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 (2.3.3) (judge verdict: Time Limit Exceeded)

def s(d, i, n, dp) #現在　足した数
  return if d > n
  dp[d] ||= 999
  return if dp[d] < i
  dp[d] = i
  (1..5).each do |m|
    s(d+9**m, i+1, n, dp)
  end
  (1..6).each do |m|
    s(d+6**m, i+1, n, dp)
  end
  s(d+1, i+1, n, dp) if n-d <= 7
end

n=gets.to_i
dp = []
s(0, 0, n, dp)
p dp[n]