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;

int main() {
  int N;
  cin>>N;

  vector<int> a(100001);
  vector<int> p6(6);
  vector<int> p9(5);
  for(int i=0;i<6;i++) p6[i]=int(pow(6,i+1));
  for(int i=0;i<5;i++) p9[i]=int(pow(9,i+1));

  for(int i=0;i<=N;i++) a[i]=i;
  for(int i=1;i<=N;i++){
    for(int j=0;j<6;j++){
      if(i>=p6[j]) a[i]=min(a[i-p6[j]]+1,a[i]);
    }
    for(int j=0;j<5;j++){
      if(i>=p9[j]) a[i]=min(a[i-p9[j]]+1,a[i]);
    }

  }
  cout<<a[N]<<endl;
}