You are given an integer n and a $2 ext{D}$ integer array requirements, where requirements[i] = [end_i, cnt_i] denotes that the prefix of a permutation ending at index end_i must have exactly cnt_i inversions.

An inversion in an array nums is a pair of indices (i, j) such that i $<$ j and nums[i] $>$ nums[j].

Return the number of permutations of the integers from $0$ to n $- 1$ that satisfy all the given conditions. Since the result can be large, return it modulo $10^9 + 7$.

Constraints:

• $2 \leq$ n $\leq 300$

• $1 \leq$ requirements.length $\leq$ n

• requirements[i] = [end_i, cnt_i]

• $0 \leq$ end_i $\leq$ n $- 1$

• $0 \leq$ cnt_i $\leq 400$

• The input is generated such that there is at least one index i satisfying end_i $= $ n $- 1$.

• The input is generated such that all end_i values are unique.

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