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)

h, w = gets.chomp.split(" ").map(&:to_i)

hash = Hash.new(0)

h.times do
  input = gets.chomp.split("")
  input.each do |c|
    hash[c] += 1
  end
end

hash = hash.sort { |(k1, v1), (k2, v2)| v2 <=> v1 }

remain_h = h

if h == 1
  if w == 1
    puts "Yes"
    exit
  else
    (w/2).times do |i|
      hash[0][1] -= 2
      if hash[0][1] < 0
        puts "No"
        exit
      elsif hash[0][1] == 0
        hash = hash[1..hash.size-1]
      else
        hash = hash.sort { |(k1, v1), (k2, v2)| v2 <=> v1 }
      end
    end
    if w%2 == 1
      if hash[0][1] >= 1
        puts "Yes"
        exit
      else
        puts "No"
        exit
      end
    end
    puts "Yes"
    exit
  end
elsif w == 1
  if h == 1
    puts "Yes"
    exit
  else
    (h/2).times do |i|
      hash[0][1] -= 2
      if hash[0][1] < 0
        puts "No"
        exit
      elsif hash[0][1] == 0
        hash = hash[1..hash.size-1]
      else
        hash = hash.sort { |(k1, v1), (k2, v2)| v2 <=> v1 }
      end
    end
    if h%2 == 1
      if hash[0][1] >= 1
        puts "Yes"
        exit
      else
        puts "No"
        exit
      end
    end
    puts "Yes"
    exit
  end
else
  (h-1).times do |j|
    (w/2).times do |i|
      hash[0][1] -= 4
      if hash[0][1] < 0
        puts "No"
        exit
      elsif hash[0][1] == 0
        hash = hash[1..hash.size-1]
      else
        hash = hash.sort { |(k1, v1), (k2, v2)| v2 <=> v1 }
      end
    end
    if w%2 == 1
      hash[0][1] -= 2
      if hash[0][1] < 0
        puts "No"
        exit
      elsif hash[0][1] == 0
        hash = hash[1..hash.size-1]
      else
        hash = hash.sort { |(k1, v1), (k2, v2)| v2 <=> v1 }
      end
    end

    remain_h -= 2

    if remain_h == 1
      (w/2).times do |i|
        hash[0][1] -= 2
        if hash[0][1] < 0
          puts "No"
          exit
        elsif hash[0][1] == 0
          hash = hash[1..hash.size-1]
        else
          hash = hash.sort { |(k1, v1), (k2, v2)| v2 <=> v1 }
        end
      end

      puts "Yes"
      exit
    elsif remain_h == 0

      puts "Yes"
      exit
    end

  end
end

puts "Yes"