Cody

Problem 597. The Birthday Phenomenon

Solution 103377

Submitted on 27 Jun 2012 by Aurelien Queffurust
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Test Suite

Test Status Code Input and Output
1   Pass
%% x = 1; y_correct = 0; assert(isequal(bday_phenom(x),y_correct))

sol = 1 y = 0

2   Pass
%% x = 2; y_correct = 0.0027; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 y = 0.0027 x = 0.0027397 y = 0.0027

3   Pass
%% x = 5; y_correct = 0.0271; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 y = 0.0271 x = 0.027136 y = 0.0271

4   Pass
%% x = 10; y_correct = 0.1169; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 sol = 0.9595 sol = 0.9438 sol = 0.9257 sol = 0.9054 sol = 0.8831 y = 0.1169 x = 0.11695 y = 0.1169

5   Pass
%% x = 20; y_correct = 0.4114; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 sol = 0.9595 sol = 0.9438 sol = 0.9257 sol = 0.9054 sol = 0.8831 sol = 0.8589 sol = 0.8330 sol = 0.8056 sol = 0.7769 sol = 0.7471 sol = 0.7164 sol = 0.6850 sol = 0.6531 sol = 0.6209 sol = 0.5886 y = 0.4114 x = 0.41144 y = 0.4114

6   Pass
%% x = 30; y_correct = 0.7063; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 sol = 0.9595 sol = 0.9438 sol = 0.9257 sol = 0.9054 sol = 0.8831 sol = 0.8589 sol = 0.8330 sol = 0.8056 sol = 0.7769 sol = 0.7471 sol = 0.7164 sol = 0.6850 sol = 0.6531 sol = 0.6209 sol = 0.5886 sol = 0.5563 sol = 0.5243 sol = 0.4927 sol = 0.4617 sol = 0.4313 sol = 0.4018 sol = 0.3731 sol = 0.3455 sol = 0.3190 sol = 0.2937 y = 0.7063 x = 0.70632 y = 0.7063

7   Pass
%% x = 50; y_correct = 0.9703; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 sol = 0.9595 sol = 0.9438 sol = 0.9257 sol = 0.9054 sol = 0.8831 sol = 0.8589 sol = 0.8330 sol = 0.8056 sol = 0.7769 sol = 0.7471 sol = 0.7164 sol = 0.6850 sol = 0.6531 sol = 0.6209 sol = 0.5886 sol = 0.5563 sol = 0.5243 sol = 0.4927 sol = 0.4617 sol = 0.4313 sol = 0.4018 sol = 0.3731 sol = 0.3455 sol = 0.3190 sol = 0.2937 sol = 0.2695 sol = 0.2467 sol = 0.2250 sol = 0.2047 sol = 0.1856 sol = 0.1678 sol = 0.1513 sol = 0.1359 sol = 0.1218 sol = 0.1088 sol = 0.0968 sol = 0.0860 sol = 0.0761 sol = 0.0671 sol = 0.0590 sol = 0.0517 sol = 0.0452 sol = 0.0394 sol = 0.0342 sol = 0.0296 y = 0.9704 x = 0.97037 y = 0.9703

8   Pass
%% x = 366; y_correct = 1; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 sol = 0.9595 sol = 0.9438 sol = 0.9257 sol = 0.9054 sol = 0.8831 sol = 0.8589 sol = 0.8330 sol = 0.8056 sol = 0.7769 sol = 0.7471 sol = 0.7164 sol = 0.6850 sol = 0.6531 sol = 0.6209 sol = 0.5886 sol = 0.5563 sol = 0.5243 sol = 0.4927 sol = 0.4617 sol = 0.4313 sol = 0.4018 sol = 0.3731 sol = 0.3455 sol = 0.3190 sol = 0.2937 sol = 0.2695 sol = 0.2467 sol = 0.2250 sol = 0.2047 sol = 0.1856 sol = 0.1678 sol = 0.1513 sol = 0.1359 sol = 0.1218 sol = 0.1088 sol = 0.0968 sol = 0.0860 sol = 0.0761 sol = 0.0671 sol = 0.0590 sol = 0.0517 sol = 0.0452 sol = 0.0394 sol = 0.0342 sol = 0.0296 sol = 0.0256 sol = 0.0220 sol = 0.0189 sol = 0.0161 sol = 0.0137 sol = 0.0117 sol = 0.0099 sol = 0.0083 sol = 0.0070 sol = 0.0059 sol = 0.0049 sol = 0.0041 sol = 0.0034 sol = 0.0028 sol = 0.0023 sol = 0.0019 sol = 0.0016 sol = 0.0013 sol = 0.0010 sol = 8.4042e-04 sol = 6.7925e-04 sol = 5.4712e-04 sol = 4.3919e-04 sol = 3.5136e-04 sol = 2.8012e-04 sol = 2.2256e-04 sol = 1.7622e-04 sol = 1.3905e-04 sol = 1.0933e-04 sol = 8.5668e-05 sol = 6.6891e-05 sol = 5.2047e-05 sol = 4.0354e-05 sol = 3.1178e-05 sol = 2.4003e-05 sol = 1.8413e-05 sol = 1.4075e-05 sol = 1.0720e-05 sol = 8.1353e-06 sol = 6.1516e-06 sol = 4.6348e-06 sol = 3.4793e-06 sol = 2.6023e-06 sol = 1.9393e-06 sol = 1.4398e-06 sol = 1.0651e-06 sol = 7.8495e-07 sol = 5.7635e-07 sol = 4.2160e-07 sol = 3.0725e-07 sol = 2.2307e-07 sol = 1.6134e-07 sol = 1.1626e-07 sol = 8.3450e-08 sol = 5.9672e-08 sol = 4.2506e-08 sol = 3.0162e-08 sol = 2.1320e-08 sol = 1.5012e-08 sol = 1.0529e-08 sol = 7.3557e-09 sol = 5.1187e-09 sol = 3.5481e-09 sol = 2.4496e-09 sol = 1.6845e-09 sol = 1.1538e-09 sol = 7.8711e-10 sol = 5.3480e-10 sol = 3.6191e-10 sol = 2.4391e-10 sol = 1.6372e-10 sol = 1.0945e-10 sol = 7.2865e-11 sol = 4.8311e-11 sol = 3.1898e-11 sol = 2.0974e-11 sol = 1.3734e-11 sol = 8.9552e-12 sol = 5.8148e-12 sol = 3.7597e-12 sol = 2.4206e-12 sol = 1.5518e-12 sol = 9.9063e-13 sol = 6.2966e-13 sol = 3.9850e-13 sol = 2.5111e-13 sol = 1.5754e-13 sol = 9.8411e-14 sol = 6.1204e-14 sol = 3.7896e-14 sol = 2.3361e-14 sol = 1.4336e-14 sol = 8.7589e-15 sol = 5.3273e-15 sol = 3.2256e-15 sol = 1.9442e-15 sol = 1.1665e-15 sol = 6.9671e-16 sol = 4.1421e-16 sol = 2.4512e-16 sol = 1.4439e-16 sol = 8.4654e-17 sol = 4.9401e-17 sol = 2.8693e-17 sol = 1.6587e-17 sol = 9.5432e-18 sol = 5.4645e-18 sol = 3.1140e-18 sol = 1.7660e-18 sol = 9.9671e-19 sol = 5.5980e-19 sol = 3.1287e-19 sol = 1.7401e-19 sol = 9.6301e-20 sol = 5.3031e-20 sol = 2.9058e-20 sol = 1.5843e-20 sol = 8.5942e-21 sol = 4.6385e-21 sol = 2.4908e-21 sol = 1.3307e-21 sol = 7.0728e-22 sol = 3.7399e-22 sol = 1.9673e-22 sol = 1.0294e-22 sol = 5.3588e-23 sol = 2.7748e-23 sol = 1.4292e-23 sol = 7.3223e-24 sol = 3.7314e-24 sol = 1.8912e-24 sol = 9.5339e-25 sol = 4.7800e-25 sol = 2.3835e-25 sol = 1.1819e-25 sol = 5.8287e-26 sol = 2.8585e-26 sol = 1.3940e-26 sol = 6.7599e-27 sol = 3.2596e-27 sol = 1.5628e-27 sol = 7.4501e-28 sol = 3.5311e-28 sol = 1.6640e-28 sol = 7.7957e-29 sol = 3.6309e-29 sol = 1.6811e-29 sol = 7.7379e-30 sol = 3.5403e-30 sol = 1.6101e-30 sol = 7.2786e-31 sol = 3.2704e-31 sol = 1.4605e-31 sol = 6.4821e-32 sol = 2.8592e-32 sol = 1.2534e-32 sol = 5.4599e-33 sol = 2.3635e-33 sol = 1.0166e-33 sol = 4.3450e-34 sol = 1.8451e-34 sol = 7.7849e-35 sol = 3.2633e-35 sol = 1.3589e-35 sol = 5.6219e-36 sol = 2.3104e-36 sol = 9.4314e-37 sol = 3.8243e-37 sol = 1.5402e-37 sol = 6.1607e-38 sol = 2.4474e-38 sol = 9.6555e-39 sol = 3.7828e-39 sol = 1.4717e-39 sol = 5.6851e-40 sol = 2.1806e-40 sol = 8.3042e-41 sol = 3.1397e-41 sol = 1.1785e-41 sol = 4.3909e-42 sol = 1.6240e-42 sol = 5.9623e-43 sol = 2.1725e-43 sol = 7.8569e-44 sol = 2.8199e-44 sol = 1.0043e-44 sol = 3.5496e-45 sol = 1.2448e-45 sol = 4.3312e-46 sol = 1.4951e-46 sol = 5.1203e-47 sol = 1.7395e-47 sol = 5.8619e-48 sol = 1.9593e-48 sol = 6.4953e-49 sol = 2.1354e-49 sol = 6.9621e-50 sol = 2.2508e-50 sol = 7.2148e-51 sol = 2.2929e-51 sol = 7.2243e-52 sol = 2.2563e-52 sol = 6.9854e-53 sol = 2.1435e-53 sol = 6.5185e-54 sol = 1.9645e-54 sol = 5.8665e-55 sol = 1.7358e-55 sol = 5.0886e-56 sol = 1.4778e-56 sol = 4.2512e-57 sol = 1.2113e-57 sol = 3.4182e-58 sol = 9.5522e-59 sol = 2.6432e-59 sol = 7.2417e-60 sol = 1.9642e-60 sol = 5.2737e-61 sol = 1.4015e-61 sol = 3.6861e-62 sol = 9.5941e-63 sol = 2.4708e-63 sol = 6.2955e-64 sol = 1.5868e-64 sol = 3.9561e-65 sol = 9.7549e-66 sol = 2.3786e-66 sol = 5.7347e-67 sol = 1.3669e-67 sol = 3.2206e-68 sol = 7.5001e-69 sol = 1.7260e-69 sol = 3.9250e-70 sol = 8.8178e-71 sol = 1.9568e-71 sol = 4.2889e-72 sol = 9.2829e-73 sol = 1.9837e-73 sol = 4.1849e-74 sol = 8.7137e-75 sol = 1.7905e-75 sol = 3.6300e-76 sol = 7.2601e-77 sol = 1.4321e-77 sol = 2.7858e-78 sol = 5.3426e-79 sol = 1.0100e-79 sol = 1.8816e-80 sol = 3.4539e-81 sol = 6.2453e-82 sol = 1.1122e-82 sol = 1.9501e-83 sol = 3.3660e-84 sol = 5.7175e-85 sol = 9.5554e-86 sol = 1.5707e-86 sol = 2.5390e-87 sol = 4.0346e-88 sol = 6.3006e-89 sol = 9.6667e-90 sol = 1.4566e-90 sol = 2.1550e-91 sol = 3.1292e-92 sol = 4.4580e-93 sol = 6.2290e-94 sol = 8.5329e-95 sol = 1.1455e-95 sol = 1.5064e-96 sol = 1.9398e-97 sol = 2.4446e-98 sol = 3.0140e-99 sol = 3.6333e-100 sol = 4.2803e-101 sol = 4.9252e-102 sol = 5.5325e-103 sol = 6.0630e-104 sol = 6.4783e-105 sol = 6.7445e-106 sol = 6.8369e-107 sol = 6.7432e-108 sol = 6.4661e-109 sol = 6.0232e-110 sol = 5.4456e-111 sol = 4.7743e-112 sol = 4.0549e-113 sol = 3.3328e-114 sol = 2.6479e-115 sol = 2.0313e-116 sol = 1.5026e-117 sol = 1.0703e-118 sol = 7.3312e-120 sol = 4.8205e-121 sol = 3.0376e-122 sol = 1.8309e-123 sol = 1.0534e-124 sol = 5.7719e-126 sol = 3.0046e-127 sol = 1.4817e-128 sol = 6.9011e-130 sol = 3.0251e-131 sol = 1.2432e-132 sol = 4.7684e-134 sol = 1.6983e-135 sol = 5.5836e-137 sol = 1.6827e-138 sol = 4.6102e-140 sol = 1.1368e-141 sol = 2.4915e-143 sol = 4.7783e-145 sol = 7.8548e-147 sol = 1.0760e-148 sol = 1.1792e-150 sol = 9.6918e-153 sol = 5.3106e-155 sol = 1.4550e-157 sol = 0 y = 1

9   Pass
%% x = 4873; y_correct = 1; assert(isequal(bday_phenom(x),y_correct))

sol = 1 sol = 0.9973 sol = 0.9918 sol = 0.9836 sol = 0.9729 sol = 0.9595 sol = 0.9438 sol = 0.9257 sol = 0.9054 sol = 0.8831 sol = 0.8589 sol = 0.8330 sol = 0.8056 sol = 0.7769 sol = 0.7471 sol = 0.7164 sol = 0.6850 sol = 0.6531 sol = 0.6209 sol = 0.5886 sol = 0.5563 sol = 0.5243 sol = 0.4927 sol = 0.4617 sol = 0.4313 sol = 0.4018 sol = 0.3731 sol = 0.3455 sol = 0.3190 sol = 0.2937 sol = 0.2695 sol = 0.2467 sol = 0.2250 sol = 0.2047 sol = 0.1856 sol = 0.1678 sol = 0.1513 sol = 0.1359 sol = 0.1218 sol = 0.1088 sol = 0.0968 sol = 0.0860 sol = 0.0761 sol = 0.0671 sol = 0.0590 sol = 0.0517 sol = 0.0452 sol = 0.0394 sol = 0.0342 sol = 0.0296 sol = 0.0256 sol = 0.0220 sol = 0.0189 sol = 0.0161 sol = 0.0137 sol = 0.0117 sol = 0.0099 sol = 0.0083 sol = 0.0070 sol = 0.0059 sol = 0.0049 sol = 0.0041 sol = 0.0034 sol = 0.0028 sol = 0.0023 sol = 0.0019 sol = 0.0016 sol = 0.0013 sol = 0.0010 sol = 8.4042e-04 sol = 6.7925e-04 sol = 5.4712e-04 sol = 4.3919e-04 sol = 3.5136e-04 sol = 2.8012e-04 sol = 2.2256e-04 sol = 1.7622e-04 sol = 1.3905e-04 sol = 1.0933e-04 sol = 8.5668e-05 sol = 6.6891e-05 sol = 5.2047e-05 sol = 4.0354e-05 sol = 3.1178e-05 sol = 2.4003e-05 sol = 1.8413e-05 sol = 1.4075e-05 sol = 1.0720e-05 sol = 8.1353e-06 sol = 6.1516e-06 sol = 4.6348e-06 sol = 3.4793e-06 sol = 2.6023e-06 sol = 1.9393e-06 sol = 1.4398e-06 sol = 1.0651e-06 sol = 7.8495e-07 sol = 5.7635e-07 sol = 4.2160e-07 sol = 3.0725e-07 sol = 2.2307e-07 sol = 1.6134e-07 sol = 1.1626e-07 sol = 8.3450e-08 sol = 5.9672e-08 sol = 4.2506e-08 sol = 3.0162e-08 sol = 2.1320e-08 sol = 1.5012e-08 sol = 1.0529e-08 sol = 7.3557e-09 sol = 5.1187e-09 sol = 3.5481e-09 sol = 2.4496e-09 sol = 1.6845e-09 sol = 1.1538e-09 sol = 7.8711e-10 sol = 5.3480e-10 sol = 3.6191e-10 sol = 2.4391e-10 sol = 1.6372e-10 sol = 1.0945e-10 sol = 7.2865e-11 sol = 4.8311e-11 sol = 3.1898e-11 sol = 2.0974e-11 sol = 1.3734e-11 sol = 8.9552e-12 sol = 5.8148e-12 sol = 3.7597e-12 sol = 2.4206e-12 sol = 1.5518e-12 sol = 9.9063e-13 sol = 6.2966e-13 sol = 3.9850e-13 sol = 2.5111e-13 sol = 1.5754e-13 sol = 9.8411e-14 sol = 6.1204e-14 sol = 3.7896e-14 sol = 2.3361e-14 sol = 1.4336e-14 sol = 8.7589e-15 sol = 5.3273e-15 sol = 3.2256e-15 sol = 1.9442e-15 sol = 1.1665e-15 sol = 6.9671e-16 sol = 4.1421e-16 sol = 2.4512e-16 sol = 1.4439e-16 sol = 8.4654e-17 sol = 4.9401e-17 sol = 2.8693e-17 sol = 1.6587e-17 sol = 9.5432e-18 sol = 5.4645e-18 sol = 3.1140e-18 sol = 1.7660e-18 sol = 9.9671e-19 sol = 5.5980e-19 sol = 3.1287e-19 sol = 1.7401e-19 sol = 9.6301e-20 sol = 5.3031e-20 sol = 2.9058e-20 sol = 1.5843e-20 sol = 8.5942e-21 sol = 4.6385e-21 sol = 2.4908e-21 sol = 1.3307e-21 sol = 7.0728e-22 sol = 3.7399e-22 sol = 1.9673e-22 sol = 1.0294e-22 sol = 5.3588e-23 sol = 2.7748e-23 sol = 1.4292e-23 sol = 7.3223e-24 sol = 3.7314e-24 sol = 1.8912e-24 sol = 9.5339e-25 sol = 4.7800e-25 sol = 2.3835e-25 sol = 1.1819e-25 sol = 5.8287e-26 sol = 2.8585e-26 sol = 1.3940e-26 sol = 6.7599e-27 sol = 3.2596e-27 sol = 1.5628e-27 sol = 7.4501e-28 sol = 3.5311e-28 sol = 1.6640e-28 sol = 7.7957e-29 sol = 3.6309e-29 sol = 1.6811e-29 sol = 7.7379e-30 sol = 3.5403e-30 sol = 1.6101e-30 sol = 7.2786e-31 sol = 3.2704e-31 sol = 1.4605e-31 sol = 6.4821e-32 sol = 2.8592e-32 sol = 1.2534e-32 sol = 5.4599e-33 sol = 2.3635e-33 sol = 1.0166e-33 sol = 4.3450e-34 sol = 1.8451e-34 sol = 7.7849e-35 sol = 3.2633e-35 sol = 1.3589e-35 sol = 5.6219e-36 sol = 2.3104e-36 sol = 9.4314e-37 sol = 3.8243e-37 sol = 1.5402e-37 sol = 6.1607e-38 sol = 2.4474e-38 sol = 9.6555e-39 sol = 3.7828e-39 sol = 1.4717e-39 sol = 5.6851e-40 sol = 2.1806e-40 sol = 8.3042e-41 sol = 3.1397e-41 sol = 1.1785e-41 sol = 4.3909e-42 sol = 1.6240e-42 sol = 5.9623e-43 sol = 2.1725e-43 sol = 7.8569e-44 sol = 2.8199e-44 sol = 1.0043e-44 sol = 3.5496e-45 sol = 1.2448e-45 sol = 4.3312e-46 sol = 1.4951e-46 sol = 5.1203e-47 sol = 1.7395e-47 sol = 5.8619e-48 sol = 1.9593e-48 sol = 6.4953e-49 sol = 2.1354e-49 sol = 6.9621e-50 sol = 2.2508e-50 sol = 7.2148e-51 sol = 2.2929e-51 sol = 7.2243e-52 sol = 2.2563e-52 sol = 6.9854e-53 sol = 2.1435e-53 sol = 6.5185e-54 sol = 1.9645e-54 sol = 5.8665e-55 sol = 1.7358e-55 sol = 5.0886e-56 sol = 1.4778e-56 sol = 4.2512e-57 sol = 1.2113e-57 sol = 3.4182e-58 sol = 9.5522e-59 sol = 2.6432e-59 sol = 7.2417e-60 sol = 1.9642e-60 sol = 5.2737e-61 sol = 1.4015e-61 sol = 3.6861e-62 sol = 9.5941e-63 sol = 2.4708e-63 sol = 6.2955e-64 sol = 1.5868e-64 sol = 3.9561e-65 sol = 9.7549e-66 sol = 2.3786e-66 sol = 5.7347e-67 sol = 1.3669e-67 sol = 3.2206e-68 sol = 7.5001e-69 sol = 1.7260e-69 sol = 3.9250e-70 sol = 8.8178e-71 sol = 1.9568e-71 sol = 4.2889e-72 sol = 9.2829e-73 sol = 1.9837e-73 sol = 4.1849e-74 sol = 8.7137e-75 sol = 1.7905e-75 sol = 3.6300e-76 sol = 7.2601e-77 sol = 1.4321e-77 sol = 2.7858e-78 sol = 5.3426e-79 sol = 1.0100e-79 sol = 1.8816e-80 sol = 3.4539e-81 sol = 6.2453e-82 sol = 1.1122e-82 sol = 1.9501e-83 sol = 3.3660e-84 sol = 5.7175e-85 sol = 9.5554e-86 sol = 1.5707e-86 sol = 2.5390e-87 sol = 4.0346e-88 sol = 6.3006e-89 sol = 9.6667e-90 sol = 1.4566e-90 sol = 2.1550e-91 sol = 3.1292e-92 sol = 4.4580e-93 sol = 6.2290e-94 sol = 8.5329e-95 sol = 1.1455e-95 sol = 1.5064e-96 sol = 1.9398e-97 sol = 2.4446e-98 sol = 3.0140e-99 sol = 3.6333e-100 sol = 4.2803e-101 sol = 4.9252e-102 sol = 5.5325e-103 sol = 6.0630e-104 sol = 6.4783e-105 sol = 6.7445e-106 sol = 6.8369e-107 sol = 6.7432e-108 sol = 6.4661e-109 sol = 6.0232e-110 sol = 5.4456e-111 sol = 4.7743e-112 sol = 4.0549e-113 sol = 3.3328e-114 sol = 2.6479e-115 sol = 2.0313e-116 sol = 1.5026e-117 sol = 1.0703e-118 sol = 7.3312e-120 sol = 4.8205e-121 sol = 3.0376e-122 sol = 1.8309e-123 sol = 1.0534e-124 sol = 5.7719e-126 sol = 3.0046e-127 sol = 1.4817e-128 sol = 6.9011e-130 sol = 3.0251e-131 sol = 1.2432e-132 sol = 4.7684e-134 sol = 1.6983e-135 sol = 5.5836e-137 sol = 1.6827e-138 sol = 4.6102e-140 sol = 1.1368e-141 sol = 2.4915e-143 sol = 4.7783e-145 sol = 7.8548e-147 sol = 1.0760e-148 sol = 1.1792e-150 sol = 9.6918e-153 sol = 5.3106e-155 sol = 1.4550e-157 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = 0 sol = ...