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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <limits.h>

#define MAX(a,b) ((a)<(b)?(b):(a))
#define MIN(a,b) ((a)<(b)?(a):(b))

int dp[100001];

int fill(int n){
    for(int i=1; i<=n; i++)
        dp[i] = INT_MAX;
    while(dp[n] == INT_MAX){
        for(int i=0; i<=n; i++){
            for(int d=1; i+d<=n; d*=6){
                dp[i+d] = MIN(dp[i+d], dp[i]+1);
            }
            for(int d=1; i+d<=n; d*=9){
                dp[i+d] = MIN(dp[i+d], dp[i]+1);
            }
        }
    }
}

int main(){
    int n;
    scanf("%d", &n);
    fill(n);
    printf("%d\n", dp[n]);
}