Sum of Goodness

You are given an array $A = A_1, A_2, \ldots, A_N$ of size $N$. Consider a subsequence $S = S_1, S_2, \ldots, S_M$ of $A$. Let us define the *Goodness* of subsequence $S$ as follows: - Sort the subsequence $S$ in non-decreasing order. - Then, the *Goodness* of subsequence $S$ is the number of indices such that $S_i = i,$ where $(1 \le i \le |S|).$ For example, suppose $A = [ 10, 3, 2, 5,