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(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int n;
  cin >> n;
  map<long long int, long long int> mp;
  for (int i = 0; i < n; i++) {
    long long int r;
    cin >> r;
    mp[r]++;
  }
  long long int cnt = 0;
  for (long long int j = 0; j <= 60; j++) {
    for (auto i : mp) {
      long long int x = pow(2, j) - i.first;
      if (i.first <= x && mp.find(x) != mp.end()) {
        if (x == i.first)
          cnt += mp[x] * (mp[x] - 1) / 2;
        else
          cnt += mp[x] * (mp[i.first]);
      }
    }
  }
  cout << cnt << endl;
}
