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 < (n); ++i)
typedef long long ll;

const int MAX = 101000;


int main() {
    int N;
    cin >> N;
    vector<int> dp(MAX,-1);
    dp[0]=0;
    queue<int> q;
    q.push(0);

    while(!q.empty()) {
        int v = q.front();
        q.pop();
        
        for(int i=1;v+i<=N;i*=6) {
            if(dp[v+i] == -1) {
                dp[v+i] = dp[v]+1;
                q.push(v+i);
            }
        }

        for(int i=9;v+i<=N;i*=9) {
            if(dp[v+i] == -1) {
                dp[v+i] = dp[v] + 1;
                q.push(v+i);
            }
        }
    }
    cout << dp[N] << endl;
}