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: Runtime Error)

h, w = readline.split.map(&:to_i)
s = h.times.flat_map do
    readline.chomp.chars
end
res = s.reduce(Hash.new(0)){|a, x| a[x] += 1; a}.values.sort.reverse

u4 = (h / 2) * (w / 2)
u2 = if h % 2 == 1 then w / 2 else 0 end + if w % 2 == 1 then h / 2 else 0 end
u1 = if h % 2 == 1 && w % 2 == 1 then 1 else 0 end

raise "No matched" unless u4 * 4 + u2 * 2 + u1 == h * w

if res.map{|i| i / 4}.sum < u4
    puts "No"
    exit
end

res.map!{|i|
    a = i / 4
    d = [a, u4].min
    u4 -= d
    i - d
}

if res.map{|i| i / 2}.sum < u2
    puts "No"
    exit
end

puts "Yes"