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;
const int mod = 1e9 + 7;
void solve() {
  int n;
  cin >> n;
  vector<long long> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  map<long long, long long> M;
  for (int i = 0; i < n; i++) M[v[i]]++;
  vector<long long> X;
  long long p = 1;
  for (int i = 0; i <= 34; i++) {
    X.push_back(p);
    p *= 2;
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    M[v[i]]--;
    for (int j = 0; j < X.size(); j++) {
      ans += M[X[j] - v[i]];
    }
  }
  cout << ans << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tests = 1;
  while (tests--) {
    solve();
  }
}
