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 N = 1e5 + 5;
int v[N];
vector<long long> w;
map<int, int> m;
int main() {
  long long p = 2;
  while (p <= 3100000000) {
    w.push_back(p);
    p <<= 1;
  }
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> v[i];
    m[v[i]]++;
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    int k = v[i];
    for (int j = 0; j < w.size(); j++) {
      int x = w[j] - k;
      if (m[x]) {
        if (x == k)
          ans += (m[x] - 1);
        else
          ans += m[x];
      }
    }
  }
  cout << ans / 2 << "\n";
  return 0;
}
