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;

const int MN = 200010;

int N;
multiset<int> st;
int chk[MN];

int main() {
    scanf("%d", &N);

    for(int i = 0; i < N; i++) {
        int t; scanf("%d", &t);
        st.insert(t);
    }

    int ans = 0;
    while(st.size() > 1) {
        int t = *st.rbegin(); st.erase(st.find(t));

        int p = 1;
        while(p <= t) p <<= 1;
        int d = *st.lower_bound(p - t);
        if(d == p - t) {
            ans++;
            st.erase(st.find(d));
        }
    }
    printf("%d", ans);
}
