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() {
  int n, a[200005], i, j, ans = 0;
  cin >> n;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 1; i < n - 1; i++) {
    if (a[i] < a[i - 1] || a[i] < a[i + 1]) continue;
    set<int> left;
    for (j = i - 1; j >= 0 && a[j] < a[i]; j--) left.insert(a[j]);
    for (j = i + 1; j < n && a[j] < a[i]; j++)
      if (left.find(a[i] - a[j]) != left.end()) ans++;
  }
  cout << ans << endl;
}
