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Windy is a stupid boy who can only write ABC. Now he has written a string S which contains only ABC and wonder how many string is a good copy of S. A copy is a permutation of S and a copy is good if and only if the distance between the positions of every letter in S and the copy is in a certain range. The range of distance of letter A B C is RA, RB and RC.
The first line of input is the number of test case.
0 ≤ RA, RB and RC ≤ 10^9
For each test case output the answer on a single line. Since the answer may be very large, just output the answer modulo 20090305.
4 1 1 0 AB 1 1 0 ABBA 2 3 4 ABBBABACCBCAABCBBCCC 3 1 5 ABCCCBCABACAAAB
2 4 645716 6660
POJ Monthly Contest – 2009.04.05, windy7926778
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