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F. The Number of Subpermutations
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You have an array a1,a2,,an.

Let's call some subarray al,al+1,,ar of this array a subpermutation if it contains all integers from 1 to rl+1 exactly once. For example, array a=[2,2,1,3,2,3,1] contains 6 subarrays which are subpermutations: [a2a3], [a2a4], [a3a3], [a3a5], [a5a7], [a7a7].

You are asked to calculate the number of subpermutations.

Input

The first line contains one integer n (1n3105).

The second line contains n integers a1,a2,,an (1ain).

This array can contain the same integers.

Output

Print the number of subpermutations of the array a.

Examples
Input
8
2 4 1 3 4 2 1 2
Output
7
Input
5
1 1 2 1 2
Output
6
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].