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, b, i, j;
int main() {
  cin >> n;
  int a[n], d[n + 1];
  for (i = 0; i < n; ++i) {
    cin >> a[i];
    d[a[i]] = i;
  }
  set<int> s = {-1, n};
  for (i = n; i > 0; --i) {
    auto t = s.upper_bound(d[i]);
    int r = *t-- - 1, l = *t + 1;
    s.insert(d[i]);
    if (2 * d[i] - l < r)
      for (j = l; j < d[i]; ++j)
        b += !(d[i - a[j]] < d[i]) & (d[i - a[j]] <= r);
    else
      for (j = r; j > d[i]; --j) b += (d[i - a[j]] >= l) & (d[i - a[j]] < d[i]);
  }
  cout << b;
}
