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;
int n;
int p[2000005], vis[2000005];
long long res;
signed main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
  }
  for (int i = 2, j, k; i < n; i++) {
    if (p[i - 1] > p[i] || p[i + 1] > p[i]) continue;
    j = i - 1;
    while (p[j] < p[i] && j > 0) {
      vis[p[j]] = 1;
      j--;
    }
    k = i + 1;
    while (p[k] < p[i] && k <= n) {
      if (vis[p[i] - p[k]]) res++;
      k++;
    }
    j = i - 1;
    while (p[j] < p[i] && j > 0) {
      vis[p[j]] = 0;
      j--;
    }
  }
  printf("%lld", res);
  return 0;
}
