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;
int main() {
  vector<long> v;
  map<long, long> m;
  long i, n, j;
  long long s = 0;
  for (i = 0; pow(2, i) <= 2000000000; i++) v.push_back(pow(2, i));
  cin >> n;
  long a[n];
  for (i = 0; i < n; i++) {
    cin >> a[i];
    m[a[i]]++;
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < 31; j++) {
      if (v[j] == a[i]) s--;
      s += m[v[j] - a[i]];
    }
  }
  cout << s / 2;
}
