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;
const int N = 100005;
long long a[N], fac[40];
map<long long, long long> mp;
int main() {
  long long n, x;
  for (long long i = 1; i <= 31; ++i) fac[i] = 1 << i;
  scanf("%lld", &n);
  for (long long i = 0; i != n; ++i) {
    scanf("%lld", &a[i]);
    mp[a[i]]++;
  }
  long long ans = 0;
  for (long long i = 0; i != n; ++i)
    for (long long j = 1; j <= 31; ++j) {
      ans += mp[fac[j] - a[i]];
      if (fac[j] - a[i] == a[i]) ans--;
    }
  printf("%lld\n", ans / 2);
  return 0;
}
