{"raw_statement":[{"iden":"problem statement","content":"Snuke arranged $N$ colorful balls in a row. The $i$\\-th ball from the left has color $c_i$ and weight $w_i$.\nHe can rearrange the balls by performing the following two operations any number of times, in any order:\n\n*   Operation $1$: Select two balls with the same color. If the total weight of these balls is at most $X$, swap the positions of these balls.\n*   Operation $2$: Select two balls with different colors. If the total weight of these balls is at most $Y$, swap the positions of these balls.\n\nHow many different sequences of colors of balls can be obtained? Find the count modulo $10^9 + 7$."},{"iden":"constraints","content":"*   $1 ≤ N ≤ 2 × 10^5$\n*   $1 ≤ X, Y ≤ 10^9$\n*   $1 ≤ c_i ≤ N$\n*   $1 ≤ w_i ≤ 10^9$\n*   $X, Y, c_i, w_i$ are all integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $X$ $Y$\n$c_1$ $w_1$\n$:$\n$c_N$ $w_N$"},{"iden":"sample input 1","content":"4 7 3\n3 2\n4 3\n2 1\n4 4"},{"iden":"sample output 1","content":"2\n\n*   The sequence of colors $(2,4,3,4)$ can be obtained by swapping the positions of the first and third balls by operation $2$.\n*   It is also possible to swap the positions of the second and fourth balls by operation $1$, but it does not affect the sequence of colors."},{"iden":"sample input 2","content":"1 1 1\n1 1"},{"iden":"sample output 2","content":"1"},{"iden":"sample input 3","content":"21 77 68\n16 73\n16 99\n19 66\n2 87\n2 16\n7 17\n10 36\n10 68\n2 38\n10 74\n13 55\n21 21\n3 7\n12 41\n13 88\n18 6\n2 12\n13 87\n1 9\n2 27\n13 15"},{"iden":"sample output 3","content":"129729600"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}