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() {
  int n;
  cin >> n;
  long long ans = 0;
  vector<long long> pow_two(33);
  vector<long long> input(n);
  unordered_map<long long, long long> mp;
  for (int i = 0; i < n; i++) {
    cin >> input[i];
    mp[input[i]]++;
  }
  for (int i = 0; i < 33; i++) {
    pow_two[i] = 1ll << i;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 32; j++) {
      auto tmp = pow_two[j] - input[i];
      if (tmp == input[i]) {
        ans += mp[tmp] - 1;
      } else {
        ans += mp[tmp];
      }
    }
  }
  ans >>= 1;
  cout << ans << endl;
  return 0;
}
