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() {
  ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::cout.tie(nullptr);
  long long int i, in, n, k, diff, ans;
  std::map<long long int, long long int> mp;
  std::vector<long long int> v;
  std::cin >> n;
  for (i = 1; i <= n; i++) {
    std::cin >> in;
    mp[in]++;
  }
  ans = 0;
  for (i = 2; i <= pow(2, 32); i += i) v.push_back(i);
  for (auto x : mp) {
    if (x.second > 0) {
      k = x.first;
      while (mp[k] != 0) {
        mp[k]--;
        for (i = 0; i < 32; i++) {
          if (k < v[i]) {
            diff = v[i] - k;
            ans = ans + mp[diff];
          }
        }
      }
    }
  }
  std::cout << ans << '\n';
  return 0;
}
