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 (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

use proconio::{fastout, input};
use std::collections::BTreeMap;

#[fastout]
fn main() {
    input! {
        n: usize,
        mut a: [usize; n],
    }
    a.sort();
    let mut nokori_kosuu: BTreeMap<usize, usize> = BTreeMap::new();
    for &ai in &a {
        if let Some(e) = nokori_kosuu.get_mut(&ai) {
            *e += 1;
        } else {
            nokori_kosuu.insert(ai, 1);
        }
    }
    let mut num_pairs = 0;
    for i in (0..n).rev() {
        let ai = a[i];
        if *nokori_kosuu.get(&ai).unwrap() == 0 {
            continue;
        }
        *nokori_kosuu.get_mut(&ai).unwrap() -= 1;
        let mut nibeki = 1;
        while nibeki <= ai {
            nibeki *= 2;
        }
        let aikata = nibeki - ai;
        if let Some(&c) = nokori_kosuu.get(&aikata) {
            if c != 0 {
                num_pairs += 1;
                *nokori_kosuu.get_mut(&aikata).unwrap() -= 1;
            }
        }
    }
    println!("{}", num_pairs);
}