CF1874F.Jellyfish and OEIS

普及/提高-

通过率：0%

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题目描述

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 $10^9+7$ .

输入格式

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 $m_1, m_2, \dots, m_n$ ( $0 \leq m_i \leq n$ ).

输出格式

Output the number of different permutations that satisfy the conditions, modulo $10^9+7$ .

输入输出样例

输入#1
```
3
1 2 3
```
输出#1
```
2
```
输入#2
```
5
2 4 3 4 5
```
输出#2
```
38
```
输入#3
```
5
5 1 1 1 1
```
输出#3
```
0
```

说明/提示

In the first example, $[2, 3, 1]$ and $[3, 1, 2]$ satisfies the condition.

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