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;
map<int, int> mapa;
int n, tab[100001];
long long number;
int main() {
  ios_base::sync_with_stdio(0);
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &tab[i]);
    for (long long j = 2; j <= 2000000000; j *= 2) {
      if (mapa.find(j - tab[i]) != mapa.end()) {
        number += mapa[j - tab[i]];
      }
    }
    if (mapa.find(tab[i]) == mapa.end()) {
      mapa.insert(make_pair(tab[i], 1));
    } else {
      mapa[tab[i]]++;
    }
  }
  cout << number << "\n";
}
