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 (2.7.1) (judge verdict: Accepted)

def gi; gets.split.map(&:to_i); end
H,W=gi

h=Hash.new(0)
$<.read.each_char do |c|
    h[c] += 1 if c != "\n"
end

x1 = (H.odd? && W.odd? ? 1 : 0)
x2 = 0
x2 += H/2 if W.odd?
x2 += W/2 if H.odd?
x4 = (H/2) * (W/2)

vs = h.values
n4 = vs.inject(0) {|n,v|n+=v/4}
n2 = vs.inject(0) {|n,v|n+=v/2} - x4*2
n1 = vs.inject(0) {|n,v|n+=v} - x4*4 - x2*2

if x4<=n4 && x2<=n2 && x1<=n1
    puts 'Yes'
else
    puts 'No'
end