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;
vector<long long int> vec;
map<long long int, long long int> mp;
int main() {
  long long int x = 0, y = 0, z = 0, sum = 0;
  cin >> x;
  for (int i = 0; i < x; i++) {
    cin >> y;
    vec.push_back(y);
    mp[y]++;
  }
  sort(vec.begin(), vec.end());
  for (int i = 0; i < vec.size(); i++) {
    for (int j = 0; j <= 30; j++) {
      z = powl(2, j) - vec[i];
      if (binary_search(vec.begin() + i + 1, vec.end(), z) == true) {
        if (z == vec[i]) {
          sum += --mp[z];
        } else {
          sum += mp[z];
        }
      }
    }
  }
  cout << sum << endl;
}
