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() {
  int n;
  int x;
  long long y = 0;
  cin >> n;
  long t;
  vector<int> a;
  map<int, int> c;
  for (int i = 0; i < n; i++) {
    cin >> t;
    a.push_back(t);
    c[t]++;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 31; j++) {
      x = pow(2, j) - a[i];
      if ((x != a[i]) && (c[x] > 0)) {
        y += c[x];
      }
      if ((x == a[i]) && (c[x] > 1)) {
        y += c[x] - 1;
      }
    }
    c[a[i]] -= 1;
  }
  cout << y;
}
