CF689C.Mike and Chocolate Thieves

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 k times more than the previous one. The value of k (k > 1) is a secret integer known only to them. It is also known that each thief's bag can carry at most n 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 n, but rumours say that the numbers of ways they could have taken the chocolates (for a fixed n, but not fixed k) is m. 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 n will help him in that. Please find the smallest possible value of n or tell him that the rumors are false and there is no such n.

坏消息传到了迈克的村庄：一些小偷从当地工厂偷走了一大批巧克力！太可怕了！

除了喜爱甜食外，这一地区的小偷还以极度贪婪而闻名。因此，当一名小偷为自己取走一定数量的巧克力后，下一名小偷取走的巧克力数量恰好是前一名的 $k$ 倍。参数 $k$（其中 $k > 1$）是一个仅小偷们知晓的秘密整数。此外，已知每名小偷的背包最多可装 $n$ 块巧克力（若某人计划取走的数量超过 $n$，则整个行动将被取消），且此次作案恰好有四名小偷参与。

遗憾的是，只有小偷知道 $n$ 的值，但据传言称：对于固定的 $n$（而 $k$ 不固定），他们取走巧克力的方案总数为 $m$。若在两种方案中，至少有一名小偷（按取巧克力的顺序编号）所取巧克力数量不同，则认为这两种方案不同。

迈克想要追查这些小偷，从而掌握他们的背包容量；而 $n$ 的值将对此大有帮助。请找出满足条件的最小可能的 $n$；若不存在这样的 $n$，则说明传言有误，并告知迈克。

The single line of input contains the integer m (1 ≤ m ≤ 1015) — the number of ways the thieves might steal the chocolates, as rumours say.

输入仅包含一个整数 $m$（$1 \le m \le 10^{15}$）—— 据传闻，这是小偷可能窃取巧克力的方式数目。

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

If there is no such n for a false-rumoured m, print  - 1.

输出唯一的整数 $n$ —— 小偷们的背包所能承载的巧克力最大数量。如果存在多个满足传言的 $n$，则输出其中最小的一个。

如果对于某个被误传的 $m$ 不存在这样的 $n$，则输出 $-1$。

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

In the second sample case the smallest n that leads to exactly 8 ways is n = 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).

There is no n leading to exactly 10 ways of stealing chocolates in the third sample case.

在第一个样例中，使得偷巧克力的方式恰好为一种的最小 $ n $ 是 $ n = 8 $，此时被偷的巧克力数量为 $ (1,,2,,4,,8) $（即四名小偷各自偷走的巧克力数量）。

在第二个样例中，使得偷巧克力的方式恰好为 8 种的最小 $ n $ 是 $ n = 54 $，对应的方案为：$ (1,,2,,4,,8),\quad (1,,3,,9,,27),\quad (2,,4,,8,,16),\quad (2,,6,,18,,54),\quad (3,,6,,12,,24),\quad (4,,8,,16,,32),\quad (5,,10,,20,,40),\quad (6,,12,,24,,48) $。

在第三个样例中，不存在使得偷巧克力的方式恰好为 10 种的 $ n $。