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 p[32];
  p[0] = 1;
  for (int i = 1; i < 32; i++) p[i] = p[i - 1] * 2;
  long long n, a, cnt = 0;
  map<long long, vector<long long>> mpv;
  vector<long long> vi;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a;
    vi.push_back(a);
    mpv[a].push_back(i);
  }
  for (int i = 0; i < vi.size(); i++) {
    for (int j = 1; j < 31; j++) {
      long long sub = p[j] - vi[i];
      if (mpv.find(sub) == mpv.end())
        continue;
      else {
        auto it = lower_bound(mpv[sub].begin(), mpv[sub].end(), i);
        long long idx = it - mpv[sub].begin();
        if (*it == i) idx++;
        cnt += mpv[sub].size() - idx;
      }
    }
  }
  cout << cnt << "\n";
}
