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 LuaJIT (2.0.4) (judge verdict: Accepted)

local tgt = io.read("*n")
tgt9 = math.floor(tgt / 9)
local first = true
local cnttot = 0
for i = 0, tgt9 do
    local tmp = i
    local cnt9, val9 = 0, 0
    local mul = 9
    while(0 < tmp) do
        local a = tmp % 9
        cnt9, val9 = cnt9 + a, val9 + mul * a
        mul, tmp = mul * 9, math.floor(tmp / 9)
    end
    local rem = tgt - val9
    local cnt6, rem6 = 0, rem
    while(0 < rem6)do
        local a = rem6 % 6
        cnt6, rem6 = cnt6 + a, math.floor(rem6 / 6)
    end
    if(first) then first, cnttot = false, cnt6 + cnt9 else cnttot = math.min(cnttot, cnt6 + cnt9) end
end
print(cnttot)