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)


a = gets.chomp.split(" ").map(&:to_i)
b = []
a[0].times do
  b << gets.chomp.split("")
end

for i in 0..a[0]-1
  box = Hash.new{|k,v| k[v]=false}
  for j in 0..a[1]-1
    box[b[i][j]] ^= true
  end
  if a[0] % 2 > box.values.select{|t| t == true}.count 
    puts "No"
    exit
  end 
  #if a[0] % 2 != 0 && b[i].uniq.size % 2 != 0
  #  puts "No"
  #  exit
  #end 
end

for i in 0..a[1]-1
  box = Hash.new{|k,v| k[v]=false}
  for j in 0..a[0]-1
    box[b[j][i]] ^= true
  end
  if a[1] % 2 > box.values.select{|t| t == true}.count 
    puts "No"
    exit
  end 
  
end

puts "Yes"