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 <iostream>
#include <cstdio>
#include <algorithm>
#include <climits>
#include <cmath>
#include <vector>
#include <string>

#define REP(i, n) for (int i=0;i<(n);i++)
#define FOR(i, a, b) for (int i=(a);i<(b);i++)

using namespace std;

int N;
int dp[100001];
vector<int> a;

int main()
{
    scanf("%d", &N);
    int i = 1;
    while(true) {
        if(pow(6, i)<100000)
            a.push_back(pow(6, i));
        else
            break;
        i++;
    }
    i = 1;
    while(true) {
        if(pow(9, i)<100000)
            a.push_back(pow(9, i));
        else
            break;
        i++;
    }
    a.push_back(1);
    sort(a.begin(), a.end());
    //REP(i, a.size())
    //    printf("%d ", a[i]);

    dp[0] = 0;
    dp[1] = 1;
    FOR(i, 2, 100001)
        dp[i] = 100000000;
    FOR(i, 2, 100001){
        REP(j, a.size()){
            if(i>=a[j])
                dp[i] = min(dp[i], dp[i-a[j]]+1);
            else
                break;
        }
    }
    printf("%d\n", dp[N]);


    return 0;
}