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;
map<long long, long long> m;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long testcases = 1;
  while (testcases--) {
    long long n;
    cin >> n;
    long long cnt = 0;
    for (long long i = 0; i < n; i++) {
      long long a;
      cin >> a;
      long long f = 1;
      for (long long j = 0; j < 34; j++) {
        f *= 2;
        long long d = f - a;
        if (d) {
          cnt += m[d];
        }
      }
      m[a]++;
    }
    cout << cnt;
    cout << "\n";
  }
  return 0;
}
