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 kMaxN = 100010;
const int kMaxA = 1000000010;
int a[kMaxN];
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a, a + n);
  long long ans = 0;
  for (long long x = 1; (1LL << x) < 2 * kMaxA; x++) {
    long long val = (1 << x);
    for (long long i = 0; i < n; i++) {
      long long num = upper_bound(a + i + 1, a + n, val - a[i]) -
                      lower_bound(a + i + 1, a + n, val - a[i]);
      ans += num;
    }
  }
  cout << ans << endl;
  return 0;
}
