记录编号	68303	评测结果	AAAAAAAA
题目名称	圈奶牛	最终得分	100
用户昵称	Hobo	是否通过	通过
代码语言	C++	运行时间	0.021 s
提交时间	2013-08-19 14:48:46	内存使用	0.31 MiB

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#define Point Vector
#define ULL unsigned long long
#define INF 1e50
using namespace std;
const double eps=1e-10;
const double PI=acos(-1.0);
double torad(double deg) { return deg/180 * PI;}

struct Point{ double x,y; Point(double x=0,double y=0):x(x),y(y) { } };

Vector operator + (Vector A, Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Point A, Point B)  {return Vector(A.x-B.x,A.y-B.y);}
Vector operator * (Vector A,double p) {return Vector(A.x*p,A.y*p);}
Vector operator / (Vector A,double p) {return Vector(A.x/p,A.y/p);}
bool   operator < (const Point &a,const Point &b) {return a.x<b.x || (a.x==b.x && a.y<b.y);}
bool   cmp        (const Point &a,const Point &b) {return a.x<b.x || (a.x==b.x && a.y<b.y);}

int dcmp(double x) {if (fabs(x)<eps) return 0;else return x<0?-1:1;}
bool operator == (const Point& a,const Point &b) {return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0;}

double Dot(Vector A, Vector B) {return A.x*B.x+A.y*B.y;}
double Length(Vector A)        {return sqrt(Dot(A,A));}
double Angle(Vector A, Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));}
double Cross(Vector A, Vector B) {return A.x*B.y-A.y*B.x;}
double Area2(Point A, Point B, Point C) {return Cross(B-A,C-A);}//返回有向积。

Vector Rotate(Vector A,double rad){return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}//逆时针旋转。
Vector Normal(Vector A) {double L=Length(A);return Vector(-A.y/L,A.x/L);}

Point GetLineIntersection(Point P, Vector v, Point Q, Vector w)
{
    Vector u=P-Q;
    double t=Cross(w,u)/Cross(v,w);
    return P+v*t;
}

Point DistanceToLine(Point P, Point A, Point B)
{
    Vector v1=B-A,v2=P-A;
    return fabs(Cross(v1,v2)/Length(v1));//不取绝对值即是有向距离。
}

Point DistanceToSegment(Point P, Point A, Point B)
{
    if (A==B) return Length(P-A);
    Vector v1=B-A,v2=P-A,v3=P-B;
    if (dcmp(Dot(v1,v2))<0) return Length(v2);
    else if(dcmp(Dot(v1,v3))>0) return Length(v3);
    else return fabs(Cross(v1,v2))/Length(v1);
}

bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2)
{
    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;
}

bool OnSegment(Point p, Point a1, Point a2) {return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dot(a1-p,a2-p))<0;}

double Circumference(Point* p,int n)//Array
{
    double circum=0;
    for (int i=0;i<n-1;i++) circum+=Length(p[i+1]-p[i]);
    return circum;
}

double Circumference(vector<Point> p)//Vector
{
    double circum=0;
    int n=p.size();
    for (int i=0;i<n;i++) {int j=(i+1)%n;circum+=Length(p[j]-p[i]);}
    return circum;
}

double PolygonArea(Point* p,int n)//Array
{
    double area=0;
    for (int i=1;i<n-1;i++) area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2;
}

double PolygonArea(vector<Point> p)//Vector
{
    double area=0;
    int n=p.size();
    for (int i=1;i<n-1;i++) area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2;
}

int ConvexHull(Point* p,int n, Point* ch)//Require No Same Points//Array
{
    make_heap(p,p+n);
    sort_heap(p,p+n);//bool operator <
    //sort(p,p+n);
    int m=0;
    for (int i=0;i<n;i++)
    {
        while (m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    int k=m;
    for (int i=n-2;i>=0;i--)
    {
        while (m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    if (n>1) m--;
    return m;
}

vector<Point> ConvexHull(vector<Point> p)//Vector
{
    make_heap(p.begin(), p.end());
    sort_heap(p.begin(), p.end());//bool operator <
    //sort(p.begin(),p.end());
    p.erase(unique(p.begin(),p.end()),p.end());
    int n=p.size();
    int m=0;
    vector<Point> ch(n+1);
    for (int i=0;i<n;i++)
    {
        while (m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    int k=m;
    for (int i=n-2;i>=0;i--)
    {
        while (m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    if (n>1) m--;
    ch.resize(m);
    return ch;
}

Point READ()
{
    double x,y;
    scanf("%lf%lf",&x,&y);
    return Point(x,y);
}
int N;
double x,y;
vector<Point> P;
int main()
{
freopen("fc.in","r",stdin);
freopen("fc.out","w",stdout);
    scanf("%d",&N);
    for (int i=0;i<N;i++)
        {
        scanf("%lf%lf",&x,&y);
        Point o(x,y);
        P.push_back(o);
        }
    printf("%.2lf",Circumference(ConvexHull(P)));
    return 0;
}