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)

#[test]
fn test_solve() {
    assert_eq!(solve("3 4\naabb\naabb\naacc\n"), "Yes\n");
    assert_eq!(solve("2 2\naa\nbb\n"), "No\n");
    assert_eq!(solve("5 1\nt\nw\ne\ne\nt\n"), "Yes\n");
    assert_eq!(solve("2 5\nabxba\nabyba\n"), "No\n");
    assert_eq!(solve("1 1\nz\n"), "Yes\n");
}

fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let h: usize = sc.read();
    let w: usize = sc.read();
    let crd = |c: char| c as usize - 'a' as usize;
    let mut cnt = vec![0; crd('z') + 1];
    for _ in 0..h {
        let s = sc.get().chars();
        for c in s {
            cnt[crd(c)] += 1;
        }
    }
    let mut c1 = 0;
    let mut c2 = 0;
    for mut c in cnt {
        if c & 1 == 1 {
            c1 += 1;
        }
        c >>= 1;
        if c & 1 == 1 {
            c2 += 1;
        }
    }
    let (a1, a2) = match (h & 1, w & 1) {
        (0, 0) => (0, 0),
        (1, 1) => (1, (h + w) / 2 - 1),
        (1, 0) => (0, w / 2),
        (0, 1) => (0, h / 2),
        (_, _) => unreachable!(),
    };
    if c1 == a1 && c2 <= a2 && (a2-c2) & 1 == 0 {
        "Yes\n".to_string()
    } else {
        "No\n".to_string()
    }
}

fn main() {
    let mut buf = String::new();
    use std::io;
    use std::io::{Read, Write};
    io::stdin().read_to_string(&mut buf).unwrap();
    io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}

struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}