output_description: Output the number of integers that meet the above criteria.
input_description: The input is given in the following format.
  
      
      
      $a$ $n$ $m$
      
  
  The input line provides three integers: $a$ ($0 \leq a \leq 50$), $n$ ($2 \leq
  n \leq 10$) and the upper limit $m$ ($1000 \leq m \leq 10^8$).
attempt: a, n, m = map(int, input().split())
  cnt = 0
  for y in range(1, m + 1):
      s = (sum(list(map(int, str(y)))) + a) ** n
      if s > m:
          break
      if s == y:
          cnt += 1
  print(cnt)
  
problem_description: Dudeney Number
  
  A Dudeney number is a positive integer for which the sum of its decimal digits
  is equal to the cube root of the number. For example, $512$ is a Dudeney
  number because it is the cube of $8$, which is the sum of its decimal digits
  ($5 + 1 + 2$).
  
  In this problem, we think of a type similar to Dudeney numbers and try to
  enumerate them.
  
  Given a non-negative integer $a$, an integer $n$ greater than or equal to 2
  and an upper limit $m$, make a program to enumerate all $x$’s such that the
  sum of its decimal digits $y$ satisfies the relation $x = (y + a)^n$, and $x
  \leq m$.
samples: [{"input": "16 2 1000", "output": "##\n\n    \n    \n    2\n    \n\nTwo: $400 = (4 + 0 + 0 + 16)^2$ and $841 = (8 + 4 + 1 + 16)^2$"}, {"input": "0 3 5000", "output": "3\n    \n\nThree: $1=1^3$, $512 = (5 + 1 + 2)^3$ and $4913 = (4 + 9 + 1 + 3)^3$."}, {"input": "2 3 100000", "output": "0\n    \n\nThere is no such number $x$ in the range below $100,000$ such that its sum of\ndecimal digits $y$ satisfies the relation $(y+2)^3 = x$."}]