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: Runtime Error)

from collections import Counter, defaultdict
H, W = map(int, input().split(' '))
d = defaultdict(int)
for i in range(H):
    for k, v in Counter(input()).items():
        d[k] += v
if H % 2 == 0 and W % 2 == 0:
    for i in d.values():
        if i % 4 != 0:
            print('No')
            exit()
    print('Yes')
elif H % 2 == 0 or W % 2 == 0:
    cnt = H//2 if not H % 2 else W//2
    for i in d.values():
        if i % 4 == 0:
            continue
        elif i % 2 == 0:
            cnt -= 1
            if cnt >= 0:
                continue
        print('No')
        exit()
    print('Yes')
else:
    raise TypeError
    odd = 1
    cnt = H+W-1
    for i in d.values():
        if i % 2 != 0 and odd:
            odd -=1
            continue
        elif i % 4 == 0:
            continue
        elif i % 2 == 0 and cnt:
            cnt -= 1
            continue
        else:
            print('No')
            exit()
    print('Yes')