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 (GCC 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<stdbool.h>
#include<math.h>
#include<limits.h>
#define MAX 100002
#define BIG 1000000007
int min(int a,int b){
    if(a>b) return b;
    else return a;
}
int main(){
    int N;
    scanf("%d",&N);
    int DP[MAX];
    memset(DP,BIG,sizeof(DP));
    DP[0] = 0;
    for(int i=1;i<=N;i++){
        if(i<6)
            DP[i] = DP[i-1] + 1;
        else if(i<9)
            DP[i] = min(DP[i-1]+1,DP[i-6]+1);
        else{
            int six_tmp=6,nine_tmp=9;
            while(six_tmp<=i){
                DP[i] = min(DP[i],DP[i-six_tmp]+1);
                six_tmp *= 6;
            }
            while(nine_tmp<=i){
                DP[i] = min(DP[i],DP[i-nine_tmp]+1);
                nine_tmp *= 9;
            }
        }
    }
    printf("%d",DP[N]);

}