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.strip.to_i

def chmin(a, b) a < b ? a : b end

INF = N
dp = Array.new(1001000) { INF } 

dp[0] = 0
N.times do |i|
  dp[i + 1] = chmin(dp[i] + 1, dp[i + 1])

  [6, 9].each do |p|
    j = p
    while j <= N
      dp[i + j] = chmin(dp[i] + 1, dp[i + j])
      j *= p
    end
  end
end

puts dp[N]