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)

fn main() {
  let (h,w): (usize, usize) = read_tuple();
  let mut mat: Vec<Vec<String>> = read_mat(h);
  
  let mut vec: Vec<String> = vec![];
  for line in mat.clone().as_mut_slice() {
    vec.append(&mut (line.clone()));
  }
  
  vec.sort();
  let last = vec.pop().unwrap();
  vec.push(last.clone());
  vec.push(last);
  let mut buf = vec![0; h*w];
  let mut i = 0;
  for w in vec.windows(2) {
    if w[0].as_str() != w[1].as_str() {
      buf[i] += 1;
      i += 1;
    } else {
      buf[i] += 1;
    }
  }
  
  let max = buf.iter().max().unwrap();
  let odd = buf.iter().filter(|&x| x%2 == 1).count();
  
  let ans =
    if (h*w) % 2 == 1 && (h==1 || w==1) {
      *max == 2 && odd == 1
    } else if (h*w) % 2 == 1 {
      *max == 4 && odd == 1
    } else if h==1 || w==1 {
      *max == 2 && odd == 0
    } else {
      *max == 4 && odd == 0
    };
  
  println!("{}", ans);
}

fn read_tuple<T1: std::str::FromStr, T2: std::str::FromStr>() -> (T1, T2) {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  let mut it = buf.trim().split_whitespace();
  let x = it.next().unwrap().parse::<T1>().ok().unwrap();
  let y = it.next().unwrap().parse::<T2>().ok().unwrap();
  (x, y)
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
}

fn read_mat<T: std::str::FromStr>(h: usize) -> Vec<Vec<T>> {
  let mut mat: Vec<Vec<T>> = vec![];
  for _ in 0 .. h {
    mat.push(read_vec());
  }
  mat
}