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(){
	cin.tie(0);
    ios::sync_with_stdio(false);
 	int n;
 	cin>>n;
 	vector<int>v;
 	v.push_back(1);
 	for(int i=6; i<=n; i*=6){
 		v.push_back(i);
 	}
 	for(int i=9; i<=n; i*=9){
 		v.push_back(i);
 	}
 	sort(v.begin(),v.end());
 	int MAX=100001;
 	int dp[MAX];
 	for(int i=0; i<MAX; i++){
 		dp[i]=MAX;
 	}
 	dp[0]=0;
  	 	for(int i=0; i<=n; i++){
 		for(int j=0; j<v.size(); j++){
 			if(i>=v[j]){
 				dp[i]=min(dp[i],dp[i-v[j]]+1);
 			}
 		}
 	}
  cout<<dp[n]<<endl;

}