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<int, int> M;
long long result = 0;
int n, a;
int main(void) {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a);
    for (int j = 0; j < 31; ++j) {
      int sucht = (1 << j) - a;
      result += M[sucht];
    }
    M[a]++;
  }
  cout << result << endl;
  return 0;
}
