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 Python (3.4.3) (judge verdict: Wrong Answer)

import itertools
import sys

h, w = map(int, input().split())

a = [input() for i in range(h)]
words = list(set(itertools.chain(*a)))
at = list(itertools.chain(*a))

mods = []
for word in words:
    mod = at.count(word) % 4
    if mod:
        mods.append(mod)
    else:
        mods.append(4)

mods = list(sorted(mods))
def count_down(l, n):
    for i in range(len(l)):
        if l[i] - n >= 0:
            l[i] -= n
            if not l[i]:
                del l[i]
            return True
    return False

if h % 2 and w % 2:
    flg = False
    for i in range(w // 2 + h // 2):
        flg = count_down(mods, 2)
    if flg and count_down(mods, 1):
        print("Yes")
        sys.exit()

elif h % 2:
    flg = False
    for i in range(w // 2):
        flg = count_down(mods, 2)
    if flg:
        print("Yes")
        sys.exit()

elif w % 2:
    flg = False
    for i in range(h // 2):
        flg = count_down(mods, 2)
    if flg:
        print("Yes")
        sys.exit()

else:
    if mods.count(4) == len(mods):
        print("Yes")
        sys.exit()

print("No")