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 a[100100];
int main() {
  long long n, val;
  cin >> n;
  map<long long, long long> mp;
  for (long long i = 0; i < n; i++) {
    cin >> val;
    mp[val]++;
  }
  long long ans = 0;
  for (map<long long, long long>::iterator it = mp.begin(); it != mp.end();
       it++)
    for (long long i = 0; i <= 30; i++)
      if (mp.find(val = ((1LL << i) - it->first)) != mp.end()) {
        ans += mp[val] * (it->second + (val == it->first ? -1 : 0));
      }
  cout << ans / 2;
  return 0;
}
