Jellyfish and OEIS
本题没有可用的提交语言。
Description
Jellyfish always uses OEIS to solve math problems, but now she finds a problem that cannot be solved by OEIS:
Count the number of permutations $p$ of $[1, 2, \dots, n]$ such that for all $(l, r)$ such that $l \leq r \leq m_l$, the subarray $[p_l, p_{l+1}, \dots, p_r]$ is not a permutation of $[l, l+1, \dots, r]$.
Since the answer may be large, you only need to find the answer modulo $10^9+7$.
The first line of the input contains a single integer $n$ ($1 \leq n \leq 200$) — the length of the permutation.
The second line of the input contains $n$ integers $m_1, m_2, \dots, m_n$ ($0 \leq m_i \leq n$).
Output the number of different permutations that satisfy the conditions, modulo $10^9+7$.
Input
The first line of the input contains a single integer $n$ ($1 \leq n \leq 200$) — the length of the permutation.
The second line of the input contains $n$ integers $m_1, m_2, \dots, m_n$ ($0 \leq m_i \leq n$).
Output
Output the number of different permutations that satisfy the conditions, modulo $10^9+7$.
3
1 2 3
5
2 4 3 4 5
5
5 1 1 1 1
2
38
0
Note
In the first example, $[2, 3, 1]$ and $[3, 1, 2]$ satisfies the condition.