The Number of Subpermutations

2000ms

262144K

Description:

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.

Input:

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.

Output:

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

Sample Input:

8
2 4 1 3 4 2 1 2

Sample Output:

Sample Input:

5
1 1 2 1 2

Sample Output:

Note:

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 $$$[4, 5]$$$.

Informação

Provedor Codeforces

Código CF1175F