745, 268, 1437, 752, 1735, 308, 1944, 1576, 776, 1180, 222, 1111, 1381, 817, 1331, 1881, 1905, 1893, 310, 1179, 1992, 368, 475, 279, 1145, 1281, 28, 1782, 616, 1520, 317, 1267, 1081, 663, 1430, 1975, 1311, 1683, 1507, 1556, 832, 134, 212, 214, 1877, 1887, 1157, 481, 800, 1062, 464, 1371, 1389, 1419, 196, 668, 168, 1708, 1932, 593, 1180, 62, 1417, 1362, 971, 1648, 1270, 1684, 439, 1217, 816, 1908, 838, 1957, 215, 126, 916, 633, 852, 868, 291, 1992, 819, 172, 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1290, 1391, 1773, 602, 1366, 1242, 1294, 1105, 519, 869, 28, 1166, 89, 183, 646, 918, 1361, 1733, 180, 471, 1581, 625, 1060, 359, 1792, 1725, 1865, 1893, 1043, 659, 1315, 1512, 141, 1157, 1942, 1643, 458, 84, 699, 1487, 164, 278, 786, 852, 1037, 1866, 491, 746, 911, 1861, 1893, 224, 1786, 1068, 1980, 1179, 248, 1535, 1168, 1733, 1685, 1907, 1782, 888, 835, 1243, 544, 142, 1778, 187, 1589, 766, 1910, 1108, 250, 901, 928, 1464, 1579, 747, 1471, 1333, 1681, 1559, 1050, 185, 188, 1611, 840, 1859, 1492, 1577, 1268, 1150, 826, 1062, 840, 1616, 39, 1482, 248, 155, 1978, 1408, 1887, 711, 1950, 1658, 1523, 1265, 274, 1250, 1351, 1043, 587, 1131, 1576, 1466, 913, 1977, 1600, 1258, 197, 1907, 1429, 1419, 1316, 521, 1905, 764, 170, 1536, 1139, 593, 1954, 1247, 1737, 50, 354, 1148, 892, 1214, 403, 1454, 1253, 778, 222, 1252, 1080, 403, 1626, 187, 1167, 487, 1998, 1524, 85, 1211, 1292, 1502, 1866, 1169, 110, 358, 1121, 1697, 1835, 170, 166, 106, 559, 446, 1043, 1725, 1421, 418, 1107, 1388, 1294, 309, 1045, 1212, 979, 707, 675, 669, 1977, 208, 1333, 718, 1088, 1926, 1321, 267, 561, 699, 1399, 419, 312, 559, 1033, 1977, 1521, 1313, 945, 1946, 1653, 471, 1536, 389, 1556, 1701, 1663, 1581, 1771, 1479, 1458, 1118, 1683, 700, 833, 1430, 255, 149, 20, 151, 121, 266, 55, 998, 1152, 1035, 1592, 436, 1629, 423, 48, 1445, 131, 447, 600, 267, 1331, 1570, 1084, 1707, 1947, 1935, 1650, 1292, 339, 1456, 815, 894, 1035, 1719, 1177, 132, 591, 1114, 352, 205, 656, 1392, 1108, 268, 46, 1929, 1652, 141, 913, 135, 720, 12, 1938, 1935, 1912, 1306, 797, 1530, 1777, 1920, 1905, 1340, 1952, 1549, 189, 106, 1341, 886, 1493, 395, 1708, 1731, 1448, 1945, 1705, 1803, 1989, 1406, 663, 1574, 1109, 1179, 1721, 568, 715, 1719, 1121, 462, 1725, 1737, 66, 1452, 1735, 1928, 1650, 1679, 1179, 280, 317, 663, 408, 224, 1993, 520, 928, 1307, 667, 1915, 1044, 1569, 853, 661, 1362, 1472, 814, 395, 296, 887, 1294, 571, 224, 633, 542, 142, 1330, 399, 1725, 248, 1037, 1418, 1040, 837, 607, 1423, 743, 1464, 1064, 549, 1707, 1867, 1212, 477, 377, 1130, 1786, 196, 1098, 131, 791, 944, 666, 435, 1999, 762, 766, 1992, 669, 873, 1333, 104, 458, 745, 914, 1596, 1536, 1558, 1021, 1989, 423, 1870, 105, 127, 1458, 1153, 1458, 810, 1582, 697, 1108, 832, 1183, 1149, 629, 316, 655, 89, 713, 265, 1816, 686, 1091, 561, 1684, 1018, 1469, 528, 1885, 734, 627, 1628, 1752, 669, 1735, 1524, 115, 609, 41, 129, 684, 1237, 1658, 715, 1342, 562, 1976, 896, 1907, 386, 1838, 546, 323, 1912, 905, 381, 423, 1651, 1893, 1847, 1510, 1576, 1568, 642, 1323, 638, 1775, 969, 151, 633, 1929, 1616, 766, 1494, 1996, 1721, 1863, 1942, 1708, 1964, 1993, 1108, 1902, 1149, 1002, 1661, 665, 931, 404, 1840, 1649, 589, 1715, 1891, 1615, 837, 1036, 1443, 1582, 705, 105, 248, 1419, 567, 960, 1786, 1881, 1347, 1088, 182, 1456, 1839, 268, 1387, 462, 1341, 1055, 1967, 745, 1558, 1889, 1549, 1668, 233, 136, 1577, 1985, 1880, 294, 168, 1737, 301, 1698, 312, 1177, 391, 1046, 1907, 447, 1550, 652, 34, 1472, 165, 986, 915, 401, 1443, 435, 438, 172, 37, 50, 933, 1284, 1041, 1997, 1528, 1265, 1548, 869, 1107, 213, 1855, 1250, 1683, 1173, 756, 1104, 824, 1592, 857, 563, 1673, 526, 1841, 1776, 1698, 1979, 740, 500, 349, 1121, 1562, 1289, 235, 268, 1908, 938, 1770, 634, 1804, 235, 709, 202, 375, 1377, 309, 1623, 833, 1423, 1943, 1582, 1756, 1943, 1260, 1330, 1238, 663, 1889, 392, 933, 1153, 1421, 1083, 652, 966, 286, 1709, 708, 1135, 868, 661, 873, 1545, 1033, 1492, 384, 1558, 833, 1784, 256, 627, 1983, 400, 1421, 1985, 1554, 1675, 1208, 1285, 1572, 161, 1988, 1004, 633, 1980, 1930, 629, 1080, 1445, 1863, 66, 1263, 1656, 629, 1481, 115, 1883, 1267, 1279, 1382, 1560, 1904}

Returns: 514
"(())()(()(()()))))))((((()())(()())))()(())))())())()())(())))())(((())))(()())(()((())()(()(())())((()()()(()))()())(((()))))))(())(())()()()(()())()))()(()((((()())()()))(()(((())(()(()()(()()))))((()((()())(())))()))(((()((((()((()()))((()))))))((())())()())))))((((()(())))(((()))(()(())())(()()()())(()()(())()()()(()()()((()))(())(()))()))(((()())())((()())(()()))()))((()))()(()())(()))(()))(())(()(()())))((((()))())())()()(())()()))(((())(((())))))())))(()))()(((()(()()()))()((()((())())()))))()()(())()()))))(())()(())))(())))))))()())()()()(((())(((()(()))((())(((()((()(())())((((()))()(((())()()(((((())())()()))(())))(()())()()(((())(((((((())))()((()()()))()(())))()())((()()()()(())(())(()()(()())((())(()()())(())()()()()(())))()()(())(())()()(())(())(()())(())))))))))(())((())))((((()()()))(())())())(()((((())((()(((()(((())))()()))()))())()())((())((()())()((()))()))(())))))))(()()((((()()()((((()()(((()())()(((((((()(()())(((())((())))(()(())(()((()))(((())((((()))))(())()))(())((()())())()((())))))))(()()())))(()(())()))))()())(()(((((()))))()))((()((((())((((()(()()()(((()()()())))))()((()))()()((((()))()()()((()(()((()(((()()(()(()()()))(()()(()()(()())((()))))()))))())))))(()()))())((()()()(()))()()(()(())())()()()((()())())()()((((()(()(())))(())(())(((((()(()()()(())((()(((()())(()())))))))))))(())((((()))))()))))())(()()())())(()((((())()()))())))(())()((()(()(((()))((((((()()))(())())()))(()))())(()(()))(((((()())()))(()((((()))(()))()((()()()((((((((((()(()(())()(()()())()))(())(((()(()))())((((()))()(()()((((((()()))(((()())())()(())()))))()))))(()(())()()))()((()())()()))))())))()(()))(())))((())))(((())((((()()(()(()))))((()()((()())))()))()))(())))))()()((()((((((()())((((((())())))())()(((()))())(()()))())))()(())(()()))()(((()()))(())(()))((()()((())()((())()(((()())(()()))))()(()()()()((((()())()())(()()())()((()())()((()(()))))(()))()(())())(())))())))((()((((((((())))))))))))()(()())()(((((((())()()()())(((()))((())((()((()((())()())()))"

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554, 51, 1705, 587, 609, 1865, 1987, 1827, 528, 1607, 757, 184, 1134, 1462, 1720, 1395, 947, 809, 1123, 1052, 957, 1472, 1494, 1967, 748, 805, 1479, 1647, 1560, 1209, 127, 1097, 1695, 1082, 857, 1386, 1578, 182, 1190, 1959, 546, 1481, 1117, 1125, 1446, 1343, 828, 1789, 537, 1410, 91, 1557, 391, 1337, 301, 212, 1328, 805, 1792, 51, 1006, 435, 1876, 753, 1140, 1016, 863, 1697, 184, 1580, 1112, 843, 1610, 1228, 1433, 1883, 1664, 261, 475, 847, 1980, 981, 1094, 1711, 403, 1778, 1308, 367, 1695, 1297, 862, 1984, 570, 926, 1176, 753, 1629, 507, 1971, 1687, 789, 1888, 1546, 1919, 1284, 887, 832, 1459, 518, 70, 1228, 1168, 1767, 232, 1815, 1207, 904, 276, 1312, 1963, 1982, 1869, 1975, 1752, 757, 626, 1002, 307, 1016, 94, 1176, 649, 850, 1436, 1982, 1276, 35, 1293, 1993, 1725, 1629, 505, 733, 796, 786, 1431, 1144, 1704, 731, 170, 1126, 748, 643, 1888, 1591, 1413, 1974, 359, 523, 661, 890, 1898, 182, 1296, 1145, 1996, 1424}

Returns: 498
"))(())(((()()()((()())()()(()(()((()))((())(())(()((((((()))()))))))())(((()))))(((()((()((((()))))()((())))(((())()()())()))()()))(()()())(((((((()()()()(()(()((())()()))()()))()())))))))()))())())((())(())(()))()())(()((((()(((((()(())))()(()(())((()(()))))))()()(()())))(())))()(((((()())()()(((())()())))())())))))())(())()()(()()))(())))()()())(((((((((((((()()(())(()()((()())())(()())))))()()()((()))()))(((((()((((())((()((()())()(()((()()()()))()(((())()))()))())((()))))())()()(()()(())))))))(((())()(((())(((()()))((()((())((((()()))((()))((()()()((()((()()(()))(()())))))()))())()((()))()))()))((()()())()((()))(()))((()))())()))(()())(())()(())))()()((((()()(()(()((())())(()()())))))()))((()(()()()))())(((()())((())(())(()())())((()(()))())))()(())())((((((())(()))()())((()())(())()))(()((())()((((())()((((()(((())()())()())(()))())()))))))()(()()((((()())())())((())((()((()()())(((())(())((()(())()((()()()()())(())())(()()((()()((()())((()(()((()))())()))((((((((()()(((((()())())())))()()())))(()()((())))()))())))))()()))()))()))(((((()()()))())((()()))()))(()()((((()()))(()()())()(()()())(()()()(()()())(()((())((()))())((()()())())))()()))((()()()(()))())()()((()(())())())()()((()()(()))))()))((()))(()()())))))))))))(())))()())(()()())(())))((()))))())()((()())(((())()(()))(()()()())()()()())(((()((()())(((((()()(()))))())())()(())))(()()))))(()))((()(()))())(()()(()))))())()((((()()()((()(((()((()(())(((()(((())))(((()))((())()((()()(())))))(())((())()()()(())))))(((()())()))(()))(((()))(()())(()))()))()())(()))(()))()()))())))((()()()()))())))()))(()())())())()()()(((())(()()((((())(()((())(()(((())())())((()(()()))((()())((())()))((((((()())(((()())((()(()))()()))())))()))()()((())())))))()((())())())())))(((()(()()))()())())(((()()(()((())(()(((()())())((((())()())()())((()()(()()(())(()))(())()(((((()(()((()(())((()()()))()(()()((()(()())()()()()(((((((()(()()())))((())()((((()))))))(())(())(((())()(())))(((()(((()))))()))())()(())())()()(((((()))())))))"

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1539, 601, 1334, 999, 872, 970, 1247, 1362}

Returns: 511
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Returns: 412
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418, 1435, 1082, 1149, 1486, 1149, 1165, 667, 1145, 678, 562, 903, 457, 1773, 1629, 251, 925, 1878, 273, 923, 1149, 1104, 694, 1576, 620, 1513, 1852, 1656, 715, 1746, 754, 312, 987, 1745, 1725, 1269, 917}

Returns: 471
"())((()(((()()())()(()()())))())(()))())())()(())()(()()((())()))()))))((((((((((())))()(((()(()))()(()(())())(())))))((()))())())(()())(((((()()(()(()))(((()))()(())))()((()())())((((())()))())))((((())())((()())(())(())()())()))()))(()()((((())()(()))))))(()((()))(((((()))()(())()())))((()())))(()))(((())((()))(()())()()()())()(()((())()(()()((((())))()))()((((()(()()(()((())())))))(((()((())())(())()()()))(((())()()((((()())()()((((()(((()(())())())(()(()))(((()((()(())())(()))())())()))((()(()))((()()()(()())()))))()(()))(()()((())()()))(())()))((((())))))(())())((()))))())()((()))(()()))((((())()()()()()()(())(((()))((((()()))()))(()())()))()()))()))(()()))())((()))(()()))))()(()())())())())()(()()))()()(()(((()(())()()((()(())((())()()(()))()())(((()()(())))()()()()))()())))(((()))((()))()())((())())))((()(((()()))())))()())(()(()()(())()(((())))())())()))))())(((()(()(((()(((()))))())()()))(()))()())()(()(()()())(()()(()((()()(()()(()(((((())(())(())))(((((()((((()()((()(()((((()(())()((((((())))))()))))(((((()())()((()(()(()))))()(()((())))))(()())((()))()(())()()((()))))())))(()(())())()((((((())(()())))))((())(())))())(()()(())()()((((()()())()(()()()((()))(()((())()(()()(()(()()())))((((())(()))))(()(((()(())()()((((())())())((()())))))())))(()))()()()()((()())(()()((()())((()()(((())(())(()()())())))(()(()()())))())()()())(((((((()(())())()())()))(())))(())((()((()()(()()((()()))(())(((()())))())()())(())((()()(())())))(()())()(()))(((()(((())()()()))(((()(((()()(()(()))())()(())())(()))()))(((()))((()))()((())(()))()()))()((())())()))))()((()())())((()()(((()))())(())((())()))(()(()())))((()()((()()()))())()()(((()))())))(()())()))))())()))()(())))((((())(()())((()()(()()()((()(()))))(()))))()())))((()))()())()()(())(((((())))())(())(())())))))((((()()((()))))(()(()))((())())))()))()((()((((((()(((((())))()((()()(())))(((()((())()()))()((())())(()))()))(())))()()()()()(((()()((()((())(()()(()(((()))((()))((()"

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344, 534, 1483, 209, 612, 43, 1043, 834, 929, 341, 1435, 872, 1230, 1266, 242, 608, 1706, 756, 1204, 1932, 81, 1406, 685, 1068, 418, 1341, 1314, 1086, 1654, 1583, 0, 813, 1262, 216, 1323, 199}

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1508, 124, 1651, 1675, 1940, 1468, 1737, 1497, 925, 1901, 1488, 461, 818, 4, 1394, 141, 1504, 1449, 1148, 875, 1617, 1080, 1455, 867, 1398, 1809, 1862, 214, 1938, 363, 539, 1664, 214, 865, 44, 1044, 837, 940, 1724, 1458, 873, 1475, 1305, 251, 887, 1719, 761, 1213, 1933, 84, 1407, 686, 1069, 461, 1360, 1315, 1087, 1655, 1636, 11, 818, 1335, 257, 1324, 214}

Returns: 484
")(((()())())(()(())((()())()()()(()()())((()))))(())))()((((()((()(()))(()(((())()))))())))(()(())())()(()))())))((((()()))(())(()())()))))(()((()))))((())((()(((((()()()((()))())())())(((()()))))()()(()()(()()())))()()((((((()))(()(())((((((())()())())()((((()(((()())(((((())(()))())((((()()())()()()((())((()()())(()())((((()))((()())))()))()))()))())(()()(()()(()(()()())))))(((())()(()()))((()(((())(((())()()(())())(((())((()()(((())())(())()))))()))()()((()()((())((((()))()((((((()()))())()(()(()())(()()((((()))(()(()))(()(()((()(()))())))(())()())(())((()((())))))()()((()((()((()()()((()()(())())()((((()())())))())()()()())())(())())(())())(())))))())))()())())(()(())()))(((())))(())()()()(()((())()))())()()((())()()()))()()()))(())(()))))(())()()(()))())))()()(((((((((()()))((())()))(())()(()))(((())(()()))()((())(((()()()((()(()(()))())()((((((())()())))))((())()()()()))())((()(())()()((()((())((()))()())()))()())()(())(())()((((()()))))(((()()))()((())))))))(((()(((()))()(()(()()(())))(()((((())((()())))))))()(()((())((((((()())()))(()((((()()(())()))(())(((((())())))(()(()())))()))())))()()())(())()))()((((((()(((())))((()((((((()())(()((())()((())()())()(())))(())())(()))))(()(()))(()))(((())(()))(()))((((()()()()((()()))())(()((()))))()))))()()())((((()(())())()((()(()((()(())))()(((((()))(((())(()((())((((()())())(()))()()(()(((()))()))()()()((()((()))(()((()()((((())))(((((((()()(()()()())))(()())(())()())(((())())()()())((()))((())(()(((()))(()(()()((()()()((())()())(()(((()(()))()))()))(())(((()))))))()())()(()((()))))(())())()((()((()(((())(()((()(()(()()())))(()))))())()(()))((()(((((())()((())(((()(((()(())(())(())())(((((((()))()()))))()()()())(()(((()((()(((())()((((())()())))()()((()))()()())((()(()()))(((()()((((())((()())(()(((()()())(()(()()((())())(((()())()(()()()))))(()()((()))((()))())()(()(((()))))))(((()(())()(()())((()())()))(()))(()()))())((()()((())((())))())))((()()(()))(())))(()))((())()("

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1040, 151, 363, 1235, 786, 848, 600, 857, 538, 1041, 1768, 243, 31, 1595, 1224, 197, 1665, 1632, 1390, 1472, 946, 1815, 459, 1681, 987, 244, 1370, 1577, 272, 835, 458, 1668, 768, 1802, 1036, 1603, 815, 919, 840, 783, 572, 1060, 1660, 1330, 1521, 629, 527, 1778, 636, 1472, 996, 756, 1357, 756, 1256, 1232, 1483, 1203, 1099, 987, 1580, 572, 410, 1401, 1566, 1382, 1321, 419, 1526, 870, 1432, 922, 1688, 655, 872, 314, 733, 458, 1714, 1806, 1082, 149, 1034, 1296, 837, 1648, 825, 1472, 689, 607, 1368, 1308, 1642, 1192, 647, 1047, 1782, 456, 1433, 885, 1232, 17, 1657, 688, 944, 1942, 1341, 546, 681, 700, 1177, 1578, 763, 700, 1045, 1603, 154, 1032, 1195, 1551, 983, 1181, 748, 644, 1939, 748, 1686, 513, 1753, 356, 1832, 174, 260, 188, 779, 1655, 631, 496, 1093, 585, 1720, 1288, 732, 836, 282, 596, 1533, 756, 836, 1461, 1058, 1160, 349, 183, 1717, 375, 1751, 950, 446, 133, 167, 1271, 1530, 1760, 814, 334, 1800, 932, 467, 798, 1762, 1381, 239, 1846, 1292, 952, 162, 1769, 1838, 1436, 1651, 363, 1848, 1603, 1798, 1053, 374, 1110, 933, 1597, 1451, 1731, 1513, 1800, 285, 1582, 1155, 281, 1858, 1246, 692, 350, 189, 652, 1011, 1490, 1433, 1648, 1020, 1565, 1846, 1561, 1101, 1264, 1850, 825, 564, 1583, 1236, 1629, 1060, 334, 930, 1687, 91, 518, 1925, 332}

Returns: 489
")(((())(((()))(((((((()()))()(()))()())))())(()()()))))))))())(())(()))(()((()())))(()()((((((())()((()((()()((((((((())(()())((())(())()()))(())(()(()))))()(((()(())(())(()())()))))()())()(((()(())))()(())))))(()))((())((()((()(()((())())()()((())))())))))())((((()()))(()())())(())())())))()(()((()())()())()()()(())))((()()()()((()(()(())))))))))())(((()())(((()))((())(()()))())))()))(()))())))()(((())))))()((()((())))((((())))()())((()())())((((())))())()()()()(()()())(()()()(()()(((((((()())(())(())((()((()((()(())()())()(()(())()((((())((((()))()())())()()(()))()((())))())(()))())))((())(())))()))()(()(())(()()(((()))))(()))))(()())))))(()()()))))()))(((()))))((()((()(((()((()()()(()))())()((()))())))))((((()())()(()()(())()))((()))((()))(((()())))()()(()()((()((((())())(()()(())()()())()((()()())(()())(())(())()(((()(())()))(()))((()()))))())))(((())((()()))())())())(()))((()()))))(())(((()(((((())))((((()(()()(((((()))))())())()(((()(()((((()))))()(((()()()(()()()(()()))(()))))()(())))))))(((()())(())))))(())((((())(()())()()((()(())))(()()(()(()((())((())(()(()((()))))(()())(()))))())))()))((()(())())((()()((()((())(()(())(((()())((((())(()))()(()()))(((()((((((())))())))())()(())))(())()()))()(())))())((())((()()((())()()((((()(())))(((())((()()(())())))(((((())(()((()))())()(())((())()((())())()((()))())))))()))))()(()(())))(()))(((((((())()))(()()())()(((()()()()))(()(((())))()()()(((()))))))))((((()()(()()()((()((((()())))((()))(())()(()((())((())(()((((()())))))()(((()))(((()((()())(((((())(())()()))(())())))()()())()()()))()(()()()()())()(()(())))()()(()())()))))()))))))())))()(()((()()))(()(((()()((()()((()((())))(()))())(())((()(()(()))))())((((((()))(()))(())))(((())())))())((())(()()((()))()()))))((())())))((()())(((()))(()((()))())))()(()((((()())((()()((()()(()()(((()((())((()()())(())((((())))))))()))(())()()((())(()(())((((((()(()))((())))())(())))))()((()(()())((()()(()(()))())()(()()((())())))((())("

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Returns: 454
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424, 1351, 112, 326, 431, 108, 329, 853, 1064, 1793, 1299, 1570, 227, 1159, 997, 1536, 1787, 1532, 1898, 820, 221, 949, 419, 1478, 921, 1289, 188, 1467, 1900, 1436, 1057, 727, 943, 1832, 1394, 750, 766, 211, 683, 1790, 1431, 286, 1060, 436, 1020, 23, 179, 1047, 803, 1183, 1536, 308, 1188, 1846, 1524, 343, 1655, 372, 1815, 146, 594, 1400, 108, 1604, 800, 194, 643, 423, 1355, 1034, 943, 1505, 450, 559, 802, 1414, 1453, 1190, 1351, 1803, 822, 196, 706, 1343, 997, 608, 860, 192, 3, 892, 776, 1394, 243, 1442, 314, 1445, 983, 979, 1001, 892, 992, 1438, 103, 318, 511, 919, 910, 942, 211, 1053, 1424, 1293, 1888, 1777, 428, 689, 553, 999, 1937, 452, 1039, 851, 1341, 472, 160, 1569, 737, 1337, 1120, 1570, 135, 1167, 173, 1123, 1342, 328, 949, 905, 581, 1877, 1771, 1189, 1106, 949, 1762, 504, 669, 311, 66, 248, 903, 98, 414, 1279, 705, 364, 63, 1330, 741, 663, 1337, 999, 927, 923, 138, 1846, 1751, 333, 421, 1394, 945, 1906, 1690, 945, 1692, 1019, 462, 131, 581, 1290, 615, 1442, 1684, 1293, 986, 1538, 131, 324, 331, 1001, 852, 340, 187, 1839, 612, 1329, 838, 121, 1710, 971, 1269, 677, 1297, 1172, 1458, 1670, 945, 254, 962, 1721, 851, 996, 326, 92, 870, 706, 124, 1167, 927, 766, 723, 1034, 86, 209, 1716, 1629, 1839, 1933, 1885}

Returns: 496
")(()(())))()))(()((()((((((()(((()(())(())())))()))(()())()(((((()))((((()))))))()()())(()))())()(()(((())(()()))((())())(())()()()(((()((((()()((((()(()((((((())))((()()()()((()()()()((()()(())(())())(((())()())()((()(()(()()())()(())(())()())()((()()()(()()))())())()))()))(()())()()(())(()(()(((())(((()))(()(())((())())()()()()()(((((()()))(()()(())(())())())(()(((())((()))((()(())(()))()((((()(((((((((((((())((((())(())))((()())())()()(())())))))()))))()(())))(())(()((((((())(()()())()))()(((()))()(()))((()((())(()))))()())(())))))(()(((()())(()()()())())((())()((((((())((())))()))))((())(())))()()())()(((())((((()())))()()((()))()(()((((())(())(())(()((((())()()((((()(((((()())(((())))(())()())(())()(()()))(()(((((((()))()))))))(())(()))())()())))))())(()()))))(()(()()(())))(())()()()()())()()((()))(()))(()(((())(())))))((())())())()()))((()()))((())))((((()))))))))((())))(()))()))(((()(((())(()))))))(((()())()())(((())()((((()()(()))((((())((())())(((((((((())(())()))())))))(()((()))))(()()(()()()((()()(()((()()))))))(((()((())())()(()((()()((()))(()())())))))())()((()))())((((()(()()())((()))()))(()()())))))))())(())((())))))(()(()))()))()))()((()(((())()(())())((()()(()())))(((((((((()()()))))(()))))())))(())))))(()())((()(((()(()((()))(())))()))())())()())(())())((((()))())())(())(()))))())))(()(()))()())())(()))(((((())(())())(())((((())))(()))())((((()()())(()())))(((())))(()(()))(()()())((()((()(((())))(()))())))(()(())()()()((())())(()()))))())(()))())(()()()))(()))()((()((((((()()(((()()()()))(((((((())))()))()())))()(((())))))))))))()))(()()(())))()()))()))(()()()()())((()(())))())))))()()))((()(()())(())())(((())()()()(()())))(((()))(()))()()((((()(()))()(()())()))((()())((()((()()))()(((()((())(((()(((()()((()()()(()()))))()((())()))(()()(())()((()()()(((())()))((())))((((((()(((()()())))()()))((((()())))(()))()()())))))))(()))()))))(())(()()))()))(()(())()))(((()))()())))(()(()(((((()))))((())()))())((((("

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Returns: 362
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Returns: 407
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44, 943, 1906, 941, 736, 787, 1605, 459, 325, 791, 17, 335, 613, 1056, 943, 865, 943, 1915, 751, 923, 919, 935, 921, 919, 751, 869, 842, 937, 1701, 921, 949, 965, 813, 463, 795, 943, 249, 686, 943, 557, 917, 807, 873, 935, 1178, 308, 933, 943, 791, 937, 647, 101, 1306, 869, 590, 1023, 780, 873, 635, 921, 929, 1328, 339, 795, 917, 945, 633, 791, 208, 921, 1468, 1847, 1822, 829, 921, 757, 239, 751, 869, 323, 1550, 795, 289, 813, 927, 1499, 813, 1948, 302, 1456, 639, 1850, 873, 949, 1326, 805, 1397, 1575, 1041, 162, 339, 1082, 1705, 869, 227, 865, 805, 935, 717, 489, 557, 651, 757, 939, 605, 762, 1397, 568, 1893, 1885, 751, 869, 1472, 1885, 305, 1244, 788, 73, 791, 949, 945, 757, 1680, 933, 842, 825, 612, 647, 793, 873, 643, 933, 829, 635, 732, 357, 1001, 239, 529, 613, 939, 1771, 809, 935, 805, 877, 1397, 937, 921, 921, 933, 929, 941, 941, 33, 1827, 949, 937, 150, 1650, 683, 873, 466, 1390, 1490, 647, 709, 927, 813, 1271, 791, 1397, 1558, 921, 789, 1018, 494, 225, 545, 551, 929, 490, 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178, 927, 1497, 1397, 717, 317, 829, 651, 919, 540, 1774, 1031, 176, 927, 929, 645, 927, 1024, 1712, 1047, 869, 100, 1599, 1567, 711, 428, 733, 1892, 1849, 305, 1850, 178, 639, 1207, 923, 773, 825, 645, 639, 1885, 825, 809, 917, 877, 323, 829, 645, 1653, 1317, 715, 1608, 865, 733, 1140, 1277, 949, 933, 789, 1379, 1779, 557, 937, 805, 865, 937, 1270, 325, 807, 357, 294, 1199, 545, 797, 329, 1361, 945, 873, 795, 943, 1280, 757, 537, 809, 791, 703, 711, 929, 633, 98, 503, 945, 797, 825, 244, 927, 873, 715, 939, 635, 751, 1923, 355, 795, 493, 445, 1859, 750, 795, 1381, 1143, 339, 112, 1892, 829, 1774, 635, 1901, 876, 56, 1711, 933, 793, 1212, 715, 935, 935, 733, 1200, 941, 557, 943, 795, 919, 825, 466, 805, 647, 337, 873, 869, 937, 187, 949, 751, 941, 1718, 865, 795, 825, 5, 791, 344, 733, 927, 416, 865, 647, 55, 1360, 877, 789, 639, 937, 1507, 945, 793, 249, 631, 807, 935}

Returns: 384
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Returns: 412
"))))))())(((()(()(()(()((()()(()((()(()((()())()(())))(())))))(()))))(())())(()(((((()()))))()))))(()()(()()))()))))))(((((()(()()))()(()))()))))((()))(()((((((((()(()(())(()()(()(()()()))))(())))))))(()()))())(())())((((()(((()()()()))()((())())((()((()))((())()((((((()()()())(((()()())((())())((()))()()(((())))(((()()())((()())(()((((()(()()()())(()(())))))(()(((((()((((()))))(())))()(()((((()(())((((()(((())))))))((())()())()))()))((()())(()))()(((()()())(((((()(()(())()((()(()(()))(((())()))))))())))())((()))(()())()))()()())(((()()()))(()((())((((((())())(()((((((()))))(()(((())()(()()(()((()((()(()()))()(())((((()((((((()(()))))(((()(((()))))(()()))))()))()())))())))))((((((())()()(())))())))()()))()()()))())())())))))()))((((()()(((((()(((()()((()()())()()(())(())((()(((((((()))()())))())))))((())))(()())(()((())))()(((())(())())(()))(()()(((((((()(()(()()))()()()()))(()()(())()()(())))((()((())(()()))))))(((())))((((()()())())())))(((()()))(()()))))((()()(()()())()()())())(()(()(()))())(())(()))())))()()((())((())(()(()(()()))))((()(((()(()((()))))))()))()))))()()((()()()(()(()()((()))()()))()())())))()(()()((())(()))()))()(())()()(((()()()())(()))(((())()((())())(()(((()()())(())(()()()((((())((()()(()))()()())))()))())))(((()))()()())(()))((((((()))))(())))()()())()()))(()))()())((())())))())(())())()))()(((()(()())((())()))()()))((((((())())()))()())))))))))()((((()((()(()((())((())))()((()))()(((((((((((()))(())))())())))()(())(())))(())))(())())(()()))((((()))))((()((()))()()()))()((((()))(()(()))((((()(((()))())(())()()))))())))))())(()()())))(()))())(())()(()(((())(()((()()())))(((()))()))()((((())()(())())()))()(()())((())(()((()()))(())))))(())())((()()()()())(((()()(()))(()(())(())))(())(()()((())(())))))((())))))))))(())(()())()))((((()()()()(()((())()((()((()(()((()((())(()((((((()))()())())()())(((()())())(())()(()())(()))()(()(((()())))(())()((((())()(()))((((()(((()()(()())()))(((()))((((((())))))()"

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481, 75, 138, 1137, 1331, 1636, 1385, 506, 274, 230, 1527, 1115, 31, 495, 1331, 304, 513, 1637, 495, 1391, 1158, 1527, 1383, 1137, 1527, 1108, 427, 1029, 1596, 1345, 1319, 1131, 513, 296, 1860, 1385, 407, 1345, 495, 667, 387, 1866, 1178, 1421, 980, 387, 1151, 1081, 417, 441, 401, 1383, 1113, 489, 403, 1139, 1634, 1113}

Returns: 399
"())())()))(())(((()))((((()))())()((()))((()))(()()())(()))((((()))(()(((()))(())))))))()))()(()))()())((((()(((())()))))()())()()())()))))())()()((())))()))())()(())))))))(())))))))(()((()()))())())())(())((()())))()(((())))()()())())()(((((()))())(()())))(((())(((((())))))()))(()()(()()((()(()()())))))()((()()(((())))))))((((())((((())(()((())()()()()((((((((()())()((())))(((((())))((())()((()((())()())()()())())())))))))()())()()))))))((())(((((((())(((())()())()))(()(()()))))))())))))()(()))())())())()(()((())((())))))))())(()))(()(())))())(((())()(()(())()()()))()()))()(()())(()()))()(()()((()(()()(())(())(()(((()(())))))((()((()((()(((()))))()()))))(((((()(((((()))()))(((())()((()))()(()))(()())(()))(())(())((())((()()))((()(()))((()()))(()((((((()))())(((()((()((())(()(())))()))()())((()(()((()))))))(())))()(()))())()(()()(()(())))())((())))))((())(((())((()())((()((()))((()())))(()(())()()))())(((()((()((()())))(()(()((()()())()(((())(((()(()(((((())((((())))(())((())))()))((())()()((()(()(((((())())()())(((((((((((())))(()())))()((()(())()))(()))())()()())(()))()(())((()()()())((((()(()(())()))(()(((()()()())())()))))())())()())())))()(()())())()))(((())(((()()()(()()(()))(())(()()((((()((())))())))())(((()(((((((())())))))((()()((())())))))())(()))()(()(((())())((((()((()))()))))((((((()(()(())()))))))()))(())()))()(((()(()())()()))((((((((())((())))())))(((()((()(()()()()((()())((()())()(((((((()()(((())())(()((()))(((((())(()((((()(()(())(()(())))())))))))(())(()()((()))))())())(()))()(((())(((())))(((())()())(()()()(((()()(((())(()()((()()())())())(()))()()))()())))())))))(()(()())())()))(()))())((()))())()))))()((()())(())((((())(()(()(()))))(()))())()()((()()(((((())((()))()))(())(((()()((((((())(())()()()(())())(())(()(()))((()(())(()((())(()((())())))()))(()()()(((())()))()))()())()())(((()()(()))())()))((((()()))(()(((()))(()))))())))((((()((((()()))))())))(())(()())((())((())()()()(()()))((())(((()))))("

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Returns: 405
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627, 1625, 1341, 1621, 880, 1106, 682, 641, 521, 1797, 482, 1398, 287, 1683, 1625, 523, 1423, 1219, 1267, 824, 713, 253, 535, 727, 1714, 417, 1842, 271, 529, 1621, 860}

Returns: 466
"(()))(()()(()(()()))))))())))))())))()())(((())((())((()((((()(()())())(()()(((((()())(((()((((())()())))))((((()((((()))))(())))(()((())))))()))()()()))(((()((()(((())())(((())()))())))))(((((()(()((()())(())))()())((((((((((()()())())(()(()(()(((())(())()(((())()))))))(()()()()))((()))()))))()))())))(()((()(()))()()())())(()()))((((()()())(((()))(((()(())((()()(((())(()(()((()))()()(((((()))()((()(((())((()(()(((()))((())))())(()())((())(((())))(()((()()()((()()()()(((()()(()((()()(())()))(((())()))()()()()())()))())))()))()()(()())(()()))(()())(()(((())(()(((((()(()(()(())))(()(()))(()(()()()(()()(())(()())))()))()()()))()(())()(()(()()(((((()())))((()())()()((()())(()))((((((()))())))(())))((()(()))()((()(())()()())))())()(((((((((((())()()()())()())()((()))))()(()())())())()(()(((())()()((()()()()(()()()))()()())()(())))()()))))()))()(()((())))())(())(())))))(())(()(()(()())))))))())())())((((()()()()()()()))))(()())(()((()())((())(()(())(())(((()()((()(())()())()(((((())))()(()))()((())(())()()((()(((()((()((())))(())()())(((((()())))(()(()()(()))(()))((()))))(()())()))((((((()())()(())()(())))((()()()())())((((())()((((()(()())))((())))(()))))(())))))()(()())()()(())(())(())()((()(()(()((()()()((((((()())())))()()((()((()(()((()()))(()()))))((((((((())))()))))(())())()()))))))()(((()))())()(()()))))((())(()())(()(()))))((((()()()))())(()))))))((())))))()())())))))()))))(()))))()))()((()()(((()))()))()((()()(())(()(()))(()()))()()(((()))()(())(((()()()())())()(((()()()((()))(())))()))()))(()((((()(((((())))))((()))))(()))))(((()())()))(()(())())))())((()((())))((((((()((())()(((()()((((()(()))((((()))())()((()()()))()))))))()(()((()()()))(()())(((()((())()))()())((())(()()()()))))))()((()()()((())(()()())(()())()((()((())())()))((()()())))))(()()(((())()((()(()(((()))((()()()((())()((())(((())(()))()())())))(()))))()(()())(())()()()(())()))))((()))())))(())(()())()(()())))))()())((()))))))()(()(())())()()((())()))(("

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Returns: 422
")))())(((()()()(((())))((()())((()(((()()()(())((()((()((((()((()())())())(())((()()(())())(()))())))()(())()()()(())()()((()(((())()))(()()()(()()())))(())))(()((()(()((()()()))(()(((()())))()())()(((()())(((())(()()()))))((())))())()(((()((()((((())()()((())))()))()(())()((()())()(())(()))(()()(((()(())()()(()((()()))))(()())())()))((((((())()((()())((()(()((())))()(()))(()))()))()((())())())()((())(()))))))(()))(())()((()(()())))))())()((()(()(())(((())))(())())(()())((()()((((((((((())((((((((())))(((()()(()())(()()(()))((())()((()(((())()))))))((())))()(()()((())((((()()()(()())()))((())(()())(()())()()))()(((()))(()(()))(()))())))((()((())(((())))(((())())(())))()((()))))))))()))(((((((()(())((((()()())))(((((())(()(())()(()))))))()()((((((()(()()()()(()(()()))(()))))())))((()((((())))())((()(())))())(()(()))()))(())))(()()())())((((())(((()))))()())))))()()()(())()()))()(())())(())())()))())(((())))()))())())(((()()))))(((())(()()()))()()(()(())()(())()(((())(())()())))((())))))()()())())()()(()(()()((((())())()(()())())(()((((())((()((())(()()()))())(((())(()((())())()()(()()()()))))(())()))()))((())()())())(((()(())))())(((((()))))(()()())))(())()(())()()))(())()())(()))((())((()))()))()()((()()))())(()())()(()()))))))(()))(()))))))((()(()()))(((()(())()))()(())(())))))(()(())))()()((((((()()())((((()())()(((((())()(((())()(())))(()())))))(()((())(((()((((((())(())()))))))))())))(()())()((()))))())((())))))()()())()()((()))))))))))(((((())(((()(()(())(()((())(((((()((())(((((()()))()(((()())(())()())))()))))()(((()))))()((())())()())(()))((()))))))))))()())))(())))())()((((())())()))))(((((())(())(()))))(((()))())())((()(((())()((())(())(())()(((()()(()())((((()()()((())))))((()((((((()(()()(())))))))())()()((((((()())(()()(())()(()(((())((()())((()()))()(()()))()(()))()()(()))(()((())()())(()(((()(((((((()(()())()()()(()((()((())())()((()))()())()()))(()()()())))((())((())(()()))(((()))))()()()((())()((()))())))"

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Returns: 404
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991, 460, 1948, 1609, 1478, 1790, 1235, 605, 312, 1939, 1760, 738, 630, 386, 189, 302, 183, 1816, 1777, 1230, 1382, 152, 1324, 1355, 1918, 469, 390, 284, 257, 294, 564}

Returns: 460
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636, 807, 1185, 1703, 635, 261, 1487, 1530, 1623, 605, 949, 1607, 1347, 237, 1395, 478, 1385, 1609, 1709, 1341, 122, 1324, 115, 122, 576, 658, 235, 1097, 366, 538, 1397, 1377, 1334, 903, 1035, 1041, 607, 990, 496, 1345, 1629, 1451, 1888, 1171, 454, 624, 5, 738, 1415, 91, 1377, 1370, 1203, 1389, 1045, 1377, 1377, 1036, 106, 1166, 1113, 375, 1345, 1415, 223, 1457, 1609, 673, 1389, 1623, 25, 1609, 329, 129, 1125, 1547, 1014, 1609, 1375, 561, 1613, 1371, 1197, 1609, 124, 1459, 1623, 1391, 1183, 305, 297, 209, 1027, 461, 1865, 409, 660, 1302, 1840, 1187, 579, 1609, 1613, 1487, 620, 607, 1371, 1355, 988, 1444, 1903, 895, 1061, 1506, 1519, 1345, 1195, 659, 1436, 1838, 1345, 1799, 230, 1175, 1341, 544, 210, 795, 1923, 1455, 1320, 1461, 1353, 1629, 1380, 605, 1465, 1201, 96, 811, 1655, 1351, 1303, 618, 607, 1524, 722, 1687, 1459, 1459, 1684, 827, 1195, 1389, 1455, 302, 1341, 329, 678, 579, 1375, 236, 1337, 335, 1353, 732, 1809, 994, 355, 313, 1613, 1377, 1201, 1395, 1629, 1181, 1205, 447, 81, 133, 1375, 295, 1455, 1351, 126, 1324, 268, 1457, 1486, 1565, 532, 1205, 1347, 1119, 1609, 1713, 1149, 1353, 1734, 1351, 1391, 1609, 573, 1609, 1849, 593, 1355, 1355, 1623, 151, 950, 1459, 944, 452, 593, 845, 1157, 391, 645, 971, 1355, 1449, 1487, 1292, 1113, 611, 1623, 669, 1371, 1459, 1417, 291, 906, 1709, 809, 1377, 1666, 1375, 1347, 913, 819, 644, 1167, 1623, 1574, 1187, 1549, 1628, 1487, 484, 1335, 1465, 1461, 134, 808, 909, 227, 1487, 204, 1195, 161, 1037, 1717, 1609, 1725, 1201, 863, 1731, 575, 1077, 651, 1879, 794, 1487, 1187, 1183, 1177, 537, 1167, 106, 286, 1417, 1355, 1764, 1417, 116, 1629, 1459, 234, 673, 1375, 1272, 1920, 1613, 587, 1260, 1391, 984, 1677, 1826, 1343, 192, 518, 1878, 1455, 1415, 1124, 1869, 1201, 1623, 1770, 965, 648, 605, 295, 581, 1375, 694, 1341, 1183, 1070, 1613, 1426, 1300, 1613, 1175, 540, 1397, 1080, 1397, 971, 372, 17, 1455, 1785, 1245, 1185, 365, 805, 1343, 736, 1461, 532, 1824, 1629, 156, 1629, 953, 1417, 1395, 204, 122, 883, 149, 1621, 1039, 947, 1538, 1145, 1389, 1389, 1347, 1197, 560, 844, 1936, 602, 1391, 541, 1320, 1878, 87, 1187, 1457, 950, 1294, 341, 1608, 1457, 1162, 538, 921, 1415, 1487, 1447, 1415, 1487, 1280, 1351, 1917, 1457, 587, 1765, 263, 1135, 1459, 1457, 819, 1600, 1417, 1605, 1489, 1374, 1609, 47, 1171, 1351, 749, 210, 1926, 658, 1331, 386, 33, 1391, 89, 1417, 1461, 408, 1195, 1825, 1623, 408, 1345, 1465, 827, 1389, 881, 1613, 396, 492, 546, 1465, 1220, 1157, 1487, 1603, 1838, 1487, 1185, 845, 1810, 638, 1371, 1078, 1953, 1487, 1341, 1455, 1711, 607, 1417, 1343, 1415, 522, 340, 1489, 1487, 1395, 1345, 545, 1417, 1397, 607, 1343, 1580, 126, 668, 1325, 593, 60, 1205, 1011, 1347, 1303, 829, 1351, 1391, 1391, 1415, 1489, 645, 1340, 589, 1608, 124, 1127, 934, 566, 1733, 1455, 497, 1576, 1343, 190, 1900, 1535, 1341, 1187, 1389, 705, 1461, 1629, 1117, 1391, 1181, 878, 1135, 1465, 1415, 1341, 970, 1694, 1797, 637, 1607, 1395, 1174, 818, 1224, 1371, 1205, 1197, 1375, 1569, 1201, 894, 1002, 1397, 1080, 930, 603, 1060, 800, 244, 1185, 1415, 1461, 1391, 1609, 1551, 469, 471, 186, 349, 1623, 1710, 1609, 1415, 398, 1324, 943, 707, 879, 1221, 1795, 1151, 1377, 1587, 1187, 1377, 1459, 1343, 1036, 1351, 1551, 1783, 636, 1629, 329, 1181, 1553, 1738, 1375, 315, 323, 1343, 1950, 895, 266, 112, 1353, 1417, 1459, 1397, 1465, 1613, 1351, 635, 1623, 115, 1004, 1623, 536, 827, 916, 656, 1607, 1347, 1718, 1465, 963, 1684, 1415, 195, 1542, 1461, 1593, 1345, 1883, 862, 1417, 361, 1389, 1848, 878, 1629, 909, 1756, 854, 805, 1417, 1775, 1623, 1223, 379, 915, 253, 1183, 373, 1343, 1609, 1613, 130, 1487, 1332, 1181, 265, 1192, 1201, 378, 147, 1171, 1355, 1397, 124, 891, 748, 620, 1453, 1389, 1272, 1210, 1171, 1324, 1459, 417, 838, 587, 490, 1623, 1389, 1785, 1351, 1375, 1549, 1886, 774, 1014, 1343, 1601, 1205, 1623, 503, 1613, 532, 1389, 194, 607, 1388, 658, 1353, 1639, 1389, 520, 1377, 1487, 1871, 1489, 1347, 1355, 213, 1217, 1737, 1512, 1585, 3, 1395, 1449, 772, 1417, 1459, 1183, 615, 773, 1106, 1546, 1391, 1114, 1201, 97, 275, 1159, 150, 807, 1629, 1004, 411, 1315, 1547, 1177, 1038, 1455, 942, 1609, 1355, 815, 1391, 1613, 1902, 1457, 1175, 1337, 1937, 1609, 1580, 1341, 124, 1465, 1008, 1177, 1676, 1203, 791, 1649, 1135, 1197, 1623, 1397, 66, 1151, 803, 1459, 497, 1480, 1464, 652, 656, 1457, 1851, 1371, 1465, 639, 291, 1859, 26, 1489, 965, 1459, 1322, 1395, 1613, 1629, 1201, 1530, 486, 182, 589, 1600, 1459, 746, 198, 1629, 1205, 1579, 704, 1629, 1351, 76, 518, 1331, 297, 729, 1341, 541, 1044, 492, 449, 816, 194, 1609, 1254, 1203, 285, 1576, 522, 1771, 1704, 1417, 1203, 587, 331, 1415, 1451, 541}

Returns: 418
")))))()(((())(()())((())(()()()()(()()())())((())))()())))(()())))))((((((()()(()())((())(())(()(())()()))()(()())()(((())()))()()(()())(()))()(()(()(()))()((()()(()))))(((()()))((()(()())()())))()())))()(((()()))))((())((()(((()(())()(()(((((())(((())(((((())())))((()()(()(())()())()())))())()()())(()))()))))()((()((())()()))))((()()()((((((())())())(()(((((())()(()))())))))())(((((()))))()(()()))))(())((((()))))()))())))(((((())))((()(()(()()))((()))(()())())(())(((()(()((()))(()))()))()())((())))(((((())(()(())()))))((())(()(()))(()(()((()()))())))((()()(())()()()))()((()(()))())((()))(())))(())))()))()())))(()))))((()()()(())()())()()((()(()(()()))(()))(())())((((((()(()(())))(((()(()(()(())((()(()((((()))(())(()())(()(())(())((((((((()(()))(()())(()()(()))))())((((())()(()))())))))()()(()))(()))(())))))(()())(())((())((()(((())())())(()))()))()(()((()()())))())()))()))))()())(()(((()((())(()()))))()((()))())())())))()(())()))())()(()((((()())((()()()))()()))())()))()(())()()(()(((()())())))))(()())((((((())(()((()((((((()(())()((())()((())())()(()))(()())((()())())(()(((()((())()()))())((((()()()())))()))))())()((()((()())()()(())((()(()(())()(())((((((()))))(()(()(((((())()))()())()((()()()(()(((())(((()()(()((())(((((()())((((((())))((()(()))()))())())))((((())()(()))())())(())((())())))))))()))()())((((()(()()(()()((((((())(()())()(()()())(()()())(((()()()())))(((()())))))(((((()))()())))))))((()))(())))())(()())())())()(((()()((())()()(()())()))))))()((()))(()((())(()())()))(()()()))()()()(((())((((()())))(()()(((()(((()(()))()))(((()((((()(((()()((()))(((()())()))())()(())))))()))))(((()((()((((()()(()))))(())()))())()()()(())(()()(()()(())()))()))((()())))))()())))((()))(()()((()(()())))()()((()()()))(()))(()())()))))(()))()()())))(((()()((()))))(())())((()()))))()((()((((()()(()()(()())()((()(()(()(()(((()()()(()()))())((((((()(((((((())(((()()(()))())))((()))))(())())())(()(()()))(())))))()))))()(()(((()))())"

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1752, 1786, 383, 127, 326, 161, 302, 1768, 1421, 1003, 1671, 1573, 1220, 636, 1372, 1254, 1525, 1887, 314, 1579, 1291, 1865, 1680, 222, 1880, 991, 1558, 520, 1275, 525, 251, 53, 743, 1063, 1577, 166, 517, 1209, 1658, 222, 252, 242, 923, 1109, 1318, 1062, 919, 1665, 1850, 989, 218, 509, 575, 403, 521, 1383, 831, 1772, 329, 511, 721, 310, 1905, 681}

Returns: 481
")()((())((())()(((())))(((()())))))(())())(())())())))))(()(()())))())()(((((((()(((())(()))(((())))))())()((((()())())))()()(())((())))(())()))(((((((()))()(())))()()()))(()()))(())(()(()(()))(()()())((((()()(())())))))((())(((())(()))))))()()))))()())())))))(())())((()))(((((())((()()(()()))(()())(((()(()()(()()))))(()()())(())))(())))))))))))()))()((((()())(((((((()()))(((())(()(())())())(()()((((((())())()()))(()())))))((()()(()()))))())())()())()()(()(()(()(()()(()(()()(())(((((()()(())(((()())))())))((())())()(()(((())((())()((())()))()))()(()((())))))(()()()))((((((((((((((()(((()((()(())))()(()((((((()()()()))())((((((((()(((((((((())()))(()((())()((())(())()())))())(()((())()()))())()))(((()))((((())())())))()))((()(())(()))(((()((())()))())((()()))()()(()))))()()(()()))((()()()()()(()(((((())()())((()))()))((()))(())))))()()((()()))())()())()()(())())())(((())((())()))()()(()(()((()))(()()(()))))()((())()()(()())))))()()()()()())()(((()))()))()()(())())())()))())))(()())((()((())))()(()(())))(()))((((()())))(()((()()(((((()()()))))(()(((()((()(())()))()((()(((()(()()((((()))(()(())))((())(()(())(()))())())))()))(()(()((())())(()())()(()))))()))))((((()((()(())()()())(()(((()(((()(()(()())()(((())))(()(())))()(())))()(()()(()))()()((())(((((()(()()())((()((((((()((())()(()()()()(((((())(()()(()))()()())()(()()))))(()())))))((()(((()()))()((())())())))())())()((()))((())(()(()()())(())()(()())()))()))(()))()()(((()())(((((()((())(()((((()()(())))(()((()))()())(()()))(()(()))((((((()()(()((((())()()((()())()))())())(()))(((()))())((()(()(()(()))))())()()()()))()))((())()))(())(()()()))()())(((((()))))((()())))(((()))(()()()((())((()()(())))())(((()())()()()((((()()()(()())(())())(()((()))))))(()))))())(()((()()))(()((())(()((()))))))()))))(((((((())()((())()((()()())(()((()))()())((())))()))(((()((()((())(())()(((()))))))())(((()(())()))(()()))())))))((()(())(())()()))(((())()))))))))(())()()())()(((()()())(()())(("

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807, 1241, 1779, 605, 589, 859, 1032, 1602, 1157, 1183, 1157, 1137, 90, 1243, 634, 541, 369, 357, 525, 1382, 489, 23, 1135, 1137, 1352, 1127, 963, 1408, 760, 887, 545, 1149, 605, 784, 541, 1135, 1153, 821, 16, 583, 1862, 1139, 791, 1455, 1442, 545, 312, 639, 1803, 587, 1459, 1083, 477, 605, 813, 505, 185, 1192, 1457, 279, 295, 1482, 957}

Returns: 387
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1583, 678, 1733, 712, 179, 1587, 1427, 823, 1673, 1062, 356, 1214, 487, 367, 1863, 1693, 1791, 1605, 1050, 1745, 583, 495, 1587, 544, 246, 1673, 1258, 1735, 1745, 589, 1655, 1088, 1661, 1895, 1271, 1643, 1733, 479, 1583, 1649, 1675, 367, 163, 543, 1712, 1010, 763, 1655, 334, 1770, 357, 357, 579, 550, 268, 543, 1737, 1710, 1609, 1735, 1733, 397, 402, 353, 702, 1745, 299, 111, 1743, 179, 1593, 1354, 158, 683, 1695, 1657, 1649, 1675, 1513, 1953, 1530, 443, 938, 1380, 1488, 1545, 1024, 1297, 1651}

Returns: 406
"())((((((()()(((((()()()((((())()()()(((()))))))()())))()(())((()(()((((((()(()(()((((()())()()()(((()))()))()()()(((())((()()))((()(()()((()())()))((())())())(()(()))(()(()()())()))((((((()((((()(()((()((()(()())()))))))(((((()()))((((()(((())(())()(()(((()())((())(()((()))(())(((()(()())(((()))(((((()(((()())()"

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{243, 300, 58, 171, 134, 123, 96, 304, 261, 303, 125, 141, 293, 307, 46, 163, 169, 300, 92, 202, 258, 211, 266, 9, 303, 171, 243, 235, 156, 291, 65, 247, 204, 104, 154, 55, 116, 292, 32, 292, 122, 245, 300, 295, 92, 282, 313, 238, 122, 223, 239, 153, 120, 105, 154, 77, 146, 46, 251, 305, 294, 221, 167, 218, 49, 16, 247, 190, 273, 239, 192, 153, 141, 308, 122, 231, 34, 134, 137, 243, 283, 243, 103, 267, 245, 31, 7, 295, 129, 55, 34, 2, 308, 297, 235, 204, 245, 41, 132, 298, 79, 259, 247, 216, 256, 235, 301, 102, 215, 145, 32, 151, 119, 41, 252, 245, 156, 154, 156, 303, 139, 243, 186, 149, 219, 165, 256, 51, 182, 227, 46, 256, 247, 42, 16, 37, 72, 142, 125, 51, 114, 239, 169, 313, 184, 255, 205, 235, 171, 293, 197, 171, 163, 165, 311, 141, 242, 292, 255, 259, 142, 96, 165, 288, 45, 177, 39, 245, 146, 273, 300, 312, 123, 35, 151, 80, 223, 245, 52, 167, 293, 95, 285, 252, 10, 223, 171, 286, 169, 84, 120, 300, 79, 218, 122, 154, 156, 36, 234, 312, 36, 29, 257, 299, 52, 296, 95, 298, 63, 42, 313, 85, 169, 247, 161, 139, 91, 156, 90, 303, 285, 247, 68, 207, 248, 90, 311, 153, 154, 221, 184, 53, 169, 301, 120, 55, 306, 23, 258, 309, 253, 221, 171, 297, 146, 245, 167, 156, 25, 278, 247, 172, 260, 142, 88, 271, 308, 36, 300, 247, 34, 31, 9, 247, 206, 245, 235, 185, 233, 64, 239, 93, 232, 192, 52, 310, 223, 282, 39, 53, 111, 219, 3, 167, 52, 239, 116, 300, 91, 302, 24, 239, 207, 243, 26, 233, 313, 146, 288, 281, 307, 41, 243, 125, 14, 220, 310}

Returns: -1
"((((((()(()(()((()()))()()())((()()))))(((()))(()(())(((()(((((())(()((())()((()((((())()()())((())((()(((()(()()(()()(()()((()((()((()(())))))(((()(()()))()()()((((())(((((()()(()))((()(((((()())))()(()(()(())())())()(((()(()(())(()())()())))))((()))((()((()()()(((()(()((()()))))()()))()))()()))()()()))()()()(()"

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Returns: -1
")))))()())))))))))))))))))())))())())))))))(())))))))))))())))))(())))))))))))))))()))))))))))))))))()))))))(())()))))()()))))))))))))))))()))))))))))))())))))))()))()))))))))))))()))()))))))))))))))()))()))))))))))))))())))))))))))))))))))))))))()))))))))(())()))))))))))))(()))(())))))))))))))())))()))))))))))))"

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Returns: -1
")))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))"

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Returns: -1
")))((()))())()(((()((()())()))(()()))())())))))))((()()())())))))()))((((())()(()(()))()))))(())))()()(()))()))(((((()))()((()()))()()())()((()))(()((())))((())())))()))))())(()()()(()()())(()))))))()((()(()(((()))))())(()))())())))(())(((())()))())())))))((()()()))())()))())))))())))))))()()))))))()()(()())()())"

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Returns: -1
")))()))))))))))))))))))())))())))))))))))))))))))))))))))))(()))))))))))))))))()()))))))))))()))))()))(())))())()()))())))))))()())()))))))))))))())))))))))))))(()()())))()))))))()))))))())))())))))))))))()))))()))()))))))())))))))))))))())))))())()))()))()()))((()))))))))))))())))()))()))))))))))()))())))))()())"

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Returns: -1
"((((((())))((((()((((()((((((()()(((((((()((()()(((((()(((()(()((()((((((()(((()((((((()()((((((()(((((()((((((()(((((((((((((()(((((()(((()((((()()(((()(((()))(((((((()(((((()()(((((((((()(((()()(((((((((((())()(((((((((((((((((((((())((()(((()()(((((((((()()((((()((((((((((((()()((((()()((((((((((((((()()()())("

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Returns: -1
")(()()()()((((()(()()())())()))()()))(())()(()((())(((()((((()()))))())))()(())()))((())(((((()(((((()(()((()))(((()(((((()))(((())())(()((((((()(((((((((()((()()))()))))((((()(((())((((())())))()((()(()()((())()))()))))()()(()(())()((()()))((()()))))()((()()()()()()(()())))()()(((((((()(()))((((()()())))((())))("

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Returns: -1
"(())(((((((())(((((((((((((((((((((((((((((((((((()(()())(()()(()()(()()()))((((()(((((((()()(((())(((((((((((()(((()(((((()(()()()(()(((((()(((((()(((((((()()(((()((((((((((((((()(((((())(((((((((()(((()()(())()((((((()((((()(()(((((())())((()))(((((()()((((((((((((())))))(()((()(((())((((((((()()(())(((((((())("

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Returns: -1
"())))))))(()()()))))))))))))))()))))())))()))))))())()()()))))))))))))))))))))()))))))(()))))))))))))))))))))))))(()))))))()))))))))))())))))))))))))))))))))))))))))))))))))))))))()))())))()))))())))())))()))()())()))))))))))))()))))))))())))))))))())))))))))))))))))))())))))())))))))))))))))))))))))))))())))))))"

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Returns: -1
"()()())(()(((((((((((()(())((()()())())((()((()(()()((()()))))()((())))(((()(()()((((()((()(((((()))((())()(((()())(((()(()((()(((()(())()()(((()())())(((()((()((((((((((()))()(((()(((()()))((())()())()()(((())((()(((((((())(())(((((((()()()())()(((())((((((((()))())(())(()((((()(()()((()(((((((()(((((((((((())(("

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Returns: -1
")(()(((())((()((((((())(()(((((((((()(((())()()((())))((((((((((((((()()((((((((((((((((())())(((()((()()(()(()())(())(((()())())((((((((()(()((((()(((()))(((()()()(((()))(((())((((((())((())(()(()(()(()()(()(((((((()())((()((()(((((((())(((((()(()()((((((((((((()(())((()()(((()()()((()))(()(((((((((()())())((((("

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Returns: -1
"))))))))))())))))))))))))))))))))))))))))))())))))))()))))))))))))))))))))())))))))))))))))())))))))()))))))))))))()))))))))))))))))))))))))))))))))))))())))))))()))))))))))))))))))))()))))))))))))))))))))))))))))))))))))))))()))))))))))))))()))))))))))))))))))))))())()))))))))))))))))))))))))))))))))))))))))))))"

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Returns: -1
"()()))))())))))(())))))))))))()))()))))(()))))())))(())()()))))))()()()())()))))))))))))))()((())))))))))((()())))))))()))))))(())))))))))))())()))))))())))))))))))))()))))))))()))))()())))(())())())(())()))(())))))))))))))())))))))))(())))())()))))()))))()(())))))))())()))()())))))()(()(((()(())())))))()))())(()"

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Returns: -1
"(())()))))((()()))))())(()(())))()()()))))(()))))))()()())()()))((()(()))((()))))((()((()()()))())))())))())(((()(((()(((())))))))())))()())()))())))))(())()()(()()()()()(()()))(()()))()))(())()(((((()())()((()())))))((()))()()))(()))())()))()((()(((())))))))())))))))()))))()(()()())())))))))()())((())()))(()))()"

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Returns: -1
"(()))((())()()(()))(()))))))))()(((((()()()()()()())((()(()(())((()(())()()(())(()())()(((((((((()()))()))))(()))()())(()(()((()())())))))))()()((((()(()))())))()))))))()(()()())(()))(())))((((()(()()(()()()())))(())()(((()))))()()))()(((())((((())()()(((((())(((()(()())))(())))()()))))))))())((()(((()()()())(())"

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Returns: -1
")()()((((()()(())))((()(()(()()(()((()(((()((())(((())))((())()(())((()))))(((((((()()())(())(())()((()(()(()((((())(())(((()(())))())((()()()()((())()))(((((((())()(((((((())))())()(((())(())()()()())((()))((()((())(((((()((())((((()()())()()()((((()())(()((()((((()(()(()))(()(()(()())()())(((((((((()()())()())("

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{75, 235, 159, 87, 313, 27, 50, 170, 313, 85, 38, 81, 83, 61, 26, 139, 87, 165, 131, 230, 82, 131, 82, 306, 165, 89, 97, 82, 7, 139, 36, 296, 83, 123, 58, 122, 99, 91, 103, 199, 130, 97, 81, 226, 89, 255, 139, 32, 131, 182, 313, 144, 91, 296, 139, 165, 9, 276, 146, 99, 271, 48, 23, 70, 16, 165, 159, 22, 311, 270, 17, 139, 130, 139, 131, 97, 165, 85, 16, 165, 85, 292, 27, 14, 294, 75, 87, 305, 59, 313, 276, 124, 80, 6, 299, 85, 290, 164, 308, 91, 309, 89, 81, 87, 274, 58, 225, 95, 17, 139, 106, 40, 91, 277, 312, 278, 313, 139, 174, 9, 204, 208, 131, 130, 218, 99, 61, 91, 99, 3, 290, 228, 165, 38, 97, 126, 91, 227, 313, 115, 91, 131, 246, 304, 202, 73, 27, 97, 99, 295, 72, 305, 27, 235, 97, 307, 56, 131, 111, 87, 165, 97, 211, 156, 71, 56, 280, 99, 126, 9, 165, 139, 47, 146, 17, 136, 89, 23, 153, 80, 232, 302, 97, 291, 298, 116, 40, 157, 149, 164, 58, 97, 312, 57, 139, 131, 305, 54, 83, 306, 17, 113, 177, 87, 171, 260, 232, 313, 91, 78, 78, 17, 165, 11, 130, 38, 303, 99, 40, 91, 266, 116, 301, 235, 85, 137, 99, 22, 131, 230, 312, 27, 124, 89, 313, 204, 159, 89, 153, 139, 131, 148, 131, 179, 215, 292, 87, 160, 278, 23, 32, 116, 11, 289, 184, 36, 184, 131, 165, 288, 23, 129, 114, 17, 124, 139, 242, 99, 159, 165, 240, 277, 11, 313, 97, 23, 99, 85, 97, 131, 292, 232, 247, 180, 23, 313, 87, 81, 180, 313, 157, 305, 23, 82, 104, 113, 11, 313, 36, 313, 297, 130, 85, 139, 304, 99, 284, 3, 40, 148, 85, 205, 228, 181, 85, 82, 165, 99, 27, 152, 38, 313, 83, 130, 87, 89, 303, 126, 308, 83, 27, 310, 230, 165, 123, 162, 80, 40, 139, 306, 11, 313, 131, 27, 193, 313, 233, 297, 83, 304, 293, 7, 99, 233, 89, 131, 215, 64, 139, 97, 30, 206, 208, 242, 162, 9, 131, 165, 83, 91, 76, 164, 89, 157, 259, 181, 165, 89, 139, 83, 214, 89, 280, 76, 233, 179, 148, 99, 126, 59, 165, 80, 50, 85, 82, 280, 91, 313, 305, 87, 97, 78, 194, 119, 87, 205, 124, 99, 193, 191, 292, 97, 91, 96, 313, 1, 138, 313, 224, 165, 126, 89, 20, 239, 83, 232, 106, 61, 139, 7, 235, 35, 91, 43, 300}

Returns: -1
")()(())))((()())((()(()())((())((((()()()()))(()(())))(()(()())((()()(())))(()))()(()()(((()))()(()(()()(()())())))(()(()))((((((())))(()()(()()))()(()())())((()((()(((((()(())())()))(())()(((())())())()))))((())))((()))()))(())))())((()())))()(()())()()())()))())(()()))(()))()(()(())())(()()((((()))(())())((()))"

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{191, 241, 308, 156, 59, 241, 219, 34, 49, 218, 188, 237, 138, 163, 166, 313, 156, 143, 238, 59, 36, 260, 180, 239, 92, 45, 86, 200, 162, 40, 51, 129, 150, 274, 233, 55, 43, 174, 92, 105, 307, 219, 63, 127, 63, 36, 55, 57, 76, 174, 129, 220, 162, 102, 197, 299, 310, 307, 61, 250, 172, 103, 174, 84, 294, 59, 313, 214, 158, 72, 24, 174, 61, 45, 77, 87, 70, 192, 63, 304, 63, 38, 154, 49, 218, 40, 43, 164, 193, 252, 63, 136, 214, 302, 55, 266, 8, 61, 59, 41, 211, 218, 270, 285, 243, 307, 5, 141, 301, 51, 38, 61, 185, 90, 199, 305, 252, 304, 194, 270, 245, 137, 205, 7, 38, 108, 63, 36, 303, 214, 300, 131, 313, 158, 48, 63, 55, 38, 38, 307, 40, 200, 211, 107, 77, 307, 92, 264, 10, 285, 132, 57, 61, 275, 127, 70, 306, 49, 17, 193, 143, 313, 51, 245, 270, 231, 34, 311, 175, 313, 166, 312, 164, 183, 284, 199, 268, 232, 63, 118, 61, 223, 51, 88, 59, 243, 218, 279, 86, 109, 51, 153, 193, 73, 312, 109, 43, 313, 57, 153, 258, 97, 185, 313, 158, 194, 100, 55, 107, 57, 281, 102, 68, 266, 100, 306, 33, 175, 200, 162, 298, 115, 311, 59, 57, 61, 304, 241, 40, 162, 23, 306, 30, 303, 31, 268, 300, 57, 55, 49, 219, 102, 40, 153, 133, 102, 307, 313, 245, 200, 209, 98, 7, 218, 194, 153, 131, 55, 151, 284, 313, 61, 243, 218, 161, 28, 304, 114, 131, 63, 30, 156, 61, 101, 31, 45, 297, 282, 51, 243, 214, 151, 166, 209, 30, 208, 309, 90, 173, 245, 192, 34, 162, 148, 219, 245, 211, 49, 125, 131, 268, 137, 32, 171, 180, 25, 28, 10, 151, 281, 290, 72, 179, 57, 36, 59, 72, 105, 57, 304, 259, 217, 107, 214, 313, 129, 176, 13, 54, 239, 154, 298, 109, 212, 313, 265, 303, 40, 158, 59, 249, 61, 313, 41, 270, 1, 149, 63, 213, 45, 59, 26, 33, 63}

Returns: -1
"(((()()(()))(((((())((())))))))())(()()))))()()((()()(((()())((((()))))())(((())()))))))(((()(()))))))((()(((())))((())(()())(((()())))))())()())()()()()))(())()((())((((()(())))()(()())))))))()(())(((())(())(()()))((()(()))())))()(()((((()(()(()(()()(((()))(()())(())))()(())(()))(()())))))((())(()()()())))(())))"

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Returns: -1
")))((()()()()((())))())()((()())))((()))))(()())()))(()()())((())))(()())))))(()))())))))(()()))())))()))()))))((())))(()))))))))()))))))))))())))())())((())(()()())))())(()))))))()())()))))())())))()(()(())))()()()))))())()(())(()())())))))())))))))))()))))(())))())))(()())))(())))()))))))(()(((()((())()()(()((("

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Returns: -1
"(())"

{0, 1 }

{3, 2 }

Returns: 0
"(())"

{2 }

{3 }

Returns: 1

Statistics

Problem Statement for "ParenthesesDiv1Medium"

Problem Statement

Definition

Constraints

Examples