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: Accepted)

import java.util.Scanner;

public class Main {
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) throws Exception {
		int n=sc.nextInt();
		int m=sc.nextInt();
		sc.nextLine();
		int[] map=new int[128];
		for(int i=0;i<n;i++){
			String str=sc.nextLine();
			for(char c:str.toCharArray()){
				map[c]++;
			}
		}

		int one=(n%2)*(m%2);
		int two=(n/2)*(m%2)+(n%2)*(m/2);
		int four=(n/2)*(m/2);

	
		for(int i='a';i<='z';i++){
			four-=map[i]/4;
			map[i]%=4;
			two-=map[i]/2;
			one-=(map[i]&1);
		}
		String ans="Yes";
		if(four>0)ans="No";
		two+=2*four;
		if(two>0)ans="No";
		System.out.println(ans);
		
		
	
		
	}
}