13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T581,

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 $$$10^9+7$$$.

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 $$$10^9+7$$$.

Note

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

Jellyfish and OEIS

Examples