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: Wrong Answer)

N=gets.to_i
A6=[]
A9=[]
n=1
while n*6<=N
	n*=6
	A6<<n
end
n=1
while n*9<=N
	n*=9
	A9<<n
end
q=[[0,0]]
min=N
until A6.empty? && A9.empty?
	l=[]
	#warn q.inspect
	if A9.empty? || A6[-1]>A9[-1]
		a=A6.pop
		b=6
	else
		a=A9.pop
		b=9
	end
	warn [a,b].inspect
	d=a*b+(A6.empty? ? 0 : A6[-1]*6)+(A9.empty? ? 0 : A9[-1]*9)+5
	q.each{|n,r|
		#warn [n,r].inspect
		next if n>N
		next if n+d<N
		if n>N-6
			if r+(N-n)<min
				min=r+(N-n)
			end
			next
		end
		b.times{|i|
			break if n+a*i>N
			l << [n+a*i, r+i]
		}
	}
	q=l
end
puts min