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 fs first
#define sc second
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<double,double> P;
const LL mod=1e9+7;
const LL LINF=1LL<<62;
const LL INF=1<<30;
int main(){
    int N;
    cin >> N;
    int dp[N+1];
    for(int i=0;i<N+1;i++){
        dp[i]=INF;
    }
    dp[0]=0;
    for(int i=0;i<N;i++){
        int s=1;
        while(1){
            if(i+s>N) break;
            dp[i+s]=min(dp[i+s],dp[i]+1);
            s*=6;
        }
        s=1;
        while(1){
            if(i+s>N) break;
            dp[i+s]=min(dp[i+s],dp[i]+1);
            s*=9;
        }
    }
    cout << dp[N] << endl;
    return 0;
}