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)

n, m = gets.chomp.split(" ").map(&:to_i)
h = Hash.new(0)
n.times do
  row = gets.chomp.split("")
  row.each do |c|
    h[c] += 1
  end
end
if n.even? && m.even? then
  g1 = 0
  g2 = 0
elsif n.odd? && m.odd? then
  g1 = 1
  g2 = (n / 2) + (m / 2)
else
  g1 = 0
  g2 = 0
  g2 += (n / 2) if n.even?
  g2 += (m / 2) if m.even?
  g4 = (n / 2) * (m / 2)
end

flag = true
h.each do |k, v|
  if g1 < 0 || g2 < 0 then
    flag = false
    break
  end
  if v % 4 == 0 then
    next
  elsif v % 4 == 2 then
    g2 -= 1
  elsif v % 4 == 3 then
    g2 -= 1
    g1 -= 1
  else
    g1 -= 1
  end
end

if flag then
  puts "Yes"
else
  puts "No"
end