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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

int m,n,num[26]; char s[100009];
int main(){
	scanf("%d%d",&m,&n);
	int s1=(m>>1)*(n>>1),s2=(m&1)*(n>>1)+(m>>1)*(n&1),s3=m&n&1;
	int i,j;
	for (i=1; i<=m; i++){
		scanf("%s",s+1);
		for (j=1; j<=n; j++) num[s[j]-'a']++;
	}
	for (i=0; i<26; i++){
		while (num[i]>=4 && s1){ num[i]-=4; s1--; }
		while (num[i]>=2 && s2){ num[i]-=2; s2--; }
		while (num[i] && s3){ num[i]--; s3--; }
		if (num[i]) break;
	}
	puts(i<26?"No":"Yes");
	return 0;
}