You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long n;
  cin >> n;
  vector<long> v(n + 1);
  map<long, long> m;
  for (int i = 1; i <= n; i++) {
    cin >> v[i];
    m[v[i]]++;
  }
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long j = 0;
    while (j <= 31) {
      long long curr = pow(2, j);
      if (curr - v[i] == v[i])
        ans += m[curr - v[i]] - 1;
      else
        ans += m[curr - v[i]];
      j++;
    }
    m[v[i]]--;
  }
  cout << ans << endl;
}
