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)

from collections import Counter

H, W = map(int, input().split())
lis = []
for i in range(H):
    a = list(input())
    lis += a

lis = list(Counter(lis).values())
length = len(lis)

check_4 = 0
check_2 = 0
check_kisu = 0
for i in lis:
    if i % 4 == 0:
        check_4 += 1
    elif i % 2 == 0:
        check_2 += 1
    else:
        if check_kisu:
            print('No')
            exit()
        else:
            check_kisu = i % 4

if (H % 2 == 0) & (W % 2 == 0):
    if (check_kisu != 0) | (check_2 != 0):
        print('No')
        exit()

elif (H % 2 == 1) & (W % 2 == 1):
    if (H + W - 1 < check_kisu + 2 * check_2) | ((H + W - 1 - check_kisu - 2 * check_2) % 4 != 0):
        print('No')
        exit()

elif H % 2 == 1:
    if (W < 2 * check_2) | ((W - 2 * check_2) % 4 != 0):
        print('No')
        exit()


elif W % 2 == 1:
    if (H < 2 * check_2) | ((H - 2 * check_2) % 4 != 0):
        print('No')
        exit()

print('Yes')