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 main() {
  long long int n, i, x, j, arr[100008];
  long long int powers[10000], len = 0;
  unordered_map<long long int, long long int> map;
  long long int val = 1;
  for (i = 0; val < 2000000000; i++) {
    powers[len++] = val;
    val = (val << 1);
  }
  scanf("%I64d", &n);
  for (i = 0; i < n; i++) {
    scanf("%I64d", &arr[i]);
    map[arr[i]]++;
  }
  long long int ans = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < len; j++) {
      ans += map[powers[j] - arr[i]];
      if ((powers[j] - arr[i]) == arr[i]) {
        ans--;
      }
    }
  }
  printf("%I64d", ans / 2);
  return 0;
}
