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)

def halt(ans)
	puts ans
	exit
end
n, m = gets.split.map(&:to_i)
hash = n.times.map { gets.chomp }.flatten.inject({}) { |sum, s| sum.merge(s.each_char.group_by(&:itself).inject({}) { |h, (k, v)| h[k] = v.count; h }) { |_,a,b| a + b } }
remain = (n / 2) * (m / 2)
hash.each do |c, count|
	i = count / 4
	hash[c] -= i * 4
	remain -= i
end
halt 'No' if remain > 0

odd = hash.find { |k,v| v.odd? }
hash[odd.first] -= 1 unless odd.nil?
halt 'No' if hash.any? { |k,v| v.odd? }
halt 'Yes'