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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <set>
#include <iterator>
typedef long long ll;
typedef unsigned int uint;
using namespace std;


int main() {
    cin.sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;

    multiset<ll> st;
    for (int i = 0; i < n; i++) {
        ll a;
        cin >> a;
        st.insert(a);
    }

    int ans = 0;
    while (!st.empty()) {
        ll mx = *--st.end();
        st.erase(--st.end());

        for (int i = 0; i <= 32; i++) {
            ll mn = (1LL << i) - mx;
            if (st.find(mn) != st.end()) {
                ans++;
                st.erase(st.find(mn));
                break;
            }
        }
    }

    cout << ans << "\n";
    return 0;
}