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: Runtime Error)

H,W=gets.chomp.split(" ").map(&:to_i)
A={}
H.times do
    array=gets.chomp.split("")
    array.each do |a|
        A[a]||=0
        A[a]+=1
        A[a]%=4
    end
end
values=A.map{|_,v|v}.sort
values.delete(0)
if H.odd? && W.odd?
    found=false
    values.each_with_index do |v,i|
        if v.odd?
            found=true
            values[i]-=1
            values.delete(0)
            break
        end
    end
    if !found
        puts "No"
        exit
    end
end
values.each do |v|
    if v.odd?
        puts "No"
        exit
    end
end
if H.odd?
    (W/2).times do
        values[0]-=2
        values.delete(0)
    end
end
if W.odd?
    (H/2).times do
        values[0]-=2
        values.delete(0)
    end
end
values.each do |v|
    if v%4==2
        puts "No"
        exit
    end
end
puts "Yes"