Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define fi first
#define se second
typedef pair<ll,ll> P;
#define Mod 1000000007
using VP = vector<P>; using VVP = vector<VP>;
using VI = vector<ll>; using VVI = vector<VI>; using VVVI = vector<VVI>;
#define INF 1ll<<59

ll pa(ll k){
    ll t=1;
    while(t<=k) t*=2;
    return t-k;
}

int main(){
    ll i,j;
    ll n;
    cin>>n;
    vector<ll> a(n);
    for(i=0;i<n;i++) cin>>a[i];
    sort(a.begin(),a.end(),greater<ll>());

    map<ll,ll> m;
    for(i=0;i<n;i++) m[a[i]]++;

    ll ans=0;
    for(i=0;i<n;i++){
        if(m[a[i]]>0) {
            m[a[i]]--;
            if(m[a[i]]==0) m.erase(a[i]);
            ll p=pa(a[i]);
            if(m.count(p)) {
                m[p]--;
                ans++;
                if(m[p]==0) m.erase(p);
            }
        }
    }
    cout<<ans<<endl;
   
  
}