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 vet[100100];
int pot2(int n);
int main() {
  int n;
  int i;
  long long cont = 0;
  int *ini, *fim;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &vet[i]);
  }
  std::sort(vet, vet + n);
  for (i = 0; i < n; i++) {
    int p = pot2(vet[i]);
    ini = lower_bound(vet, vet + i, p - vet[i]);
    fim = upper_bound(vet, vet + i, p - vet[i]);
    cont += (fim - ini);
  }
  printf("%I64d", cont);
}
int pot2(int n) {
  int pot = 2;
  while (pot <= n) {
    pot *= 2;
  }
  return pot;
}
