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, a[200030], l1, r1, l2, r2, b[200030], ans;
set<int> s;
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    b[a[i]] = i;
  }
  s.insert(0);
  s.insert(n + 1);
  for (int i = n; i >= 1; i--) {
    auto x = s.upper_bound(b[i]);
    l2 = b[i] + 1;
    r2 = (*x) - 1;
    l1 = (*(--x)) + 1;
    r1 = b[i] - 1;
    if (r1 - l1 > r2 - l2) {
      swap(r1, r2);
      swap(l1, l2);
    }
    for (int j = l1; j <= r1; j++)
      if (l2 <= b[i - a[j]] && b[i - a[j]] <= r2) ans++;
    s.insert(b[i]);
  }
  printf("%d", ans);
  return 0;
}
