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.split.map(&:to_i)
if H % 2 == 0 && W % 2 == 0
    n4, n2, n1 = H*W/4, 0, 0
elsif H % 2 == 0
    n4, n2, n1 = H*(W-1)/4, H/2, 0
elsif W % 2 == 0
    n4, n2, n1 = (H-1)*W/4, W/2, 0
else
    n4, n2, n1 = (H-1)*(W-1)/4, (H+W)/2-1, 1
end

hash = Hash.new(0)
H.times do |i|
    gets.chomp.split('').each do |c|
        hash[c] += 1
    end
end

nums = hash.values
nums.length.times do |i|
    if nums[i] % 2 == 1 && n1 == 1
        nums[i] -= 1
        n1 = 0
    end
    while nums[i] > 0
        if n4 > 0 && nums[i] >= 4
            nums[i] -= 4
            n4 -= 1
        else
            nums[i] -= 2
            n2 -= 1
        end
    end
end

puts nums.all?(&:zero?) && [n4, n2, n1].all?(&:zero?) ? 'Yes' : 'No'