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 (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;
use std::collections::HashMap;

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

    let mut map = HashMap::new();

    for line in aa {
        for c in line.chars() {
            *map.entry(c).or_insert(0usize) += 1;
        }
    }

    let mut has_center = false;

    let u = 
        match (h % 2 == 1, w % 2 == 1) {
            (true, true) => {
                has_center = true;
                h + w - 1
            },
            (true, false) => {
                w
            },
            (false, true) => {
                h
            },
            (false, false) => {
                0
            }
        };

    let mut u = u as isize;

    for (_, value) in map {
        let rem = value % 4;

        if rem % 2 != 0 {
            if has_center {
                has_center = false;
            } else {
                println!("No");
                return;
            }
        }

        u -= rem as isize;
    }
    if u == 0 && !has_center {
        println!("Yes");
    } else {
        println!("No");
    }
}