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: Accepted)

def main():
    h, w = map(int, input().split())
    alp = [0]*26
    for _ in range(h):
        s = input()
        for c in s:
            p = ord(c) - ord("a")
            alp[p] += 1
    f = True
    cnt_1, cnt_2, cnt_4 = 0, 0, 0
    if h%2 == 1 and w%2 == 1:
        cnt_1 = 1
        cnt_2 = w-1 + h-1
        cnt_4 = (w-1)*(h-1)
    elif h%2 == 1 and w%2 == 0:
        cnt_2 = w
        cnt_4 = w*(h-1)
    elif h%2 == 0 and w%2 == 1:
        cnt_2 = h
        cnt_4 = (w-1)*h
    else:
        cnt_4 = w*h
    for i in range(26):
        while cnt_4 > 0 and alp[i]>=4:
            alp[i] -= 4
            cnt_4 -= 4
    if cnt_4 > 0:
        f = False
    for i in range(26):
        while cnt_2 > 0 and alp[i]>=2:
            alp[i] -= 2
            cnt_2 -= 2
    if cnt_2 > 0:
        f = False
    for i in range(26):
        while cnt_1 > 0 and alp[i]>=1:
            alp[i] -= 1
            cnt_1 -= 1
    if cnt_1 > 0:
        f = False
    if f:
        print("Yes")
    else:
        print("No")

if __name__ == "__main__":
    main()