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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
)

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	var N int
	scanner.Scan()
	fmt.Sscanf(scanner.Text(), "%d", &N)

	memo = make(map[int]int)
	fmt.Println(rec(N))
}

var memo map[int]int

func rec(n int) int {
	if _, e := memo[n]; e {
		return memo[n]
	}
	if n == 0 {
		return 0
	}
	if n == 1 {
		return 1
	}
	n6 := power(6, count6(n))
	n9 := power(9, count9(n))
	count := min(
		1+rec(n-n6),
		1+rec(n-n9),
	)
	memo[n] = count
	return count
}

func min(ns ...int) int {
	ret := math.MaxInt64
	for _, n := range ns {
		if n < ret {
			ret = n
		}
	}
	return ret
}
func count6(n int) int {
	ret := 1
	for power(6, ret) <= n {
		ret++
	}
	return ret - 1
}

func count9(n int) int {
	ret := 1
	for power(9, ret) <= n {
		ret++
	}
	return ret - 1
}

func power(a, pow int) int {
	if pow == 0 {
		return 1
	} else if pow == 1 {
		return a
	} else if pow%2 == 0 {
		rt := power(a, pow/2)
		return rt * rt //% MOD
	} else {
		return a * power(a, pow-1) //% MOD
	}
}