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 input::*;
use std::cmp::*;
use std::io::*;
use std::num::*;
use std::str::*;

mod input {
    use super::*;
    pub fn read<T: FromStr>() -> T {
        stdin()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<T>()
            .ok()
            .unwrap()
    }
    pub fn string() -> String {
        read()
    }
    pub fn int() -> i64 {
        read()
    }
    pub fn char() -> char {
        read::<String>().pop().unwrap()
    }
    pub fn vecchar() -> Vec<char> {
        string().chars().collect()
    }
    pub fn vecint(n: i64) -> Vec<i64> {
        let mut vec = Vec::new();
        for i in 0..n {
            vec.push(int())
        }
        vec
    }
}
fn main() {
    let (h, w) = (int() as usize, int() as usize);
    let mut a = Vec::new();
    for _ in 0..h {
        a.push(vecchar());
    }
    let mut count: Vec<usize> = vec![0; 26];
    for row in a {
        for ch in row {
            count[ch as usize - 'a' as usize] += 1;
        }
    }
    count.sort();
    if h % 2 == 0 && w % 2 == 0 {
        for c in count {
            if c % 4 != 0 {
                println!("No");
                return;
            }
        }
        println!("Yes");
    } else if h % 2 == 0 {
        let mut v = 0;
        for c in count {
            if c % 4 != 0 {
                if c % 2 != 0 {
                    println!("No");
                    return;
                }
                v += 1;
            }
        }
        if v <= h / 2 {
            println!("Yes");
        } else {
            println!("No");
        }
    } else if w % 2 == 0 {
        let mut v = 0;
        for c in count {
            if c % 4 != 0 {
                if c % 2 != 0 {
                    println!("No");
                    return;
                }
                v += 1;
            }
        }
        if v <= w / 2 {
            println!("Yes");
        } else {
            println!("No");
        }
    } else {
        let mut two = 0;
        let mut one = 0;
        for c in count {
            if c % 4 != 0 {
                match c % 4 {
                    1 => {
                        one += 1;
                    }
                    2 => {
                        two += 1;
                    }
                    3 => {
                        one += 1;
                        two += 1;
                    }
                    _ => (),
                }
            }
        }
        if one > 1 || two > (h - 1) / 2 + (w - 1) / 2 {
            println!("No");
        } else {
            println!("Yes");
        }
    }
}