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)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
      return Array.new(size1){init}
  else
      return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

H,W=get_i
kind=Hash.new(0)
H.times do|i|
    get_nsp.each do|a|
        kind[a]+=1
    end
end

if W.even? or H.even?
  kind.each do|k,v|
      if kind[k].odd?
          puts "No"
          exit
      end
      kind[k]/=2
  end
  cnt=kind.count{|x| x[1].odd?}
  if W.even? and H.even?
    if cnt.zero?
        puts "Yes"
    else
        puts "No"
    end
  else
      even=(W.even? ? W : H)
      if cnt<=even/2
          puts "Yes"
      else
          puts "No"
      end
  end
else
    g={}
    g[1]=0
    g[2]=0
    g[4]=0
    kind.each do|k,v|
      if v>=4
          g[4]+=v/4
          v%=4
      end
      if v>=2
          g[2]+=1
          v%=2
      end
      if v==1
          g[1]+=1
      end
    end
    if g[1]==1 and g[4]>=(H/2)*(W/2) and (g[4]-(H/2)*(W/2))*2+g[2]>=H/2+W/2
        puts "Yes"
    else
        puts "No"
    end
end