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() {
  map<long long, long long> count;
  int m = 31;
  long long total(0);
  long long n;
  cin >> n;
  while (n--) {
    long long int x;
    cin >> x;
    long long int t = 1;
    int p = m;
    while (p--) {
      t *= 2;
      total += count[t - x];
    }
    count[x]++;
  }
  cout << total << endl;
  return 0;
}
