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 long long int MOD = 1e9 + 7;
const long long int INF = 1e10;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  map<long long int, long long int> make_pair;
  vector<long long int> a(n + 1);
  long long int ans = 0;
  for (long long int i = 1; i <= n; i++) {
    cin >> a[i];
    for (long long int j = 0; j < 31; j++) {
      long long int x = (1 << j);
      if ((x - a[i] >= 0) && make_pair.count(x - a[i])) {
        ans += make_pair[(1 << j) - a[i]];
      }
    }
    make_pair[a[i]]++;
  }
  cout << ans;
  return 0;
}
