CF991C Candies

原题链接：http://codeforces.com/contest/991/problem/C

Candies

After passing a test, Vasya got himself a box of nnn candies. He decided to eat an equal amount of candies each morning until there are no more candies. However, Petya also noticed the box and decided to get some candies for himself.

This means the process of eating candies is the following: in the beginning Vasya chooses a single integer k" role="presentation" style="position: relative;">kkk, same for all days. After that, in the morning he eats kk k candies from the box (if there are less than k" role="presentation" style="position: relative;">kkk candies in the box, he eats them all), then in the evening Petya eats 10%10%10\% of the candies remaining in the box. If there are still candies left in the box, the process repeats — next day Vasya eats kkk candies again, and Petya — 10%" role="presentation" style="position: relative;">10%10%10\% of the candies left in a box, and so on.

If the amount of candies in the box is not divisible by 101010, Petya rounds the amount he takes from the box down. For example, if there were 979797 candies in the box, Petya would eat only 999 of them. In particular, if there are less than
10" role="presentation" style="position: relative;">101010 candies in a box, Petya won’t eat any at all.

Your task is to find out the minimal amount of kkk that can be chosen by Vasya so that he would eat at least half of the n" role="presentation" style="position: relative;">nnn candies he initially got. Note that the number kkk must be integer.

Input

The first line contains a single integer n" role="presentation" style="position: relative;">nnn (1≤n≤1018)(1≤n≤1018)(1≤n≤10^{18}) — the initial amount of candies in the box.

Output

Output a single integer — the minimal amount of kkk that would allow Vasya to eat at least half of candies he got.

Example

input

output

Note

In the sample, the amount of candies, with k=3" role="presentation" style="position: relative;">k=3k=3k=3, would change in the following way (Vasya eats first):

68→65→59→56→51→48→44→41→37→34→31→28→26→23→21→18→17→14→13→10→9→6→6→3→3→068→65→59→56→51→48→44→41→37→34→31→28→26→23→21→18→17→14→13→10→9→6→6→3→3→068→65→59→56→51→48→44→41→37→34→31→28→26→23→21→18→17→14→13→10→9→6→6→3→3→0.

In total, Vasya would eat 393939 candies, while Petya — 292929.

题解

因为每次糖果都会缩水10%10%10\%，1018101810^{18}只要300300300多次就没了，那么就愉快的二分答案吧，复杂度O(log2n×log1091018)O(log2n×log1091018)O(log_2n\times log_{\frac{10}{9}}10^{18})。

代码

#include<bits/stdc++.h>
using namespace std;
long long n,le,ri,mid;
bool check(long long k)
{long long less=0,res=n;for(;res>0;res-=k,less+=(res>0?res:0)/10,res-=res/10);return less<=n/2;
}
void in(){scanf("%I64d",&n);}
void ac()
{le=1,ri=n/2+1;while(le^ri)mid=le+ri>>1,check(mid)?ri=mid:le=mid+1;printf("%I64d",le);
}
int main(){in();ac();}

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