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.chomp.split.map(&:to_i)

chars = ""

h.times do |i|
  chars << gets.chomp
end

ec = ("a".."z").map do |c|
  chars.count(c)
end

x4 = (h/2) * (w/2)
x2 = (h%2) * (w/2) + (h/2) * (w%2)
x1 = (h%2) * (w%2)

res = true

ec.each do |c|
  hoge = c

  s4 = [((hoge/4)), x4].min
  x4 -= s4
  hoge -= s4 * 4
  s2 = [((hoge/2)), x2].min
  x2 -= s2
  hoge -= s2 * 2
  s1 = [((hoge)), x1].min
  x1 -= s1
  hoge -= s1 * 1

  res = false if hoge>0
end

res = false if x4 > 0 or x2 > 0 or x1 > 0

puts (res ? "Yes" : "No")