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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
  input! {
    n: usize,
  }
  
  let max_value = 100_000;
  let mut dp: Vec<usize> = vec![max_value+1;max_value+1];
  let mut choices: Vec<usize> = vec![1];
  dp[1] = 1;
  
  let mut v = 6;
  while v <= max_value {
    dp[v] = 1;
    choices.push(v);
    v *= 6;
  }

  let mut v = 9;
  while v <= max_value {
    dp[v] = 1;
    choices.push(v);
    v *= 9;
  }
  
  for i in 2..=max_value {
    for v in choices.iter() {
      if &i < v { continue }
      let mut temp = std::cmp::min(dp[i-v]+1, dp[i-1]+1);
      dp[i] = std::cmp::min(dp[i], temp);
    }
  }
  
  println!("{}", dp[n]);
}