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)

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

cA = Counter(A)

if H % 2 == 1 and W % 2 == 1:
  one = 1
  two = H // 2 + W // 2
  four = (H // 2) * (W // 2)
else:
  one = 0
  two = (H * (W % 2) + W * (H % 2)) // 2
  four = (H // 2) * (W // 2)

# print(one, two, four)

vals =[val for val in cA.values()]

# print(vals)

# one
while one > 0:
  for i in range(len(vals)):
    _, m = divmod(vals[i], 4)
    if m == 1 or m == 3:
      vals[i] -= 1
      break # 
  one -= 1

# print(vals)    

# two
if two > 0:
  for i in range(len(vals)):
    _, m = divmod(vals[i], 4)
    if two > 0 and m == 2:
      vals[i] -= 2
      two -= 1
          
# print(vals)

# four
while four > 0:
  for i in range(len(vals)):
    _, m = divmod(vals[i], 4)
    if vals[i] != 0 and m == 0:
      vals[i] -= 4
      break
  four -= 1

# print(vals)      
# print(one, two, four)

# two
while two > 0:
  for i in range(len(vals)):
    _, m = divmod(vals[i], 2)
    if vals[i] != 0 and m == 0:
      vals[i] -= 2
      break
  two -= 1

# print(vals)      
# print(one, two, four)
  
if all([val == 0 for val in vals]):
  print("Yes")
else:
  print("No")