E. Special Segments of Permutation
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You 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 $[1, 3]$.