Problem:
Score : 400 points

Problem Statement

We have an H-by-W matrix.
Let a_{ij} be the element at the i-th row from the top and j-th column from the left.
In this matrix, each a_{ij} is a lowercase English letter.

Snuke is creating another H-by-W matrix, A', by freely rearranging the elements in A.
Here, he wants to satisfy the following condition:

Every row and column in A' can be read as a palindrome.

Determine whether he can create a matrix satisfying the condition.

Note

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are all palindromes, while ab, abab and abcda are not.

Constraints

1 ≤ H, W ≤ 100

a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}

Output

If Snuke can create a matrix satisfying the condition, print Yes; otherwise, print No.

Sample Input 1

3 4
aabb
aabb
aacc

Sample Output 1

Yes

For example, the following matrix satisfies the condition.

abba
acca
abba

Sample Input 2

2 2
aa
bb

Sample Output 2

No

It is not possible to create a matrix satisfying the condition, no matter how we rearrange the elements in A.

Sample Input 3

5 1
t
w
e
e
t

Sample Output 3

Yes

For example, the following matrix satisfies the condition.

t
e
w
e
t

Sample Input 4

2 5
abxba
abyba

Sample Output 4

No

Sample Input 5

1 1
z

Sample Output 5

Yes

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(unused_imports)]
use itertools::Itertools;
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

fn main() {
    input! {
        h: usize,
        w: usize,
        map:[Chars;h]
    }

    let mut alphabet_count: HashMap<char, i64> = HashMap::new();

    for i in 0..h {
        for j in 0..w {
            let c = map[i][j];
            *alphabet_count.entry(c).or_insert(0) += 1;
        }
    }

    if alphabet_count.len() > (h + 1) / 2 + (w + 1) / 2 {
        println!("No");
        return;
    }

    let mut count: HashMap<i64, i64> = HashMap::new();

    for (_, mut v) in alphabet_count {
        while v >= 4 {
            *count.entry(4).or_insert(0) += 1;
            v -= 4;
        }
        *count.entry(v).or_insert(0) += 1;
    }

    let requied_4 = (h as i64 / 2) * (w as i64 / 2);
    let n = count.get(&4).unwrap_or(&0);
    if *n < requied_4 {
        println!("No");
        return;
    }

    if h % 2 == 0 && w % 2 == 0 {
        println!("Yes");
        return;
    }

    *count.entry(2).or_insert(0) += (n - requied_4) * 2;

    if h % 2 + w % 2 == 1 {
        let requied_2 = if h % 2 == 0 { h / 2 } else { w / 2 };
        let &n = count.get(&2).unwrap_or(&0);
        if n == requied_2 as i64 {
            println!("Yes");
            return;
        }
    } else if h % 2 == 1 && w % 2 == 1 {
        let requied_2 = (h + 1) / 2 + (w + 1) / 2 - 2;
        if let Some(n) = count.get(&3) {
            *count.entry(2).or_insert(0) += 1;
            *count.entry(1).or_insert(0) += 1;
        }
        let &n = count.get(&2).unwrap_or(&0);
        if n == requied_2 as i64 && count.get(&1) == Some(&1) {
            println!("Yes");
            return;
        }
    }

    println!("No");
}
*/

fn main() {
    let exe = "/tmp/bin7522DB10";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";