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 FOR(i,a,n) for(ll i=(ll)a;i<(ll)n;i++)
#define rep(i,n) FOR(i,0,n)
using namespace std;
typedef long long ll;

ll n,a;
multiset<ll,greater<ll>>st;
map<ll,ll>mp;

int main(){
    cin>>n;
    rep(i,n){
        cin>>a;
        st.insert(a);
    }
    ll ans=0;
    while(!st.empty()){
        ll b=*st.begin(),x=1;
        while(x<=b)x*=2;
        st.erase(st.begin());
        if(st.find(x-b)!=st.end()){
            st.erase(st.find(x-b));
            ans++;
        }
    }
    cout<<ans<<endl;
}