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: Wrong Answer)

// The input macro written by @tanakh,
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

use std::collections::HashMap;

fn main() {
    input!{
        n: usize,
        arr: [u32; n],
    }

    let mut map = HashMap::new();
    for a in arr {
        let r = map.entry(a).or_insert(0);
        *r += 1;
    }

    let mut result = 0;

    while !map.is_empty() {
        let init = {
            let (init, _) = map.iter().next().unwrap();
            *init
        };
        remove(&mut map, init);

        let (left, right) = rec(&mut map, init);

        result += ::std::cmp::min(left, right);
    }

    println!("{}", result);
}

fn rec(map: &mut HashMap<u32, u32>, init: u32) -> (u32, u32) {
    let mut left = 1;
    let mut right = 0;
    for d in diffs(init) {
        if remove(map, d) {
            let (ls, rs) = rec(map, d);
            left += rs;
            right += ls;
        }
    }
    (left, right)
}
fn diffs(val: u32) -> Vec<u32> {
    let mut result = Vec::with_capacity(30);
    let mut tar = 2;
    while tar <= 2 * 1000000000 {
        if tar <= val {
            tar *= 2;
            continue;
        }
        let d = tar - val;
        result.push(d);
        tar *= 2;
    }
    result
}

fn remove(map: &mut HashMap<u32, u32>, key: u32) -> bool {
    let v = {
        let v = map.get(&key);
        if v.is_none() {
            return false;
        }
        *v.unwrap()
    };
    if v > 1 {
        map.insert(key, v - 1);
    } else {
        map.remove(&key);
    }
    return true;
}