Codeforces Round #361 (Div. 2) C. Mike and Chocolate Thieves（二分判断）

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 exactlyk times more than the previous one. The value ofk (k > 1) is a secret integer known only to them. It is also known that each thief's bag can carry at mostn chocolates (if they intend to take more, the deal is cancelled) and that there wereexactly 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 fixedn, but not fixed k) ism. 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 ofn 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 suchn.

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 onen satisfying the rumors, print the smallest one.

If there is no such n for a false-rumouredm, 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 isn = 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 exactly8 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.

题意：让你求一个n，使得最大项不超过n的长度为4的等比数列的个数为k。

分析：二分n的值，然后暴力判断。

#include <cstdio>#include <queue>    #include <vector>    #include <cstdio>    #include <utility>    #include <cstring>    #include <iostream>    #include <algorithm>    #define INF 0x3f3f3f3fusing namespace std;long long m;long long check(long long x){long long ans = 0;for(long long i = 2;i*i*i <= x;i++) ans += x / (i*i*i);return ans;}int main(){cin.sync_with_stdio(false);cin>>m;long long s = 1ll,t = 9223372036854775807;while(s != t){long long mid = (s+t)/2;if(check(mid) < m) s = mid+1ll;else t = mid; }if(check(s) != m) cout<<-1<<endl;else cout<<s<<endl;}