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 main() {
  ios_base::sync_with_stdio(0);
  int n;
  cin >> n;
  int p[n + 2];
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
  }
  p[0] = n + 1;
  p[n + 1] = n + 2;
  int place[n + 3];
  for (int i = 0; i <= n + 1; i++) {
    place[p[i]] = i;
  }
  int res = 0;
  int left[n + 1];
  int right[n + 1];
  stack<int> largeNums;
  largeNums.push(p[0]);
  for (int i = 1; i <= n; i++) {
    bool done = false;
    while (!done) {
      if (largeNums.top() > p[i]) {
        left[i] = place[largeNums.top()];
        largeNums.push(p[i]);
        done = true;
      } else {
        largeNums.pop();
      }
    }
  }
  stack<int> largeNumsRight;
  largeNumsRight.push(p[n + 1]);
  for (int i = n; i >= 1; i--) {
    bool done = false;
    while (!done) {
      if (largeNumsRight.top() > p[i]) {
        right[i] = place[largeNumsRight.top()];
        largeNumsRight.push(p[i]);
        done = true;
      } else {
        largeNumsRight.pop();
      }
    }
  }
  for (int i = 2; i < n; i++) {
    if (right[i] - i > i - left[i]) {
      for (int j = left[i] + 1; j < i; j++) {
        if (place[p[i] - p[j]] > i && place[p[i] - p[j]] < right[i]) {
          res++;
        }
      }
    } else {
      for (int j = i + 1; j < right[i]; j++) {
        if (place[p[i] - p[j]] < i && place[p[i] - p[j]] > left[i]) {
          res++;
        }
      }
    }
  }
  cout << res;
}
