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: Time Limit Exceeded)

@dp = {}
@dp[1] = 1
list = [1]
6.times do |i|
  list.push(6**(i+1))
end
5.times do |i|
  list.push(9**(i+1))
end
@list = list.sort.reverse
def solve(n)
  remain = n
  ans = {}
  @list.each do |c|
    # puts c
    next if remain < c
    ans[c] = find(c, remain, 0)
  end
  min = ans.map {|_,v| v}.min

  puts min
end

def find(c, remain, count)
  return 1 if @list.include?(remain)
  if remain < c
    @dp["#{c}-#{remain}"] = Float::INFINITY
    return Float::INFINITY
  end
  return @dp["#{c}-#{remain}"] if @dp["#{c}-#{remain}"]


  count = count + 1
  cs = []
  @list.select{|i| remain - c >= i}.each do |c2|
    if @dp["#{c2}-#{remain-c}"]
      cs.push(@dp["#{c2}-#{remain-c}"])
    else
      rt = find(c2, remain - c, count - 1)
      cs.push(rt) if rt < 100
    end
  end
  r = count + cs.min
  @dp["#{c}-#{remain}"] = r
  r
end

def main
  n = gets.chomp.to_i
  solve(n)
end

main