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)

N=gets.chomp.to_i
MEMO=Array.new(N+1,nil)
MEMO[N]=0
targets=[N]
flg=true
while flg do
    targets_new=[]
    targets.each do |t|
        d=1
        if MEMO[t-d]==nil
            MEMO[t-d]=MEMO[t]+1
            targets_new.push(t-d)
            flg=false if t==d
        end
        d=6
        while t>=d do
            if MEMO[t-d]==nil
                MEMO[t-d]=MEMO[t]+1
                targets_new.push(t-d)
                flg=false if t==d
            end
            d*=6
        end
        d=9
        while t>=d do
            if MEMO[t-d]==nil
                MEMO[t-d]=MEMO[t]+1
                targets_new.push(t-d)
                flg=false if t==d
            end
            d*=9
        end
    end
    targets=targets_new
end
puts MEMO[0]