Description：

Solution：

Code：

#include<algorithm>

#include<iostream>

#include<cstdlib>

#include<cstdio>

#include<cmath>

#include<cctype>

#include<cstring>

using namespace std;

int n;

#define MAXN 200010

struct point

{

	double x,y;

}p[MAXN];

typedef point vector;

vector operator + (vector a,vector b){return (vector){a.x + b.x,a.y + b.y};}

vector operator - (vector a,vector b){return (vector){a.x - b.x,a.y - b.y};}

vector operator * (vector a,double k){return (vector){a.x * k,a.y * k};}

double cross(vector a,vector b){return a.x * b.y - a.y * b.x;}

double angle(vector k){return atan2(k.y,k.x);}

struct plane

{

	point p;vector v;

}pl[MAXN],q[MAXN];

bool equal(double a,double b){return fabs(a - b) <= 1e-6;}

int sign(double k){return (equal(k,0.0) ? 0 : (k < 0 ? -1 : 1));}

bool in(point p,plane k){return sign(cross(p - k.p,k.v)) >= 0;}

point intersection(plane a,plane b){return b.p + b.v * (cross(a.v,a.p - b.p) / cross(a.v,b.v));}

point middle(point a,point b,double f,double g)

{

	return (point){(a.x * f + b.x * g) / (f + g),(a.y * f + b.y * g) / (f + g)};

}

bool cmp(plane a,plane b){return angle(a.v) < angle(b.v);}

double len(vector a){return sqrt(a.x * a.x + a.y * a.y);}

int ptr = 0;

int head,tail;

double dis(point a,point b){return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));}

int main()

{

	scanf("%d",&n);

	for(int i = 1;i <= n;++i)

	{

		scanf("%lf%lf",&p[i].x,&p[i].y);

	}

	p[n + 1] = p[1];

	double area = 0.0;

	for(int i = 1;i <= n;++i)

	{

		area += cross(p[i],p[i + 1]);

	}

	double ans = 0;

	for(int i = 2;i <= n;++i)

	{

		if(cross(p[2] - p[1],p[i + 1] - p[i]) == 0)

		{

			point a = middle(p[2],p[i],dis(p[1],p[2]),dis(p[i + 1],p[i]));

			point b = middle(p[1],p[i + 1],dis(p[1],p[2]),dis(p[i + 1],p[i]));

			if(sign(cross(p[i] - b,a - b)) >= 0)pl[++ptr] = (plane){a,b - a};

			else pl[++ptr] = (plane){a,a - b};

		}

		else

		{

			point x = intersection((plane){p[2],p[2] - p[1]},(plane){p[i],p[i + 1] - p[i]});

			vector a = middle(p[2],p[1],1,1) - x,b = middle(p[i + 1],p[i],1,1) - x;

			double l;

			l = len(a);a.x /= l;a.y /= l;

			l = len(b);b.x /= l;b.y /= l;

			a = a * dis(p[1],p[2]);

			b = b * dis(p[i + 1],p[i]);

			if(sign(cross(a,b)) < 0)pl[++ptr] = (plane){x,a * -1.0 + b * -1.0};

			else pl[++ptr] = (plane){x,a + b};

		}

	}

	for(int i = 1;i <= n;++i)

	{

		pl[++ptr] = (plane){p[i],p[i] - p[i + 1]};

	}

	sort(pl + 1,pl + 1 + ptr,cmp);

	int tot = 0;

	for(int i = 1;i <= ptr;++i)

	{

		if(tot == 0)pl[++tot] = pl[i];

		else if(!equal(angle(pl[tot].v),angle(pl[i].v)))pl[++tot] = pl[i];

		else if(!in(pl[tot].p,pl[i]))pl[tot] = pl[i];

	}

	head = 1;tail = 2;

	q[1] = pl[1];q[2] = pl[2];

	for(int i = 3;i <= tot;++i)

	{

		while(head < tail && !in(intersection(q[tail],q[tail - 1]),pl[i]))--tail;

		while(head < tail && !in(intersection(q[head],q[head + 1]),pl[i]))++head;

		q[++tail] = pl[i];

	}

	while(head < tail && !in(intersection(q[tail],q[tail - 1]),q[head]))--tail;

	int m = tail - head + 1;

	if(m <= 2)puts("0.0000");

	else

	{

		for(int i = 1;i < m;++i)p[i] = intersection(q[head + i - 1],q[head + i]);

		p[0] = p[m] = intersection(q[head],q[tail]);

		for(int i = 0;i < m;++i)

		{

			ans += cross(p[i],p[i + 1]);

		}

		printf("%.4lf\n",ans / area);

	}

	return 0;

}