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 (3.8.2) (judge verdict: Accepted)

H, W = map(int,input().split())
S = []
for _ in range(H):
  S.append(input())

# check palindrome

def main():
  num1 = (H*W) % 2 
  num2 = (W % 2)*H//2 + (H % 2)*W//2
  num4 = ((H*W) - num1 - num2*2)//4
  #print(num1,num2,num4)
  d = {}
  for i in range(H):
    for j in range(W):
      ch = S[i][j]
      if ch in d:
        d[ch] += 1
      else:
        d[ch] = 1

  check1 = sum([val % 2 for key,val in d.items()])
  #print(check1)
  if check1 != num1:
    return False
  
  check4 = 0
  for key,val in d.items():
    if val >= 4:
      deduct = min(num4-check4,val//4)
      d[key] = val - deduct*4
      check4 += deduct
      
      if check4 == num4:
        break
    
  #print(check4)
  if check4 != num4:
    return False
  
  check2 = sum([val//2 for key,val in d.items()])
  #print(check2)
  if check2 != num2:
    return False
      
  return True
      
  
ans = main()
if ans:
  print("Yes")
else:
  print("No")