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<long long, long long> map1;
int main() {
  long long i, j;
  long long N;
  scanf("%lld", &N);
  long long arr[N];
  for (i = 0; i < N; i++) scanf("%lld", &arr[i]);
  long long ans = 0;
  for (i = 0; i < N; i++) {
    for (j = 0; j < 31; j++) ans += map1[(2 << j) - arr[i]];
    map1[arr[i]]++;
  }
  printf("%lld\n", ans);
  return 0;
}
