CF1874F Jellyfish and OEIS

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 $ .

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