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: Wrong Answer)



tate,yoko=gets.split
tate=tate.to_i

yoko=yoko.to_i

syoki=0
kkk=0

if tate.even? && yoko.even?
    syoki=1
elsif tate.even? || yoko.even?  
      syoki=2
      
      
else syoki=3
    
end



if syoki==2 && tate.even?
    kkk=tate
elsif syoki==2 
   kkk=yoko
end
array=[]
tate.times{
    array<<gets.chomp.split("")}


array2=array.flatten
array3=array2.uniq

larray=[]
i=0
array3.length.times{

larray<<array2.count(array3[i])
i=i+1}

yon=0
guu=0
yon2=0
guu2=0
j=0
larray.length.times{
    if larray[j]%4==0
      yon=yon+1
      yon2+=larray[j]
    end

   if larray[j]%2==0
      guu=guu+1
      guu2+=larray[j]
  end
    
  j=j+1  
    
}

if syoki==1 && yon==larray.length
 puts "Yes"
elsif syoki==1
 puts "No"
 
elsif syoki==2 &&   guu<larray.length
  puts "No"
  
elsif syoki==2 &&  tate*yoko-guu2<=kkk
  puts "Yes"
   
elsif  syoki==2
  puts "No"
  
elsif syoki==3&& guu<larray.length-1
     puts "No"
elsif  syoki==3 && yon2>=tate*yoko-tate-yoko+1
  puts "Yes"
elsif syoki==3 
  puts "No"
  end