Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
#include <bits/stdc++.h>
using namespace std;

int main() {
  long n,ans=0,xx=1;
  cin >> n;
  vector<long> a(n);
  map<long,long> mp;
  for(long i=0;i<n;i++) cin >> a[i];
  for(long i=0;i<31;i++) xx*=2;
  sort(a.begin(),a.end());
  reverse(a.begin(),a.end());
  for(long i=0;i<n;i++) {
    bool b=true;
    long x=xx;
    while(x>a[i]&&b) {
      if(mp[x-a[i]]>0) {
        b=false;
        ans++;
        mp[x-a[i]]--;
      }
      x/=2;
    }
    if(b)mp[a[i]]++;
  }
  cout << ans << endl;
}