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 _{i = l}^{r} p_i. Please calculate the number of special subsegments.

Input

The first line contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ 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].
#include <bits/stdc++.h>
using namespace std;
const int N = 2E5 + 5;
int vis[N];
int n, a[N], s;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) {
    if (a[i] < a[i - 1] || a[i] < a[i + 1]) continue;
    int l = i - 1;
    while (a[l] < a[i] && l) {
      vis[a[l]] = 1;
      l--;
    }
    l = i + 1;
    while (a[l] < a[i] && l <= n) {
      s += (vis[a[i] - a[l]]);
      l++;
    }
    l = i - 1;
    while (a[l] < a[i] && l) {
      vis[a[l]] = 0;
      l--;
    }
  }
  printf("%d", s);
}
