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.HashMap;
import java.util.Scanner;
import java.util.stream.IntStream;
 
public class Main{
	static IntStream REPS(int v){return IntStream.range(0,v);}
	static IntStream REPS(int l,int r){return IntStream.rangeClosed(l,r);}
	static IntStream INS(int n){return REPS(n).map(i->getInt());}
	static Scanner s=new Scanner(System.in);
	static int getInt(){return Integer.parseInt(s.next());}
 
	public static void main(String[]$){
		int h=getInt(),w=getInt();
		HashMap<Integer,Integer>charcount=new HashMap<>();
		REPS(h).flatMap(i->s.next().chars()).forEach(o->charcount.merge(o,1,Integer::sum));
 
		HashMap<Integer,Integer>cc=new HashMap<>();
		cc.put(0,0);
		cc.put(1,0);
		cc.put(2,0);
		cc.put(3,0);
		charcount.forEach((a,b)->cc.merge(b%4,1,Integer::sum));
		//System.out.println(cc);
 
		if(h==1||w==1) {
			out(cc.get(1)+cc.get(3)<=1);
			return;
		}
		
		if(h%2==0&&w%2==0) {
			out(cc.get(1)+cc.get(2)+cc.get(3)==0);
			return;
		}
		out(cc.get(1)+cc.get(3)<=1&&cc.get(2)<h%2+w%2);
	}
	private static void out(boolean b){
		System.out.println(b?"Yes":"No");
	}
}