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: Time Limit Exceeded)

#include<bits/stdc++.h>
#define rep(i, x, y) for(register int i = x; i <= y; ++i)
#define repd(i, x, y) for(register int i = x; i >= y; --i)
#define repl(i, x) for(register int i = fi[x]; i; i = l[i].next)
using namespace std;
typedef long long ll;
const int maxn = 200010;
int n, a[maxn];
unordered_map<int, int> h;
int read(){
	int num = 0, flag = 1; char c = getchar();
	for(; c < '0' || c > '9'; c = getchar())
		if(c == '-') flag = 0;
	for(; c >= '0' && c <= '9'; c = getchar())
		num = (num<<3)+(num<<1)+c-48;
	return flag? num: -num;
}

bool mycmp(int x, int y){
	return x > y;
}

void init(){
	n = read();
	rep(i, 1, n) a[i] = read();
}

void work(){
	int ans = 0;
	sort(a+1, a+n+1, mycmp);
	rep(i, 1, n) ++h[a[i]];
	rep(i, 1, n){
		if(!h[a[i]]) continue;
		--h[a[i]];
		for(int j = log2(a[i]); (1<<j) <= a[i]*2; ++j){
			if((1<<j) < a[i]) continue;
			if(h[(1<<j)-a[i]]){
				--h[(1<<j)-a[i]];
				++ans;
			}
		}
	}
	printf("%d\n", ans);
}

int main(){
	//freopen(".in", "r", stdin);
	//freopen(".out", "w", stdout);
	init();
	work();
	return 0;
}