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>
#define ll long long
#define f first
#define s second
#define pb push_back
using namespace std;
ll n,a[200005],ans;
map<ll,ll>mp;
int main(){
  cin >> n;
  for(int i=1; i<=n; i++){
   cin >> a[i];
   mp[a[i]]++;
  }
  
  sort(a+1,a+n+1);
  
  for(int i=n; i>=1; i--){
    if(mp[a[i]]){
    	mp[a[i]]--;
      ll p = 1;
      while(p <= a[i])p *= 2;
      if(mp[p - a[i]]){
        mp[p-a[i]]--;
        ans++;
      }
    }
  }
  
  cout << ans;
  
  return 0;
}