A12585. The Number of Subpermutations

You have an array $a_1, a_2, \dots, a_n$ .

Let's call some subarray $a_l, a_{l + 1}, \dots , a_r$ of this array a subpermutation if it contains all integers from $1$ to $r-l+1$ exactly once. For example, array $a = [2, 2, 1, 3, 2, 3, 1]$ contains $6$ subarrays which are subpermutations: $[a_2 \dots a_3]$ , $[a_2 \dots a_4]$ , $[a_3 \dots a_3]$ , $[a_3 \dots a_5]$ , $[a_5 \dots a_7]$ , $[a_7 \dots a_7]$ .

You are asked to calculate the number of subpermutations.

The first line contains one integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ).

The second line contains $n$ integers $a_1, a_2, \dots , a_n$ ( $1 \le a_i \le n$ ).

This array can contain the same integers.

Print the number of subpermutations of the array $a$ .

There are $7$ subpermutations in the first test case. Their segments of indices are $[1, 4]$ , $[3, 3]$ , $[3, 6]$ , $[4, 7]$ , $[6, 7]$ , $[7, 7]$ and $[7, 8]$ .

In the second test case $6$ subpermutations exist: $[1, 1]$ , $[2, 2]$ , $[2, 3]$ , $[3, 4]$ , $[4, 4]$ and $[4, 5]$ .