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 (3.8.2) (judge verdict: Wrong Answer)

from collections import Counter

def solve(h, w, a):
    c = Counter(list("".join(a)))
    d = Counter(c.values())
    if (h % 2 == 0) and (w % 2 == 0):
        return "Yes" if list(d.keys()) == [4] else "No"
    if 3 in d:
        return "No"
    if (h % 2 == 1) and (w % 2 == 1):
        if (1 in d) and (d[1] != 1):
            return "No"
        if (2 in d) and d[2] > sum(x // 2 for x in [h,w]):
            return "No"
    else:
        if 1 in d:
            return "No"
        if (2 in d) and d[2] > sum((x % 2 == 0) * (x // 2) for x in [h,w]):
            return "No"
    return "Yes"

h, w = map(int, input().split())
a = [input() for r in range(h)]
print(solve(h, w, a))