Problem:
Score : 700 points

Problem Statement

Takahashi is playing with N cards.

The i-th card has an integer X_i on it.

Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:

The integers on the two cards are the same.

The sum of the integers on the two cards is a multiple of M.

Find the maximum number of pairs that can be created.

Note that a card cannot be used in more than one pair.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦X_i≦10^5

Input

The input is given from Standard Input in the following format:

N M
X_1 X_2 ... X_N

Output

Print the maximum number of pairs that can be created.

Sample Input 1

7 5
3 1 4 1 5 9 2

Sample Output 1

3

Three pairs (3,2), (1,4) and (1,9) can be created.

It is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.

Sample Input 2

15 10
1 5 6 10 11 11 11 20 21 25 25 26 99 99 99

Sample Output 2

6

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::*;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let m: usize = itr.next().unwrap().parse().unwrap();
    let mut x: Vec<usize> = (0..n)
        .map(|_| itr.next().unwrap().parse().unwrap())
        .collect();
    x.sort();

    let mut memo: Vec<Vec<usize>> = vec![Vec::new(); 100010];
    let mut ans = 0;
    for i in 0..n {
        memo[x[i] % m].push(x[i]);
    }
    for i in 0..m / 2 + 1 {
        if i == 0 || (m % 2 == 0 && i == m / 2) {
            ans += memo[i].len() / 2;
        } else {
            let mut a = memo[i].clone();
            let mut b = memo[m - i].clone();
            if a.len() < b.len() {
                std::mem::swap(&mut a, &mut b);
            }
            let mut same = 0;
            let mut idx = 0;
            while idx < a.len() {
                while idx < a.len() - 1 && a[idx] == a[idx + 1] {
                    idx += 2;
                    same += 1;
                }
                idx += 1;
            }
            ans += b.len() + std::cmp::min((a.len() - b.len()) / 2, same);
        }
    }
    println!("{}", ans);
}