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)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (H, W): (usize, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap()
        )
    };
    let S: Vec<Vec<char>> = (0..H).map(|_| {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().chars().collect()
    }).collect();

    let mut c = std::collections::HashMap::new();
    for i in 0..H { for j in 0..W { *(c.entry(S[i][j]).or_insert(0)) += 1; } }
    let mut dp = vec![0, 0, 0, 0];
    for (_, &v) in &c { dp[v % 4] += 1; }

    let ans = if (H % 2 == 0 && W % 2 == 0 && dp[1] == 0 && dp[2] == 0 && dp[3] == 0) ||
        (H % 2 == 0 && W % 2 == 1 && dp[1] == 0 && dp[3] == 0 && dp[2] <= H / 2) ||
        (H % 2 == 1 && W % 2 == 0 && dp[1] == 0 && dp[3] == 0 && dp[2] <= W / 2) ||
        (H % 2 == 1 && W % 2 == 1 && dp[1] + dp[3] <= 1 && dp[2] + dp[3] <= H / 2 + W / 2) { "Yes" }
        else { "No" };

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