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;
int v[200200];
bitset<200200> bs;
int main() {
	int n;
	scanf("%d ",&n);
	for(int i=0;i<n;i++) {
		int t;
		scanf("%d ",&t);
		v[i] = t;
	}
	sort(v,v+n);
	for(int i=30;i>=0;i--) {
		int tot = 1<<i;
		int s = 0,e = n;
		while(s<e) {
			e--;
			if(bs[e]) continue;
			while(s < n && (v[s]+v[e]<tot || bs[s])) {s++;}
			if(s >= e) break;
			if(v[s]+v[e] == tot && !(bs[e] || bs[s])) {bs.set(e);bs.set(s);
			//printf("match %d %d\n",s,e);
			}
		}
	}
	printf("%d\n",bs.count()/2);
}
