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 int long long
using namespace std;
const int N = 1e5 + 5;
int arr[N], L[N], R[N];
int32_t main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0); 
	cout.tie(0);
	int n;
	cin >> n;
	multiset<int> st;
	for(int i = 0; i < n; i++){
		int num;
		cin >> num;
		st.insert(num);
	}
	int ans = 0;
	while(!st.empty()){
		int x = *st.rbegin();
		st.erase(st.find(x));
		int num = 1;
		while(num <= x){
			num *= 2;
		}
		if(st.find(num - x) == st.end()){
			continue;
		}
		st.erase(st.find(num - x));
		ans++;
	}
	cout << ans;
}