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 (2.7.1) (judge verdict: Accepted)

h, w = gets.split.map(&:to_i)
alphabes_memo = Hash.new(0)
h.times do
  gets.chomp.each_char { |c| alphabes_memo[c] += 1 }
end
same_places_memo = Hash.new(0)

# 元の場所、x軸線対称、y軸線対称、点対称が何ヶ所存在するか
def same_places (h, w, r, c)
  [[r, c], [h - 1 - r, c], [r, w - 1 - c], [h - 1 - r, w - 1 - c]].uniq.size
end

h.times do |r|
  w.times do |c|
    same_places_memo[same_places(h, w, r, c)] += 1
  end
end

mod_memo = Hash.new(0)

# 4 で割った余りがあればメモ
alphabes_memo.values.each do |v|
  mod = v % 4
  if mod == 1
    mod_memo[1] += 1
  elsif mod == 2
    mod_memo[2] += 2
  elsif mod == 3
    mod_memo[1] += 1
    mod_memo[2] += 2
  end
end

mod_memo[1] -= same_places_memo[1]
mod_memo[2] -= same_places_memo[2]

if mod_memo[1] <= 0 && mod_memo[1] + mod_memo[2] <= 0
  puts "Yes"
else
  puts "No"
end