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<cstdio>
#include<set>
#include<algorithm>
#include<iostream>
#define ll long long
using namespace std;
int n;
ll a[200001];
multiset<ll>s;
ll inv(ll x)
{
    ll t=1;
    while(t<=x) t<<=1;
    return t-x;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
    sort(a+1,a+1+n);
    int ans=0;
    for(int i=n;i>=1;i--)
    {
        const auto& f=s.find(a[i]);
        if(f!=s.end()) ans++,s.erase(f);
        else s.insert(inv(a[i]));
    }
    printf("%d\n",ans);
}
