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(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    if solve() {
        println!("Yes");
    } else {
        println!("No");
    }
}
fn solve() -> bool {
    let v = read_vec::<usize>();
    let (h, w) = (v[0], v[1]);
    let mut s = Vec::new();
    for _ in 0..h {
        s.push(read::<String>().chars().collect::<Vec<_>>());
    }
    let mut count = vec![0; 26];
    for i in 0..h {
        for &ch in s[i].iter() {
            count[ch.to_digit(36).unwrap() as usize - 10] += 1;
        }
    }
    let mut odd_count = 0;
    let mut even_count = 0;
    for i in 0..26 {
        if count[i] % 2 == 1 {
            odd_count += 1;
        } else if count[i] % 4 != 0 {
            even_count += 1;
        }
    }
    debug!(odd_count, even_count);
    if h == 1 && w == 1 {
        return true;
    } else if h == 1 || w == 1 {
        return odd_count <= 1;
    }

    if h % 2 == 0 && w % 2 == 0 {
        return odd_count == 0 && even_count == 0;
    } else if h % 2 == 1 && w % 2 == 1 {
        return odd_count == 1 && (even_count <= (h - 1) / 2 + (w - 1) / 2);
    } else if h % 2 == 0 {
        return odd_count == 0 && even_count <= h / 2;
    } else {
        assert!(w % 2 == 0);
        return odd_count == 0 && even_count <= w / 2;
    }
}

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()
}

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