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

input：standard input

output：standard output

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/contest/689/problem/C

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题意：有4个小偷偷东西，后面一个偷的是前面一个的K倍。有m种可能性，每个小偷偷的东西不能超过一个容量，求小偷的最小的容量n。

思路：假设容量为x，则可能性有cou=x/(2^3)+x/(3^3)+x/(4^3)+.....种。暴力二分求x。二分次数最多为64次，每一次最多进行10^6求cou,与m进行判断比较。

代码：

#include<bits/stdc++.h>
using namespace std;
__int64 gg[1000100];
int main()
{
    __int64 i,m;
    for(i=2; i<=1000100; i++)
        gg[i]=i*i*i;
    scanf("%I64d",&m);
    __int64 l=0,r=1e18,mid;
    int flag=0;
    __int64 ans;
    while(l<r)
    {
        mid=(l+r)>>1;
        __int64 cou=0;
        for(i=2; gg[i]<=mid; i++)
            cou+=mid/gg[i];
        cout<<l<<" "<<r<<" "<<mid<<" "<<cou<<endl;
        if(cou>m) r=mid-1;
        else if(cou<m) l=mid+1;
        else
        {
            r=mid;
            flag=1;
            ans=mid;
        }
    }
    if(flag) cout<<ans<<endl;
    else cout<<"-1"<<endl;
    return 0;
}