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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public void main(Scanner sc) {
        int h = sc.nextInt();
        int w = sc.nextInt();
        int cnt[] = new int[26];
        for (int i = 0; i < h; i++) {
            String a = sc.next();
            for (int j = 0; j < w; j++) {
                cnt[a.charAt(j) - 'a']++;
            }
        }

        cnt = Arrays.stream(cnt).filter(n -> n != 0).toArray();

        System.out.println(check(h, w, cnt) ? "Yes" : "No");
    }

    private boolean check(int h, int w, int cnt[]) {
        if (Arrays.stream(cnt).filter(n -> n % 2 == 1).count() > 1) {
            return false;
        }

        long center = h % 2 * h + w % 2 * w - (h % 2 * w % 2);
        long cnt2 = Arrays.stream(cnt).filter(n -> n % 4 >= 2).count();
        if (center % 2 == cnt2 % 2) {
            return false;
        }

        return true;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        new Main().main(sc);
        sc.close();
    }
}