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(){
  int N;cin>>N;
  vector<int>A(N);
  for(int &a:A)cin>>a;
  sort(A.begin(),A.end(),greater<int>());
  map<int,int>m;
  int ans=0;
  for(int a:A){
    if(m.count(a)&&m[a]>0)m[a]--,ans++;
    else m[(1<<(32-__builtin_clz(a)))-a]++;
  }
  cout<<ans<<endl;
}