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<iostream>
#include<set>
#include<cstdio>
using namespace std;
multiset<int>se;
int main(){
    int n,x;
    scanf("%d",&n);
    for(int i=0;i<n;i++)scanf("%d",&x),se.insert(x);
    int ans=0;
    while(se.size()>1){
        int x=*se.rbegin();
        se.erase(se.find(x));
        int now=1;
        while(now<=x) now<<=1;
        auto it=se.find(now-x);
        if(it==se.end()) continue;
        se.erase(it);
        ans++;
    }
    printf("%d",ans);
}
