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 n;
int arr[100001];
int next2(int x) {
  if (x == 0) return x;
  long long int next = 0, i = 0;
  while (next < x) {
    i++;
    next = 1 << i;
  }
  return i;
}
map<int, int> freq;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    freq[arr[i]]++;
  }
  long long int ans = 0;
  for (int i = 0; i < n; i++) {
    freq[arr[i]]--;
    int x = next2(arr[i]);
    if (x == 0) x = 1;
    for (int j = x; j < 31; j++) {
      int y;
      y = (1 << (j)) - arr[i];
      if (freq[y] != 0) ans += freq[y];
    }
  }
  cout << ans;
  return 0;
}
