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;
using Int = long long;
auto find_pair(Int a){
    for(Int i = 1; i < 32; ++i){
        Int bit = (1LL << i);
        if( bit > a) return bit - a;
    }
    return 0LL;
}
signed main(){
    Int N; cin >> N;
    vector<Int>A(N);
    for(auto& e : A) cin >> e;
    map<Int,Int,greater<>>cnt;
    for(auto e : A) cnt[e]++;
    Int ans = 0;
    for(auto itr : cnt){
        Int key = itr.first;
        Int value = itr.second;
        if(value == 0) continue;
        Int pir = find_pair(key);
        if(pir == key){
            ans  += value /2;
        } else {
            if(cnt.find(pir) == cnt.end()) continue;
            ans += min(value, cnt[pir]);
            cnt[pir] -= min(value, cnt[pir]);
            
        }
        cnt[key] = 0;
    }
    cout << ans << endl;
}