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 MAXX = 1e5 + 10;
long long n, a[MAXX], ans;
map<int, int> cnt;
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i], cnt[a[i]]++;
  for (int i = 0; i < n; i++)
    for (long long mask = 1; mask <= (1 << 30); mask *= 2)
      if (a[i] <= mask && cnt.find(mask - a[i]) != cnt.end())
        ans += cnt[(mask - a[i])] - (mask - a[i] == a[i]);
  return cout << ans / 2 << endl, 0;
}
