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: Runtime Error)

h,w,$d = gets.split(" ").map(&:to_i)
$table = []
h.times do |i|
  $table[i] = []
  w.times do |j|
    $table[i][j] = ["R", "Y", "G", "B"]
  end
end


def remove(i, j, c)
  (0..$d).each do |k|
    [-1, 1].each do |a|
      ii = i+a*k
      next if ii < 0
      next unless $table[ii]
      [-1, 1].each do |b|
        jj = j+b*($d-k)
        next if jj < 0
        next unless $table[ii][jj]
        next if $table[ii][jj] == [c]
        rep = $table[ii][jj].include? c
        $table[ii][jj] -= [c]
        #remove(ii, jj, c) if rep
      end
    end
  end
end
h.times do |i|
  w.times do |j|
    c = $table[i][j].first
    next if $table[i][j].length == 1
    $table[i][j] = [c]
    remove(i, j, c)
  end
end
$table.each do |row|
  row.each do |v|
    print v[0]
  end
  puts ""
end