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.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);

	        int H = sc.nextInt();
	        int W = sc.nextInt();
	        int[] m = new int[26];
	        for(int i=0;i<H;i++) {
	        	String S =sc.next();
	        	char[] c=S.toCharArray();
	        	for(int j=0;j<W;j++) {
	        		m[c[j]-'a']++;
	        	}
	        }
	        int f1=0;
	        int f2=0;
	        if(H%2==1&&W%2==1) {
	        	f1=H/2+W/2;
	        	f2=1;
	        } else if(H%2==1) {
	        	f1=W/2;
	        } else if(W%2==1) {
	        	f1=H/2;
	        }
	        for(int i=0;i<26;i++) {
	        	if(m[i]%2==1) {
	        		f2--;
	        	}
	        	if(m[i]%4==2) {
	        		f1--;
	        	}
	        }
	        String ans="Yes";
	        if(f1<0||f2<0) {
	        	ans="No";
	        }
	        
	        System.out.println(ans);
	       
	    }

	}