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 a[1000005];
map<long long, int> mp;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    mp[a[i]]++;
  }
  long long ans = 0;
  for (int i = 0; i <= 32; i++) {
    long long num = mp[(1LL << i)];
    ans += num * (num - 1) / 2;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= 32; j++) {
      long long res = (1LL << j);
      if (res - a[i] > a[i]) {
        ans += mp[res - a[i]];
      }
    }
  }
  printf("%I64d\n", ans);
  return 0;
}
