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 n, ans = 0;
  cin >> n;
  map<long long, long long> ma;
  long long max = 0;
  long long a[n + 1];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    ma[a[i]]++;
    if (a[i] > max) max = a[i];
  }
  vector<long long> A;
  unsigned long long p = 1;
  while (p <= 1e18) {
    A.push_back(p);
    p *= 2;
  }
  long long t = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < A.size(); j++) {
      if (A[j] - a[i] > max) break;
      t += ma[A[j] - a[i]];
      if (A[j] == a[i]) t--;
    }
  cout << t / 2;
}
