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;
typedef long long ll;
int main(){
  ll n;cin>>n;
  map<ll,ll>mp;
  ll a[n];
  for(ll i=0;i<n;i++){
    cin>>a[i];
    mp[a[i]]++;
  }
  sort(a,a+n);
  ll ans=0;
  for(ll i=n-1;i>=0;i--){
    if(mp[a[i]]==0)continue;
    ll c;
    for(ll j=0;;j++){
      if(pow(2,j)>a[i]){
        c=j;
        break;
      }
    }
      ll sa=pow(2,c)-a[i];
      mp[a[i]]--;
    ll d=0;
      if(mp[sa]>0){
        ans++;
        mp[sa]--;
        d=1;
      }
      if(d==0)mp[a[i]]++;
    
  }
  cout<<ans;
}