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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<string.h>

int main(void){
	
	int h,w,i,j,check=0,arf[30],ct=0,k;
	char a[200][200];
	
	for(i=0;i<=30;i++){
		arf[i]=0;
	}

	scanf("%d %d",&h,&w);
	
	for(i=1;i<=h;i++){
		for(j=1;j<=w;j++){
			scanf("%s",a[i][j]);
			k=a[i][j]-96;
			arf[k]++;
		}
	}
	
	if((h*w)%2==0){
		for(i=1;i<=26;i++){
			if(arf[i]%2==1){
				break;
			}
		}
		check=1;
	}else{
		for(i=1;i<=26;i++){
			if(arf[i]%2==1){
				ct++;
			}
		}
		if(ct<=1){
			check=1;
		}
	}
	
	if(check==1){
		printf("Yes\n");
	}else{
		printf("No\n");
	}
	
	return 0;
}