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;

#define int long long
const int MN = 2e5+5;
multiset<int> arr;
int n, i, j, ans;

signed main(){
    for(scanf("%lld",&n),i=1;i<=n;i++){
        int x; scanf("%lld",&x);
        arr.insert(x);
    }
    while(arr.size()){
        auto it = arr.end(); it--;
        int cur = *it; arr.erase(it);
        for(i=0;(1LL<<i)<=cur;i++){}
        int rem = (1LL<<i)-cur;
        if(arr.find(rem)!=arr.end()){
            ans++;
            arr.erase(arr.find(rem));
        }
    }
    printf("%lld\n",ans);
    return 0;
}
