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: Wrong Answer)

#include <bits/stdc++.h>
#define ll long long int
using namespace std;
string s,s1;
ll ar[250007],cr[200098],a,b, test, sum,t,x=0,p,q,y,i,j,k=0,l,cnteven=0,w=0,cnt;
map<ll,ll>mp,br;
void func()
{
    k=0;
    while(mp[k]<=1073741824)
    {
        if(k>0)
            mp[++k]=mp[k-1]*2;
        else
            mp[++k]=2;
    }
}
int main()
{
    func();
    ll test;
    scanf("%lld",&a);
    cnt=0;
    for(i=1; i<=a; i++)
    {
        scanf("%lld",&ar[i]);
        br[ar[i]]+=1;
    }

    for(i=1; i<=a; i++)
    {
        if(br[ar[i]]>=1)
            for(j=1; j<=k; j++)
            {
                ll c=mp[j];
                x=abs(ar[i]-c);
                if(br[x]>1||(br[x]==1&&ar[i]!=x))
                {
                    cnt++;
                    br[ar[i]]--;
                    br[x]--;
                    break;
                }
            }
    }


    printf("%lld\n",cnt);
}