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: Accepted)

use std::io::Read;
use std::collections::HashMap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let h: usize = iterator.next().unwrap().parse().unwrap();
    let w: usize = iterator.next().unwrap().parse().unwrap();
    let mut counts: HashMap<char, usize> = HashMap::new();
    for _ in 0..h {
        let line: Vec<char> = iterator.next().unwrap().chars().collect();
        for c in line {
            *counts.entry(c).or_insert(0) += 1;
        }
    }

    if h % 2 == 0 && w % 2 == 0 {
        let mut ok = true;
        for (_, count) in counts {
            if count % 4 != 0 {
                ok = false;
                break;
            }
        }
        return if ok {
            "Yes".to_string()
        } else {
            "No".to_string()
        };
    }

    if h % 2 == 0 && w % 2 == 1 || h % 2 == 1 && w % 2 == 0 {
        let even = if h % 2 == 0 { h } else { w };
        let mut mod4_2: usize = 0;
        for key in counts.clone().keys() {
            if counts.get(key).unwrap() % 4 == 2 {
                mod4_2 += 1;
                *counts.entry(*key).or_insert(0) -= 2;
            }
        }
        if mod4_2 > even / 2 {
            return "No".to_string();
        }
        let mut ok = true;
        for (_, count) in counts {
            if count % 4 != 0 {
                ok = false;
                break;
            }
        }
        return if ok {
            "Yes".to_string()
        } else {
            "No".to_string()
        };
    }

    for key in counts.clone().keys() {
        if counts.get(key).unwrap() % 2 == 1 {
            *counts.entry(*key).or_insert(0) -= 1;
            break;
        }
    }

    let mut mod4_2: usize = 0;
    for key in counts.clone().keys() {
        if counts.get(key).unwrap() % 4 == 2 {
            mod4_2 += 1;
            *counts.entry(*key).or_insert(0) -= 2;
        }
    }
    if mod4_2 > h / 2 + w / 2 {
        return "No".to_string();
    }
    let mut ok = true;
    for (_, count) in counts {
        if count % 4 != 0 {
            ok = false;
            break;
        }
    }
    return if ok {
        "Yes".to_string()
    } else {
        "No".to_string()
    };
}