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 powers[1000];
int main() {
  int n, s;
  cin >> n;
  int arr[n];
  for (int i = 1, j = 0; j < 33; i *= 2, j++) {
    powers[j] = i;
    s = j + 1;
  }
  map<int, int> mp;
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
  }
  long long ans = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < s; ++j) {
      ans += mp[powers[j] - arr[i]];
    }
    mp[arr[i]]++;
  }
  cout << ans << endl;
  return 0;
}
