B'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, ... , n] such that for all (l, r) such that l <= q r <= q m_l , the subarray [p_l, p_{l+1}, ... , p_r] is not a permutation of [l, l+1, ... , 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 <= q n <= q 200 ) -- the length of the permutation. The second line of the input contains n integers m_1, m_2, ... , m_n ( 0 <= q m_i <= q 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. '...