Codeforces Round #299 (Div. 1) C. Tavas and Pashmaks

C. Tavas and Pashmaks

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Tavas is a cheerleader in the new sports competition named "Pashmaks".

This competition consists of two part: swimming and then running. People will immediately start running R meters after they finished swimming exactly S meters. A winner is a such person that nobody else finishes running before him/her (there may be more than one winner).

Before the match starts, Tavas knows that there are n competitors registered for the match. Also, he knows that i-th person's swimming speed is si meters per second and his/her running speed is ri meters per second. Unfortunately, he doesn't know the values of R and S, but he knows that they are real numbers greater than 0.

As a cheerleader, Tavas wants to know who to cheer up. So, he wants to know all people that might win. We consider a competitor might win if and only if there are some values of R and S such that with these values, (s)he will be a winner.

Tavas isn't really familiar with programming, so he asked you to help him.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 2 × 105).

The next n lines contain the details of competitors. i-th line contains two integers si and ri (1 ≤ si, ri ≤ 104).

Output

In the first and the only line of output, print a sequence of numbers of possible winners in increasing order.

Sample test(s)

input

3
1 3
2 2
3 1

output

1 2 3 

input

3
1 2
1 1
2 1

output

1 3 

 

 

 

#include <iostream>
#include<stdio.h>
#include<vector>
#include<algorithm>
using namespace std;
struct node{
    __int64 x,y,index;
};
node a[300000],c[300000];
int b[300000],flg[300000],w[300000],f[300000];
vector<int> ans;
bool cmp(node a,node b)
{
    if (a.x<b.x) return true;
    if (a.x==b.x&&a.y<b.y) return true;
    return false;
}
bool dog(int index1,int index2,int index3)
{
    if (index2==1) return true;
    if ((c[index1].x-c[index2].x)*(c[index3].y-c[index2].y)*c[index3].x*c[index1].y>=
        (c[index2].x-c[index3].x)*(c[index2].y-c[index1].y)*c[index1].x*c[index3].y)
            return true;
    return false;
}
int main()
{
    int n,t1,t2;
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=1;i<=n;i++)
        {
            scanf("%I64d%I64d",&a[i].x,&a[i].y);
            a[i].index=i;
            w[i]=flg[i]=0;
        }
        for(int i=1;i<=20000;i++)
            b[i]=0;
        sort(a+1,a+1+n,cmp);
        for(int i=n;i>=1;i--)
        {
            if (b[a[i].y]==0)
            {
                flg[a[i].index]=1;
                for(int j=a[i].y;j>=1;j--)
                    if (b[j]==1) break;
                    else
                        b[j]=1;
            }
        }
        t1=1;
        c[1].x=a[n].x;
        c[1].y=a[n].y;
        c[1].index=1;
        //flg[n]=1;
        for(int i=n-1;i>=1;i--)
        {
            if (flg[a[i].index]==1)
            {
                flg[a[i].index]=++t1;
                c[t1].x=a[i].x;
                c[t1].y=a[i].y;
                c[t1].index=t1;
            }
            else
                if (flg[a[i+1].index]>=1&&a[i].x==a[i+1].x&&a[i].y==a[i+1].y)
                    flg[a[i].index]=flg[a[i+1].index];
        }
        if (t1>=2)
        {
            t2=2;
            f[1]=1;
            f[2]=2;
        }
        else
        {
            t2=1;
            f[1]=1;
        }
        for(int i=3;i<=t1;i++)
        {
            for(int j=t2;j>=1;j--)
                if (dog(i,f[j],f[j-1]))
                {
                    f[t2=j+1]=i;
                    break;
                }
        }
        for(int i=1;i<=t2;i++)
            w[c[f[i]].index]=1;
        ans.clear();
        for(int i=1;i<=n;i++)
            if (w[flg[i]]==1) ans.push_back(i);
        for(int i=0;i<ans.size();i++)
            printf("%d ",ans[i]);
        printf("\n");
    }
    return 0;
}

/*


3
1 3
2 2
3 1


18
82 38
33 69
33 69
33 69
33 69
33 69
82 38
33 69
33 69
33 69
82 38
33 69
33 69
82 38
82 38
33 69
33 69
33 69
*/