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[100500];
long long c[100500];
map<int, int> m;
int main() {
  int n = 0;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    m[a[i]]++;
  }
  long long x = 1;
  for (int i = 0; i < 40; i++) {
    x *= 2;
    c[i] = x;
  }
  sort(a, a + n);
  long long res = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 30; j++) {
      long long f = c[j] - a[i];
      long long d = *lower_bound(a, a + n, f);
      if (f == d) {
        res += m[d];
        if (d == a[i]) res--;
      }
    }
    m[a[i]]--;
  }
  cout << res << endl;
  return 0;
}
