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.split.map(&:to_i)
a = h.times.map { gets.chomp }
s = a.join("")
cnt = {}
?a.upto(?z) { |c| cnt[c] = s.count(c) }

if w == 1
  if h.odd?
    puts cnt.values.select { |x| x.odd? }.size == 1 ? "Yes" : "No"
  else
    puts cnt.values.select { |x| x.odd? }.size == 0 ? "Yes" : "No"
  end
else
  if h.even? && w.even?
    puts cnt.values.select { |x| x % 4 != 0 }.size == 0 ? "Yes" : "No"
  elsif h.odd? && w.odd?
    ume = 0
    ?a.upto(?z) do |c|
      if cnt[c] >= 4 && (h - 1) * (w - 1) > ume
        ume += (cnt[c] / 4) * 4
        cnt[c] -= (cnt[c] / 4) * 4
        if (h - 1) * (w - 1) < ume
          cnt[c] += ume - (h - 1) * (w - 1)
          ume = (h - 1) * (w - 1)
        end
      end
    end
    puts cnt.values.select { |x| x.odd? }.size == 1 ? "Yes" : "No"
  else
    ume = 0
    t = h.odd? ? w : h
    ?a.upto(?z) do |c|
      if cnt[c] >= 4 && h * w - t > ume
        ume += (cnt[c] / 4) * 4
        cnt[c] -= (cnt[c] / 4) * 4
        if h * w - t < ume
          cnt[c] += ume - h * w - t
          ume = h * w - t
        end
      end
    end
    puts cnt.values.select { |x| x.odd? }.size == 0 ? "Yes" : "No"
  end
end