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 PyPy3 (2.4.0) (judge verdict: Accepted)

from collections import Counter


def main():
    H, W = map(int, input().split())
    A = [input() for _ in range(H)]
    space = {}
    space[1] = (H % 2) * (W % 2)
    space[2] = (H % 2) * (W//2*2) + (W % 2) * (H//2*2)
    space[4] = (H//2*2) * (W//2*2)
    cnt = Counter("".join(A))
    for alpha in cnt:
        c = cnt[alpha]
        for k in (4, 2, 1):
            while c//k >= 1 and space[k]:
                y = min(c//k*k, space[k])
                space[k] -= y
                c -= y
        if c:
            print("No")
            return
    print("Yes")


if __name__ == "__main__":
    main()