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, mx = 0;
  long long temp = 0, ans = 0, val, ans1 = 0;
  cin >> n;
  vector<int> a;
  map<int, int> m;
  for (long long i = 0; i < n; i++) {
    cin >> val;
    mx = max(mx, val);
    m[val]++;
    if (m[val] == 1) a.push_back(val);
  }
  for (long long i = 0; i < a.size(); i++) {
    temp = 1;
    while (temp <= mx * 2) {
      if (temp >= a[i]) {
        val = m[temp - a[i]];
        if (a[i] == (temp - a[i]))
          ans1 += (val * (val - 1)) / 2;
        else
          ans += (val * m[a[i]]);
      }
      temp *= 2;
    }
  }
  cout << ans / 2 + ans1 << "\n";
  return 0;
}
