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: Accepted)

h,w = map(int,input().split())
lis = [0 for i in range(26)]
s = [str(input()) for i in range(h)]
for i in range(h):
  for j in range(w):
    lis[ord(s[i][j])-ord("a")] += 1
lis.sort()
cnt1 = 0
cnt4 = 0
for num in lis:
  if num % 2 == 1:
    cnt1 += 1
  cnt4 += num//4
if h % 2 == 0:
  if w % 2 == 0:
    if cnt4 == (h//2)*(w//2):
      print("Yes")
    else:
      print("No")
  else:
    if cnt1 == 0 and cnt4 >= (h//2)*(w//2):
      print("Yes")
    else:
      print("No")
else:
  if w % 2 == 0:
    if cnt1 == 0 and cnt4 >= (h//2)*(w//2):
      print("Yes")
    else:
      print("No")
  else:
    if cnt1 == 1 and cnt4 >= (h//2)*(w//2):
      print("Yes")
    else:
      print("No")