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 (7.3.0) (judge verdict: Accepted)

def main():
    from collections import Counter
    from heapq import heapify,heappop,heappush
    H,W = map(int,input().split())
    A = ''
    for i in range(H):
        A += input()
    A = list(A)
    num_chars = list(map(lambda x: -x, Counter(A).values()))
    heapify(num_chars)
    # H == 1 or W == 1

    for i in range((H//2)*(W//2)):
        num = heappop(num_chars)
        
        if -4 < num:
            print('No')
            return
        else:
            heappush(num_chars,num+4)

    if H & 1:
        for i in range(W//2):
            num = heappop(num_chars)
            if -2 < num:
                print('No')
                return
            else:
                heappush(num_chars,num+2)

    if W & 1:
        for i in range(H//2):
            num = heappop(num_chars)
            if -2 < num:
                print('No')
                return
            else:
                heappush(num_chars,num+2)

    print('Yes')
    return
    






main()