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> l={1};
    for(int i=6; i<=N; i*=6) l.push_back(i);
    for(int i=9; i<=N; i*=9) l.push_back(i);
    sort(l.begin(), l.end());
    l.erase(unique(l.begin(), l.end()), l.end());

    queue<int> q;
    q.push(N);
    set<int> used;
    for(int res = 1;; res++){
        auto n = q.size();
        for(int i=0;i<n;i++){
            auto v = q.front(); q.pop();
            for(auto j : l){
                if(v < j) continue;
                if(used.count(v - j) > 0) continue;
                if(v == j){
                    cout << res << endl;
                    return 0;
                }
                q.push(v - j);
                used.insert(v - j);
            }
        }
    }
    return 0;
}