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)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn main() {
    let hw: Vec<usize> = read_vec();
    let h = hw[0];
    let w = hw[1];
    let mut cnt: Vec<u32> = vec![0; 26];
    for _ in 0..h {
        let s: String = read();
        let cv: Vec<char> = s.chars().collect();
        for c in cv {
            cnt[c as usize - 'a' as usize] += 1;
        }
    }

    if h % 2 == 0 {
        if w % 2 == 0 {
            for c in cnt {
                if c % 4 != 0 {
                    println!("No");
                    return;
                }
            }
            println!("Yes");
        } else {
            let mut tmp = 0;
            for c in cnt {
                if c % 2 != 0 {
                    println!("No");
                    return;
                } else if c % 4 != 0 {
                    tmp += 1;
                }
            }
            if tmp <= h / 2 {
                println!("Yes");
            } else {
                println!("No");
            }
        }
    } else {
        if w % 2 == 0 {
            let mut tmp = 0;
            for c in cnt {
                if c % 2 != 0 {
                    println!("No");
                    return;
                } else if c % 4 != 0 {
                    tmp += 1;
                }
            }
            if tmp <= w / 2 {
                println!("Yes");
            } else {
                println!("No");
            }
        } else {
            let mut tmp = 0;
            for i in 0..26 {
                if cnt[i] % 2 != 0 {
                    cnt[i] -= 1;
                    tmp += 1;
                }
            }
            if tmp != 1 {
                println!("No");
                return;
            }

            let mut tmp = 0;
            for c in cnt {
                if c % 4 != 0 {
                    tmp += 1;
                }
            }
            if tmp <= w / 2 + h / 2 {
                println!("Yes");
            } else {
                println!("No");
            }
        }
    }
}