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 n, ans;
multiset<int> st;//因为数据可能重复，所以用multiset

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		int x;
		scanf("%d", &x);
		st.insert(x);
	}
	while (!st.empty()) {
		ll v = *--st.end();//取st最后一位数据
		st.erase(--st.end());//将最后一位数据抹去，避免下面find找到自己
		for (int i = 0; i <= 30; ++i) {//2^32是int范围内的极限,循环int内的2的幂
			ll t = (1 << i) - v;
			if (st.find(t) != st.end()) {//如果t在st中存在，抹去，ans++，并且break
				++ans; st.erase(st.find(t)); break;
			}
		}
	}
	printf("%d", ans);
}
