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 MAX_N = 100000 + 10;
long long n, ans = 0;
long long a[MAX_N];
long long b[100];
map<long long, int> m;
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    m[a[i]]++;
  }
  b[0] = 1ll;
  for (int i = 1; i <= 40; i++) {
    b[i] = b[i - 1] * 2ll;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 40; j++) {
      long long x = b[j] - a[i];
      if (x < 0) {
        continue;
      } else {
        ans += (m[x]);
        if (x == a[i]) {
          ans--;
        }
      }
    }
  }
  cout << ans / 2 << endl;
}
