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 = []

for i in 0..N

    if i == 0

        dp[i] = 0

    elsif i < 6

        dp[i] = dp[i-1] + 1

    elsif 6 <= i && i < 9

        dp[i] = [dp[i-1]+1,dp[i-6]+1].min

    elsif 9 <= i && i < 36

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1].min

    elsif 36 <= i && i < 81

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1].min 

    elsif 81 <= i && i < 216

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1].min
        
    elsif 216 <= i && i < 729

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1].min

    elsif 729 <= i && i < 1296

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1,dp[i-729]+1].min

    elsif 1296 <= i && i < 6561

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1,dp[i-729]+1,dp[i-1296]+1].min

    elsif 6561 <= i && i < 7776

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1,dp[i-729]+1,dp[i-1296]+1,dp[i-6561]+1].min

    elsif 7776 <= i && i < 46656

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1,dp[i-729]+1,dp[i-1296]+1,dp[i-6561]+1,dp[i-7776]+1].min

    elsif 46656 <= i && i < 59049

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1,dp[i-729]+1,dp[i-1296]+1,dp[i-6561]+1,dp[i-7776]+1,dp[i-46656]+1].min

    else

        dp[i] = [dp[i-1]+1,dp[i-6]+1,dp[i-9]+1,dp[i-36]+1,dp[i-81]+1,dp[i-216]+1,dp[i-729]+1,dp[i-1296]+1,dp[i-6561]+1,dp[i-7776]+1,dp[i-46656]+1,dp[i-59049]+1].min

    end

end

puts dp[N]