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 = 2 * 100 * 1000 + 7;
bool rr[N];
int main() {
  int n;
  scanf("%d", &n);
  int arr[n];
  int ord[n];
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
    ord[n - arr[i]] = i;
  }
  int resp = 0;
  for (int i = 0; i < n; i++) {
    int l = ord[i];
    int r = ord[i];
    memset(rr, false, sizeof rr);
    if ((l - 1) < 0 || (r + 1) >= n) continue;
    if (arr[l - 1] > (n - i) || arr[r + 1] > (n - i)) continue;
    while ((r + 1) < n && arr[r + 1] <= (n - i)) {
      r++;
      rr[arr[r]] = true;
    }
    while (l > 0 && arr[l - 1] <= (n - i)) {
      l--;
      if (rr[(n - i) - arr[l]]) resp++;
    }
  }
  printf("%d\n", resp);
  return 0;
}
