CF689C.Mike and Chocolate Thieves

普及/提高-

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题目描述

Bad news came to Mike's village, some thieves stole a bunch of chocolates from the local factory! Horrible!

Aside from loving sweet things, thieves from this area are known to be very greedy. So after a thief takes his number of chocolates for himself, the next thief will take exactly kk times more than the previous one. The value of kk ( k>1 ) is a secret integer known only to them. It is also known that each thief's bag can carry at most nn chocolates (if they intend to take more, the deal is cancelled) and that there were exactly four thieves involved.

Sadly, only the thieves know the value of nn , but rumours say that the numbers of ways they could have taken the chocolates (for a fixed nn , but not fixed kk ) is mm . Two ways are considered different if one of the thieves (they should be numbered in the order they take chocolates) took different number of chocolates in them.

Mike want to track the thieves down, so he wants to know what their bags are and value of nn will help him in that. Please find the smallest possible value of nn or tell him that the rumors are false and there is no such nn .

输入格式

The single line of input contains the integer mm (1<=m<=1015)(1<=m<=10^{15}) — the number of ways the thieves might steal the chocolates, as rumours say.

输出格式

Print the only integer nn — the maximum amount of chocolates that thieves' bags can carry. If there are more than one nn satisfying the rumors, print the smallest one.

If there is no such nn for a false-rumoured mm , print 1-1 .

输入输出样例

  • 输入#1

    1
    

    输出#1

    8
    
  • 输入#2

    8
    

    输出#2

    54
    
  • 输入#3

    10
    

    输出#3

    -1
    

说明/提示

In the first sample case the smallest nn that leads to exactly one way of stealing chocolates is n=8n=8 , whereas the amounts of stealed chocolates are (1,2,4,8)(1,2,4,8) (the number of chocolates stolen by each of the thieves).

In the second sample case the smallest nn that leads to exactly 88 ways is n=54n=54 with the possibilities: (1,2,4,8),(1,3,9,27),(2,4,8,16),(2,6,18,54),(3,6,12,24),(4,8,16,32),(5,10,20,40),(6,12,24,48)(1,2,4,8), (1,3,9,27), (2,4,8,16), (2,6,18,54), (3,6,12,24), (4,8,16,32), (5,10,20,40), (6,12,24,48) .

There is no nn leading to exactly 1010 ways of stealing chocolates in the third sample case.

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