Description

Input

The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$)  — the size of $p$.

The second line contains $n$ integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$, all $p_i$ are distinct)  — elements of the permutation.

Output

Output the number of pairs of integers $(l, r)$ such that $p[l \ldots r]$ (the subarray of $p$ from $l$ to $r$) is a Decinc array. $(1 \le l \le r \le n)$

3
2 3 1

6

6
4 5 2 6 1 3

19

10
7 10 1 8 3 9 2 4 6 5

39

Note

In the first sample, all subarrays are Decinc.

In the second sample, all subarrays except $p[1 \ldots 6]$ and $p[2 \ldots 6]$ are Decinc.