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: Accepted)

use std::io::stdin;
use std::collections::HashMap;

fn main() {
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let (h, w) = {
        let nk:Vec<_> = st.trim().split(" ").map(|x| x.parse::<i32>().unwrap()).collect();
        (nk[0], nk[1])
    };
    let mut map:HashMap<char, i32> = HashMap::new();
    for _i in 0..h {
        let mut st = String::new();
        stdin().read_line(&mut st).unwrap();
        let a:Vec<char> = st.trim().chars().collect();
        for j in a {
            let count:&mut i32 = map.entry(j).or_insert(0);
            *count += 1;
        };
    };
    let mut f:i32 = 0;
    let mut t:i32 = 0;
    let mut one:i32 = 0;
    f = w*h/4;
    if h%2==1 {
        t += w/2;
    }
    if w%2==1 {
        t += h/2;
    }
    if h%2==1 && w%2==1 {
        one = 1;
    };
    let mut result = "Yes";
    for (i, j) in map.iter() {
        let mut num = *j as i32;
        if num%2==1 {
           if one > 0 {
               num -= 1;
               one -= 1;
           } else {
               result = "No"
           };
        }
        while f > 0 && num >= 4 {
            num -= 4;
            f -= 1;
        }
        while t > 0 && num >= 2 {
            num -= 2;
            t -= 1;
        };
        if num > 0 {
            result = "No";
            break;
        } else if result =="No" {
            break;
        }
    };
    println!("{}", result);
}