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 = 2e5 + 9;
int n, ans, a[N], b[N], l[N], r[N];
int main() {
  scanf("%d", &n);
  a[0] = a[n + 1] = N;
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    b[a[i]] = i;
    for (l[i] = i - 1; a[l[i]] < a[i];) l[i] = l[l[i]];
  }
  for (int i = n; i; --i) {
    for (r[i] = i + 1; a[r[i]] < a[i];) r[i] = r[r[i]];
    int s1 = l[i], t1 = i, s2 = i, t2 = r[i];
    if (t1 - s1 > t2 - s2) swap(s1, s2), swap(t1, t2);
    for (int j = s1 + 1; j < t1; ++j)
      if (s2 < b[a[i] - a[j]] && b[a[i] - a[j]] < t2) ++ans;
  }
  printf("%d", ans);
}
