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 a[100010];
map<int, int> mp;
long long ans = 0;
int ksm(int a, int b) {
  int res = 1;
  while (b) {
    if (b & 1) res = res * a;
    a = a * a;
    b >>= 1;
  }
  return res;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int x = 1; x <= 30; x++) {
    int now = ksm(2, x);
    mp.clear();
    for (int i = n; i >= 1; i--) {
      if (now < a[i]) {
        mp[a[i]]++;
        continue;
      }
      ans += mp[now - a[i]];
      mp[a[i]]++;
    }
  }
  cout << ans << endl;
  return 0;
}
