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);
	map<int,int> mp;
	for(int i=0;i<n;i++){
		cin >> a[i];
		mp[a[i]]++;
	}
	int ans=0;
	
	for(auto it=mp.rbegin();it!=mp.rend();it++){
		auto x = it->first, y=it->second;
		
		int nx = log2(x);
		if((1<<nx)==x){
			ans+=y/2;
		}
		else{
			nx++;
			int req = (1<<nx)-x;
			if(mp.find(req)!=mp.end()){
				int avail = min(mp[req], y);
				ans+= avail;
				mp[req]-= avail;
			}
		}
	}
	cout << ans << endl;
	return 0;
}