Self-Describing Sequences

You are given a natural number $N$. A sequence $A = (A_0, A_1, \ldots, A_{N-1})$ of length $N$ is self-describing when the following holds for every $i$ with $0 \le i < N$.

$A_i$ equals the number of times the value $i$ occurs in $A$.

Count the self-describing sequences of length $N$.

The first line contains a natural number $T$, the number of test cases. Each of the next $T$ lines contains one sequence length $N$ $(1 \le N \le 100)$.

For each test case, print on one line the number of self-describing sequences of length $N$, taken modulo 1,000,000,007.

For $N = 5$ the only sequence that satisfies the condition is $(2, 1, 2, 0, 0)$. For $N = 4$ there are two, $(2, 0, 2, 0)$ and $(1, 2, 1, 0)$.