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: Wrong Answer)

N = gets.to_i

dp = Array.new(N+1, 0)
dp[1] = 1
(1..N).each do |i|
    cand = dp[i-1] + 1
    if i >= 6
        n = (Math.log(i)/Math.log(6)).floor
        c = dp[i-6**n] + 1
        cand = c if cand > c
    end
    if i >= 9
        n = (Math.log(i)/Math.log(9)).floor
        c = dp[i-9**n] + 1
        cand = c if cand > c
    end
    dp[i] = cand
end
puts dp[N]