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: Accepted)

H, W = gets.split.map &:to_i
A = ([*$<].join.chars - ["\n"]).group_by(&:itself).values.map(&:size).sort.reverse

n = (H / 2) * (W / 2)
if A.map{|a|a/4}.inject(:+) < n
  puts:No
  exit
end
i = 0
n.times{
  i += 1 while A[i] < 4
  A[i] -= 4
}
puts (if H.even? && W.even?
  A.all?{|a|a == 0}
else
  m = (H * W - n * 4) / 2
  if A.map{|a|a/2}.inject(:+) < m
    puts:No
    exit
  end
  i = 0
  m.times{
    i += 1 while A[i] < 2
    A[i] -= 2
  }
  if H.even? || W.even?
    A.all?{|a|a == 0}
  else
    *_0, _1 = A.sort
    _0.all?{|a|a == 0} && _1 == 1
  end
end)?:Yes: :No