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 Rust (1.15.1) (judge verdict: Accepted)

use std::collections::HashMap;
use std::io::*;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let mut a: Vec<i64> = (0..n).map(|_| read::<i64>()).collect();

    a.sort_by_key(|x| -x);
    let mut ans: i64 = 0;
    let mut used: HashMap<i64, i64> = HashMap::new();
    for i in &a {
        if used.contains_key(i) {
            *(used.get_mut(i).unwrap()) += 1;
        } else {
            used.insert(*i, 1);
        }
    }

    for i in 0..n {
        if used[&a[i]] == 0 {
            continue;
        }
        *(used.get_mut(&a[i]).unwrap()) -= 1;
        let mut b = a[i];
        let mut cnt = 0;
        while b > 0 {
            b /= 2;
            cnt += 1;
        }
        if let Some(x) = used.get_mut(&((1_i64 << cnt) - a[i])) {
            if *x > 0 {
                *x -= 1;
                ans += 1;
            }
        }
    }
    println!("{}", ans);
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}