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)

use std::cmp;
use std::collections::HashMap;
use std::fmt::Debug;
use std::str::FromStr;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where
    T: FromStr,
    <T as FromStr>::Err: Debug,
{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim()
        .split_whitespace()
        .map(|c| T::from_str(c).unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_as_string() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main() {
    let line = read_as_vec::<usize>();
    let (h, w) = (line[0], line[1]);
    let mut hash: HashMap<char, usize> = HashMap::new();

    for _ in 0..h {
        let row = read_as_string();
        for c in row.chars() {
            *hash.entry(c).or_insert(0) += 1;
        }
    }

    if h % 2 == 0 && w % 2 == 0 {
        if hash.iter().map(|x| x.1).all(|count| *count % 4 == 0) {
            println!("Yes");
        } else {
            println!("No");
        }
    } else if h % 2 == 1 && w % 2 == 1 {
        if (hash.iter().map(|x| x.1).filter(|x| **x % 4 == 0).count() >= (w / 2) * (h / 2))
            && (hash.iter().map(|x| x.1).filter(|x| **x % 2 != 0).count() == 1)
        {
            println!("Yes");
        } else {
            println!("No");
        }
    } else {
        let rest_row = if w % 2 == 1 { h } else { w };

        if (hash.iter().map(|x| x.1).filter(|x| **x % 4 != 0).count() >= (h * w - rest_row) / 4)
            && (hash.iter().map(|x| x.1).all(|x| *x % 2 == 0))
        {
            println!("Yes");
        } else {
            println!("No");
        }
    }
}