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;
map<long long, int> m;
int main() {
  long long n, ans = 0;
  cin >> n;
  long long arr[n];
  for (int i = 0; i < n; i++) {
    long long a;
    cin >> a;
    arr[i] = a;
    m[a]++;
  }
  for (int x = 0; x < n; x++) {
    for (long long i = 1; i <= (1LL << 31); i <<= 1)
      ans += m[i - arr[x]] - (i - arr[x] == arr[x]);
  }
  cout << ans / 2;
}
