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>
const long long N = 1e5 + 1, MOD = 2e9;
using namespace std;
long long great(long long x, long long y) { return x > y; }
int main() {
  int n;
  cin >> n;
  int arr[n];
  long long cnt = 0;
  map<int, int> mp;
  for (int i = 1; i <= n; i++) cin >> arr[i];
  for (int i = 1; i <= n; i++) {
    long long j = 1;
    while (j <= MOD) {
      cnt += mp[j - arr[i]];
      j += j;
    }
    mp[arr[i]]++;
  }
  cout << cnt << endl;
  return 0;
}
