Problem:
Score : 300 points

Problem Statement

To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:

1 yen (the currency of Japan)

6 yen, 6^2(=36) yen, 6^3(=216) yen, ...

9 yen, 9^2(=81) yen, 9^3(=729) yen, ...

At least how many operations are required to withdraw exactly N yen in total?

It is not allowed to re-deposit the money you withdrew.

Constraints

1 \leq N \leq 100000

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If at least x operations are required to withdraw exactly N yen in total, print x.

Sample Input 1

127

Sample Output 1

4

By withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.

Sample Input 2

3

Sample Output 2

3

By withdrawing 1 yen three times, we can withdraw 3 yen in three operations.

Sample Input 3

44852

Sample Output 3

16

Solution in Ruby (2.7.1) (judge verdict: Accepted)

INF = 99999999
n = gets.to_i

dp = Array.new(n+1,INF)
dp[0] = 0

for i in 0..(n-1)
  dp[i+1] = [dp[i+1], dp[i]+1].min
  
  max6 = -1
  while i+6**(max6+1) <= n
    max6 += 1
  end
  for j in 1..max6
    dp[i+6**j] = [dp[i+6**j], dp[i]+1].min
  end
  
  max9 = -1
  while i+9**(max9+1) <= n
    max9 += 1
  end
  for j in 1..max9
    dp[i+9**j] = [dp[i+9**j], dp[i]+1].min
  end
end

puts dp[n]