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;
long long int n, x, i, j, ans, counter = 1;
vector<long long int> p;
map<long long int, long long int> mp;
int main() {
  ios_base::sync_with_stdio(0);
  i = 2;
  while (counter <= 30) {
    p.push_back(i);
    i = i << 1;
    counter++;
  }
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> x;
    j = 0;
    while (j < p.size()) {
      ans += mp[p[j] - x];
      j++;
    }
    mp[x]++;
  }
  cout << ans;
  return 0;
}
