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 Ruby (2.3.3) (judge verdict: Accepted)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end

N,M=gets.chomp.split(' ').map{|n| n.to_i}
clcnt = 0
ccnt = 0
case N%2 + M%2
when 2
	clcnt = N+M-1
	ccnt = 1
when 1
	clcnt = (N%2)*(M/2*2)+(M%2)*(N/2*2)
	ccnt = 0
end
h = {}
0.upto(N-1){
	gets.chomp.split('').each{|a|
		h[a].nil? ? h[a]=1 : h[a]+=1
	}
}
# p clcnt
# p ccnt
# p h
h.each{|k,c|
	if(c%2==1)
		if(ccnt == 0 || clcnt < c-1)
			puts "No"
			exit(0)
		end
		ccnt -= 1
		if(c%4==2)
			if(clcnt < 2)
				puts "No"
				exit(0)
			end
			clcnt -= 2
		end
	elsif(c%4==2)
		if(clcnt < 2)
			puts "No"
			exit(0)
		end
		clcnt -= 2
	end
}
puts "Yes"