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 maxn = 100010, inf = 2e9;
int n, arr[maxn];
map<int, int> cnt;
long long sol;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", arr + i);
    int p = 1;
    for (int j = 0; j < 31; j++) {
      if (p >= arr[i]) sol += cnt[p - arr[i]];
      p *= 2;
    }
    cnt[arr[i]]++;
  }
  printf("%lld\n", sol);
  return 0;
}
