Score : 1000 points
Snuke arranged N colorful balls in a row. The i-th ball from the left has color c_i and weight w_i.
He can rearrange the balls by performing the following two operations any number of times, in any order:
How many different sequences of colors of balls can be obtained? Find the count modulo 10^9 + 7.
Input is given from Standard Input in the following format:
N X Y c_1 w_1 : c_N w_N
Print the answer.
4 7 3 3 2 4 3 2 1 4 4
2
1 1 1 1 1
1
21 77 68 16 73 16 99 19 66 2 87 2 16 7 17 10 36 10 68 2 38 10 74 13 55 21 21 3 7 12 41 13 88 18 6 2 12 13 87 1 9 2 27 13 15
129729600