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 static void my_add(char x, int[] sum){
        int y=x-'a';
        if(sum[y]==3)
        {
            sum[y]=0;
        }
        else{
            sum[y]++;
        }
    }
    public static int[] resres(int[] sum){
        int[] result= {0,0,0,0};
        for(int k=0;k<26;k++){
            result[sum[k]]++;
        }
        return result;

    }

    public static void main(String[] args) {
        Scanner re = new Scanner(System.in);
        int m = re.nextInt();
        int n = re.nextInt();
        int[] res = new int[26];
        for (int i = 0; i < m; i++) {
            String A = re.next();
            for (int j = 0; j < n; j++) {
                my_add(A.charAt(j), res);
            }
        }
        int[] oh = resres(res);
        if (m == 1 || n == 1) {
            if (oh[1] + oh[3] <= 1) {
                System.out.println("Yes");

            } else {
                System.out.println("No");
            }
        } else {
            if (m % 2 == 0) {
                if (n % 2 == 0) {
                    if (((oh[1] == 0) && (oh[2] == 0) && (oh[3] == 0))) {
                        System.out.println("Yes");

                    } else {
                        System.out.println("No");
                    }
                } else {
                    if (oh[1] + oh[3] > 1) {
                        System.out.println("No");
                    } else {
                        if (oh[2] +oh[3]> (n - 1) / 2) {
                            System.out.println("No");
                        } else {
                            System.out.println("Yes");
                        }
                    }
                }

            } else {
                if (n % 2 == 1) {
                    if (oh[1] + oh[3] < 1 && oh[2] + oh[3] < (m + n - 2) / 2) {
                        System.out.println("Yes");

                    } else {
                        System.out.println("No");
                    }
                } else {
                    if (oh[1] + oh[3] > 1) {
                        System.out.println("No");
                    } else {
                        if (oh[2] +oh[3]> n / 2) {
                            System.out.println("No");
                        } else {
                            System.out.println("Yes");
                        }
                    }
                }
            }

        }

    }}