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 Julia (0.5.0) (judge verdict: Wrong Answer)

function main()
	H,W=map(x->parse(Int,x),split(readline()))
	cnt=zeros(Int,26)
	for _=1:H
		for c=chomp(readline())
			cnt[Int(c)-96]+=1
		end
	end
	c4=c2=c1=0
	if H%2==1&&W%2==1
		c1=1
		c2=div(H-1,2)+div(W-1,2)
	elseif H%2==1&&W%2==0
		c2=div(W,2)
	elseif H%2==0&&W%2==1
		c2=div(H,2)
	end
	c4=div(H*W-c1-c2,4)
	for i=1:26
		t=min(c4,div(cnt[i],4))
		c4-=t
		cnt[i]-=4t
	end
	for i=1:26
		t=min(c2,div(cnt[i],2))
		c2-=t
		cnt[i]-=2t
	end
	println(c4==c2==0&&sum(cnt)==c1 ? "Yes" : "No")
end
main()