Codeforces 689C Mike and Chocolate Thieves (二分)

C. Mike and Chocolate Thieves

time limit per test：2 seconds

memory limit per test：256 megabytes

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.

Input

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.

Output

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.

Examples

Input

1

Output

8

Input

8

Output

54

Input

10

Output

-1

Note

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.

题目链接：http://codeforces.com/problemset/problem/689/C

题目大意：给一个数字n，要求结果正好包含n个四元组，求这n个四元组里的最大值，四元组形式为一个等比数列

题目分析：因为只有四个数，显然最后一个是第一个的x^3倍，二分答案，枚举x计算四元组个数即可。

#include <cstdio>
#include <iostream>
#define ll long long
using namespace std;

ll cal(ll x)
{
	ll num = 0;
	for(ll i = 2; i * i * i <= x; i++)
		num += x / (i * i * i);
	return num;
}

int main()
{
	ll n;
	cin >> n;
	ll r = 1e18, l = 1, mid, ans = -1;
	while(l <= r)
	{
		mid = (l + r) >> 1;
		ll p = cal(mid);
		if(p == n)
			ans = mid;
		if(p >= n)
			r = mid - 1;
		else
			l = mid + 1;

	}
	cout << ans << endl;
}