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)

from collections import Counter
H, W = map(int, input().split())
S = ""
for _ in range(H):
    a = str(input())
    S += a

C = Counter(S)
count_list = list(C.values())
if H % 2 == 0 or W % 2 == 0:  # どちらかが偶数であれば要素が1つのグループは存在しない
    g1 = 0
else:
    g1 = 1

g2 = int(H/2) + int(W/2)
g4 = int(H/2) * int(W/2)
flag = True
while sum(count_list) != 0:
    tmp = sum(count_list)
    for i in range(len(count_list)):
        if count_list[i] % 4 == 2 and g2 > 0:
            count_list[i] -= 2
            g2 -= 1
        elif count_list[i] % 4 == 0 and count_list[i] > 0 and g4 > 0:
            count_list[i] -= 4
            g4 -= 1
        elif count_list[i] % 4 in [1, 3] and g1 > 0:
            count_list[i] -= 1
            g1 -= 1

    if tmp == sum(count_list):
        flag = False
        break

if flag and g4 == 0:
    print('Yes')
else:
    print('No')