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;
vector<long long> v;
int main() {
  long long x = 1LL;
  for (long long i = 2;; i++) {
    x *= 2;
    if (x > 2000000000) break;
    v.push_back(x);
  }
  map<long long, long long> m;
  long long n;
  long long ans = 0LL;
  cin >> n;
  long long a[n + 4];
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (long long i = 0; i < n; i++) {
    for (auto val : v) {
      if (val > a[i] && m[val - a[i]]) ans += m[val - a[i]];
    }
    m[a[i]]++;
  }
  cout << ans << endl;
  return 0;
}
