Codeforces Round #409 div2 D

D. Volatile Kite

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a convex polygon P with n distinct vertices p1, p2, ..., pn. Vertex pi has coordinates (xi, yi) in the 2D plane. These vertices are listed in clockwise order.

You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.

Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.

Input

The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.

The next n lines contain the coordinates of the vertices. Line i contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).

Output

Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if .

Examples

input

40 00 11 11 0

output

0.3535533906

input

65 010 012 -410 -85 -83 -4

output

1.0000000000

Note

Here is a picture of the first sample

Here is an example of making the polygon non-convex.

This is not an optimal solution, since the maximum distance we moved one point is  ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most  ≈ 0.3535533906.

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题目 找到可移动的最少距离，使得无论怎么移动，这个多边形均为凸边形

O（n）扫一遍 每次找到三角形的高， 维护三角形高的一半的最小值 OK

#include <cstdio>#include <iostream>#include <cmath>#include <cstring>using namespace std;#define maxn 120009#define inf 0x3f3f3f3fstruct node{    double x;    double y;}a[maxn];int n ;double fun(int i){    double x1=a[i].x,y1=a[i].y;    i++;    if(i==n){        i=0;    }    double x2=a[i].x,y2=a[i].y;    i++;    if(i==n){        i=0;    }    double x3=a[i].x,y3=a[i].y;    double x0=x2,y0=y2;    double A=y3-y1;    double B=x1-x3;    double C=y1*x3-y3*x1;    double d=(A*x0+B*y0+C)/(sqrt(A*A+B*B));    if(d<0)        d=-d;    return d/2;}int main(){    scanf("%d",&n);    for(int i = 0 ; i<n ; i++)        scanf("%lf%lf",&a[i].x,&a[i].y);    double minn=1e20;    for(int i = 0 ; i<n ; i++){        minn=min(fun(i),minn);        //printf("%lf ",fun(i));    }    //printf("\n");    printf("%lf\n",minn);}