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)

h,w = map(int, input().split())
al = [list(input()) for _ in range(h)]
cnts = {}
for row in al:
    for a in row:
        cnts.setdefault(a,0)
        cnts[a] += 1
        cnts[a]%= 4

c4 = [0]*5
for i,v in cnts.items():
    c4[v] += 1
c4[4] = c4[0]


if w%2 == 0 and h%2 == 0:
    if c4[1] == 0 and c4[2] == 0 and c4[3] == 0:
        print('Yes')
    else:
        print('No')

elif w%2 == 1 and h%2 == 1:
    if c4[1] + c4[3] == 1 and c4[3] + c4[2] <= (h-1)//2 + (w-1)//2:
        print('Yes')
    else:
        print('No')

elif w%2 == 1 and h%2 == 0:
    if c4[1] + c4[3] == 0 and c4[2] <= h//2:
        print('Yes')
    else:
        print('No')

elif w%2 == 0 and h%2 == 1:
    if c4[1] + c4[3] == 0 and c4[2] <= w//2:
        print('Yes')
    else:
        print('No')