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: Accepted)

N = gets.to_i
dp = Array.new(N+1, N)
dp[0] = 0
(0...N).each do |n|
    dp[n+1] = [dp[n] + 1, dp[n+1]].min
    s = 1
    while n+s*6<=N
        s *= 6
        dp[n+s] = [dp[n] + 1, dp[n+s]].min
    end
    s = 1
    while n+s*9<=N
        s *= 9
        dp[n+s] = [dp[n] + 1, dp[n+s]].min
    end
end
p dp[N]