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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local memo={}
local function rec(x)
    if x==0 then 
        return 0 
    end
    if memo[x]~=-1 then
        return memo[x]
    end
    local result=x
    local six=1
    while six<=x do
        result=math.min(result,rec(x-six)+1)
        six=six*6
    end
    local nine=1
    while nine<=x do
        result=math.min(result,rec(x-nine)+1)
        nine=nine*9
    end
    memo[x]=result
    return memo[x]
end

local n=io.read("n")
for i=1,n do
    memo[i]=-1
end
print(rec(n))