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;
const int INF = 0x3f3f3f3f;
int n;
map<int, int> cnt;
int a;
int mi[35];
int main() {
  mi[0] = 1;
  for (int i = 1; i <= 31; i++) mi[i] = mi[i - 1] * 2;
  scanf("%d", &n);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a);
    for (int j = 0; j <= 30; j++) {
      int b = mi[j] - a;
      ans += cnt[b];
    }
    cnt[a]++;
  }
  printf("%lld\n", ans);
  return 0;
}
