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>
#define N 200004
#define pp pair<int,int>
#define mp make_pair
#define pb push_back
#define ff first
#define dd second


using namespace std;
int n;
int maxi = 1;
int tab[N];
map<int,int> no;

main() {
    ios_base::sync_with_stdio(false);
    cin >> n; int ans = 0;
    for(int i = 0; i < n; ++i) cin >> tab[i];
    sort(tab, tab+n);
    for(int i = 0; i < n; ++i) no[tab[i]]++;

    for(int i = n-1; i >= 0; --i) {
        if (no[tab[i]] == 0) continue;
        no[tab[i]]--;
        for(int p = 30; p >= 0; --p) {
            int col = (1 << p) - tab[i];
            if (no[col] > 0) {
                no[col]--;
                ans++; break;
            }
        }
    }

    cout << ans << endl;
}