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 (Clang 3.8.0) (judge verdict: Accepted)

#include <algorithm>
#include <iostream>
using namespace std;

const int MAXN = 100001;
int dp[MAXN];

int rec_bank(int n) {
  int ret = n;
  if (n == 0)
    return 0;
  if (dp[n] != -1)
    return dp[n];

  for (int pow6 = 1; pow6 <= n; pow6 *= 6)
    ret = min(ret, rec_bank(n - pow6) + 1);
  for (int pow9 = 1; pow9 <= n; pow9 *= 9)
    ret = min(ret, rec_bank(n - pow9) + 1);
  return dp[n] = ret;
}

int main() {
  int N;
  cin >> N;
  for (int i = 0; i < MAXN; i++)
    dp[i] = -1;
  cout << rec_bank(N) << endl;
  return 0;
}