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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

#define Nmax 100000
#define MAX(x, y) (((x) > (y)) ? (x) : (y))
#define MIN(x, y) (((x) < (y)) ? (x) : (y))
int memo[Nmax];

int dp(int n) {
    if (memo[n] != -1) return memo[n];
    if (n == 0) return 0;
    int ans = 100000000;
    for (int n6 = 1; n6 <= n; n6 *= 6) {
        ans = MIN(ans, 1 + dp(n - n6));
    }
    for (int n9 = 1; n9 <= n; n9 *= 9) {
        ans = MIN(ans, 1 + dp(n - n9));
    }
    return memo[n] = ans;
}

int main() {
    int N;
    scanf("%d",&N);  
    for (int i=0; i<Nmax; i++) memo[i] = -1;
    printf("%d", dp(N));
}