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E. Special Segments of Permutation

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou are given a permutation $$$p$$$ of $$$n$$$ integers $$$1$$$, $$$2$$$, ..., $$$n$$$ (a permutation is an array where each element from $$$1$$$ to $$$n$$$ occurs exactly once).

Let's call some subsegment $$$p[l, r]$$$ of this permutation special if $$$p_l + p_r = \max \limits_{i = l}^{r} p_i$$$. Please calculate the number of special subsegments.

Input

The first line contains one integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$p_1$$$, $$$p_2$$$, ..., $$$p_n$$$ ($$$1 \le p_i \le n$$$). All these integers are pairwise distinct.

Output

Print the number of special subsegments of the given permutation.

Examples

Input

5 3 4 1 5 2

Output

2

Input

3 1 3 2

Output

1

Note

Special subsegments in the first example are $$$[1, 5]$$$ and $$$[1, 3]$$$.

The only special subsegment in the second example is $$$[1, 3]$$$.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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