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.Arrays;
import java.util.Scanner;
 
public class Main {
	
	public static void main(String[] args) {
		new Main().solve();
	}
	
	void solve(){
		Scanner sc=new Scanner(System.in);
		int H=sc.nextInt();
		int W=sc.nextInt();
		char[][]a=new char[H][W];
		for(int i=0;i<H;i++) {
			String s=sc.next();
			a[i]=s.toCharArray();
		}
		int[]alph=new int[26];
		for(int i=0;i<H;i++) {
			for(int j=0;j<W;j++) {
				alph[a[i][j]-'a']++;
			}
		}
		int g1=(H%2)*(W%2);
		int g2=(H/2)*(W%2)+(W/2)*(H%2);
		int g3=(H/2)*(W/2);
		
		
		for(int i=0;i<26;i++) {
			g3-=alph[i]/4;
			alph[i]%=4;
			
			g2-=alph[i]/2;
			alph[i]%=2;
			
			g1-=alph[i]%2;
		}
		String ans="Yes";
		if(g3>0)ans="No";
		g2+=2*g3;
		if(g2>0)ans="No";
		System.out.println(ans);
	}
}