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())
a = [list(input()) for _ in range(h)]
 
cnt = {}
for ai in a:
    for c in ai:
        if c in cnt:
            cnt[c] += 1
        else:
            cnt[c] = 1
c1 = 0
c2 = 0
c4 = 0
for k, v in cnt.items():
    c4 += (v // 4) * 4
    c2 += ((v % 4) // 2) * 2
    c1 += v % 2
 
ans = "No"
if h % 2 == 0:
    if w % 2 == 0:
        if c4 == h * w:
            ans = "Yes"
    else:
        if c2 <= h and c1 == 0:
            ans = "Yes"
else:
    if w % 2 == 0:
        if c2 <= w and c1 == 0:
            ans = "Yes"
    else:
        if c2 <= h + w - 1 and c1 == 1:
            ans = "Yes"
print(ans)