Problem Statement

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:

• 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.
• 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.

How many different sequences of colors of balls can be obtained? Find the count modulo $10^9 + 7$.

Constraints

• $1 ≤ N ≤ 2 × 10^5$
• $1 ≤ X, Y ≤ 10^9$
• $1 ≤ c_i ≤ N$
• $1 ≤ w_i ≤ 10^9$
• $X, Y, c_i, w_i$ are all integers.

Input

Input is given from Standard Input in the following format:

N X Y
c_1 w_1
:
c_N w_N

Output

Print the answer.