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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define FOR(i, s, e) for (int i = (int)(s); i <= (int)(e); i++)
#define printYesNo(is_ok) puts(is_ok ? "Yes" : "No");
#define printVector(v) rep(i, v.size()) cout << v[i] << endl;

int main()
{
  int N;
  cin >> N;
  vector<int> moneys = {1};
  int n = 1;
  while (pow(6, n) <= N)
  {
    moneys.push_back(pow(6, n));
    n++;
  }
  n = 1;
  while (pow(9, n) <= N)
  {
    moneys.push_back(pow(9, n));
    n++;
  }
  vector<int> dp(N + 1, -1);
  dp[0] = 0;
  int ans = 0;
  while (dp[N] == -1)
  {
    vector<int> pre_dp = dp;

    rep(i, N + 1)
    {
      if (pre_dp[i] == -1)
        continue;
      rep(j, moneys.size())
      {
        int money = moneys[j] + i;
        if (money > N)
          continue;
        dp[money] = ans;
      }
    }
    ans++;
  }

  cout << ans << endl;
  return 0;
}