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 (3.4.3) (judge verdict: Wrong Answer)

H, W = map(int, input().split())

target4 = int(H / 2) * int(W / 2)
if H % 2 == 0:
    if W % 2 == 0:
        target2 = 0
    else:
        target2 = int(H / 2)
else:
    if W % 2 == 0:
        target2 = int(W / 2)
    else:
        target2 = max(int(W / 2), int(H / 2))
target1 = 1 if (H % 2 == 1 and W % 2 == 1) else 0

a = [input() for _ in range(H)]

flag = False

count1 = 0
count2 = 0
count4 = 0
for i in range(26):
    count = sum([a[h].count(chr(97 + i)) for h in range(H)])
    count4 += int(count / 4)
    count2 += int((count - int(count / 4) * 4) / 2)
    count1 += count % 2

if target1 < count1:
    print('No')
elif target2 < count2:
    print('No')
else:
    print('Yes')