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)
table = Array.new(26, 0)
a = h.times.map{gets.chomp}
a.each do |c|
  c.each_char do |cc|
    table[cc.ord - "a".ord] += 1
  end
end
c4 = 0
c2 = 0
c1 = 0
table.each do |d|
  while d > 0
  if(d / 4 > 0)
    c4 += d / 4 
    d %= 4
  elsif(d % 2 == 0)
    c2 += d
    d %= 2 
  else
    c1 += d
    d = 0
  end
  end
end
if((h%2) == 0 and (w%2) == 0)
  puts (c1 <= 0 and c2 <= 0)? "Yes" : "No"
elsif(h % 2 == 1 and w %2 == 0 )
  puts (c1 <= 0 and c2 <= (w))? "Yes" : "No"
elsif(h%2 == 0 and w %2 == 1)
  puts (c1 <= 0 and c2 <= (h))? "Yes" : "No"
else
  puts (c1 <= 1 and c2 <= (h + w - 2))? "Yes" : "No"
end