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;

const int maxn=2e5+100;

int n;
ll a[maxn];
map <ll,int> cnt;
int ans=0;

ll get(ll x){
	ll ret=1;
	while(ret<=x) ret*=2;
	return ret;
}

int main(){
	scanf("%d",&n);
	for(int i=0;i<n;i++) scanf("%lld",&a[i]);
	sort(a,a+n);
	for(int i=0;i<n;i++) cnt[a[i]]++;
	for(int i=n-1;i>=0;i--){
		ll x=get(a[i]);
		if(cnt[a[i]]==0) continue;	
		cnt[a[i]]--;
		if(cnt.find(x-a[i])!=cnt.end()){
			if(cnt[x-a[i]]>0){
				ans++;
				cnt[x-a[i]]--;
			}
		}
	}
	printf("%d\n",ans);
	return 0;
}