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

k6 = []
k9 = []

(1..10).each{ |i|
	if 6 ** i <= n then
		k6 << 6 ** i
	end
	
	if 9 ** i <= n then
		k9 << 9 ** i
	end
}

k6.reverse!
k9.reverse!

s = [n]
count = 0

while true
	min = s.min
	if min < 6 then
		puts count + min
		exit
	end

	next_s = []
	s.each{ |ss|
		next6 = k6.bsearch{ |x| x <= ss }
		
		if next6 != nil then
			next_s << ss - next6
		end
		
		next9 = k9.bsearch{ |x| x <= ss }
		
		if next9 != nil then
			next_s << ss - next9
		end
		
		s = next_s
	}

	count += 1
end