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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List
import qualified Data.ByteString.Char8 as B
import Control.Monad

main :: IO ()
main = breads >>= main'
    where
        main' [h, w] = replicateM h getLine >>= putStrLn . solve h w . concat

solve :: Int -> Int -> String -> String
solve h w = check . foldl' ff (0, 0, 0) . group . sort
    where
        ff (acc3, acc2, acc1) g
            | n `mod` 4 == 1 = (acc3, acc2, acc1 + 1)
            | n `mod` 4 == 2 = (acc3, acc2 + 1, acc1)
            | n `mod` 4 == 3 = (acc3 + 1, acc2, acc1)
            | otherwise = (acc3, acc2, acc1)
            where
                n = length g

        check (acc3, acc2, acc1)
            | (h == 1 || w == 1) && acc3 + acc1 == 1 = "Yes"
            | (even h && even w && acc3 == 0 && acc2 == 0 && acc1 == 0) || (even h && odd w && acc3 == 0 && acc1 == 0 && acc2 <= h `div` 2) || (odd h && even w && acc3 == 0 && acc1 == 0 && acc2 <= w `div` 2) = "Yes"
            | odd h && odd w && acc3 + acc1 == 1 && acc2 <= (w + h - 2) `div` 2 = "Yes"
            | otherwise = "No"

breads :: IO [Int]
breads = unfoldr uff <$> B.getLine
    where
        uff b = check <$> B.readInt b
        check (a, b)
            | B.null b = (a, b)
            | otherwise = (a, B.tail b)