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)

lines = $stdin.read
array = lines.split("\n")
N = array[0].to_i
MAX_N = 110000

dp = Array.new(MAX_N, N+1)
dp[0] = 0

for n in 0..N
  pow6 = 1
  loop {
    dp[n+pow6] = [dp[n+pow6], dp[n]+1].min
    pow6 *= 6
    break if n + pow6 > N
  }
  pow9 = 1
  loop {
    dp[n+pow9] = [dp[n+pow9], dp[n]+1].min
    pow9 *= 9
    break if n + pow9 > N
  }
end

puts dp[N]