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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  {
    int n;
    cin >> n;
    int arr[n + 10];
    map<long long int, long long int> mp;
    for (int i = 0; i < n; ++i) {
      cin >> arr[i];
      mp[arr[i]]++;
    }
    long long int cnt = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 1; j <= 31; ++j) {
        long long int a = (1 << j);
        long long int need = a - arr[i];
        cnt += mp[a - arr[i]];
        if (need == arr[i] and mp[arr[i]]) cnt--;
      }
      if (mp[arr[i]]) mp[arr[i]]--;
    }
    cout << cnt << '\n';
  }
}
