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     #define IL inline#define _ 100005#define ll long longusing namespace std ;IL int gi(){    int data = 0 , m = 1; char ch = 0;    while(ch!='-' && (ch<'0'||ch>'9')) ch = getchar();    if(ch == '-'){m = 0 ; ch = getchar() ; }    while(ch >= '0' && ch <= '9'){data = (data<<1) + (data<<3) + (ch^48) ; ch = getchar(); }    return (m) ? data : -data ; }#define ld long double#define inf 1e9#define eps 1e-6int n ; const ld PI = acos(-1.0) ;struct Point{    ld x , y ;    IL Point(){x = 0 ; y = 0 ; }    IL Point(double a , double b){x = a ; y = b ; }    IL ld cal() {return sqrt(x*x + y*y) ; }    IL void Print(){printf("(%Lf,%Lf)" , x , y) ; }} ;IL Point operator + (Point a , Point b) {return Point(a.x + b.x , a.y + b.y) ; }IL Point operator - (Point a , Point b) {return Point(a.x - b.x , a.y - b.y) ; }IL ld operator ^ (Point a , Point b) {return a.x * b.x + a.y * b.y ; }IL ld operator * (Point a , Point b) {return a.x * b.y - a.y * b.x ; }IL Point operator * (Point a , double b) {return Point(a.x * b , a.y * b) ; }IL ld Sqr(ld x) {return 1.0 * x * x ; }IL ld Dist(Point a , Point b) {return sqrt(Sqr(a.x - b.x) + Sqr(a.y - b.y)) ; }IL Point Rot(Point a , ld Arc) {    return Point(cos(Arc)*a.x - sin(Arc)*a.y , sin(Arc)*a.x + cos(Arc)*a.y) ; }struct Line {    Point p1 , p2 ;    IL Line() {p1 = Point() ; p2 = Point() ; }    IL Line(Point a , Point b) {p1 = a ; p2 = b ; }    IL void Print(){p1.Print() ; putchar('-') ; putchar('-') ; putchar('>') ; p2.Print() ; }} ;IL Line Perp(Line A) {    Point a = A.p1 , b = A.p2 , c ;    c = b - a ;    c = Rot(c , PI * 0.5) ;    return Line((a + b) * 0.5 , ((a + b) * 0.5) + c * 0.5) ; }IL Point GetCross(Line l1 , Line l2) {    Point a = l1.p2 - l1.p1 , b = l2.p2 - l2.p1 , c = l2.p1 - l1.p1 ;    ld al = (a * c) / (b * a) ;     return Point(l2.p1.x + b.x * al , l2.p1.y + b.y * al) ;}IL ld Dist(Line l1 , Point ps) {    Point w = l1.p2 - l1.p1 ;    return fabs(w * (ps - l1.p1)) / Dist(l1.p1 , l1.p2) ;}Point p[_] , circle_p ;ld circle_range ; namespace CirCle{    IL void Print_Circle() {        printf("%.8Lf %.8Lf %.8Lf\n" , circle_p.x , circle_p.y , circle_range) ;        return ;     }    IL void main() {        random_shuffle(p + 1 , p + n + 1) ; random_shuffle(p + 1 , p + n + 1) ;        circle_p = p[1] ; circle_range = 0 ;        for(int i = 2; i <= n; i ++)            if(Dist(circle_p , p[i]) > circle_range) {                circle_p = p[i] ; circle_range = 0 ;                for(int j = 1; j < i; j ++)                    if(Dist(circle_p , p[j]) > circle_range) {                        circle_p = (p[i] + p[j]) * 0.5 ; circle_range = Dist(circle_p , p[i]) ;                        for(int k = 1; k < j; k ++)                            if(Dist(circle_p , p[k]) > circle_range) {                                Line l1 , l2 ;                                l1 = Line(p[k] , p[j]) ; l2 = Line(p[i] , p[j]) ;                                   l1 = Perp(l1) ;                                l2 = Perp(l2) ;                                circle_p = GetCross(l1 , l2) ; circle_range = Dist(circle_p , p[i]) ;                            }                    }            }        Print_Circle() ;     }}Point Base_p , gm[_] ; int nG , tot ;namespace GraHam{    IL bool cmp_GraHam(Point a , Point b) {        return (a - Base_p) * (b - Base_p) > 0 ;     }    IL void Print_GraHam() {        for(int i = 0; i <= nG; i ++) {            gm[i].Print() ; putchar('-') ; putchar('-') ; putchar('>') ;         }        puts("") ; return ;    }    IL void main() {        nG = 0 ;        Base_p = p[1] ; int id = 1 ;         for(int i = 2; i <= n; i ++) if(p[i].x < Base_p.x || (fabs(p[i].x-Base_p.x)<=eps && p[i].y < Base_p.y)) Base_p = p[i] , id = i ;        tot = 0 ;        for(int i = 1; i <= n; i ++) if(id != i) p[++tot] = p[i] ; n = tot ;         sort(p + 1 , p + n + 1 , cmp_GraHam) ;        gm[nG = 0] = Base_p ;        gm[++ nG] = p[1] ;         for(int i = 2; i <= n; i ++) {            while(nG >= 1 && (p[i] - gm[nG - 1]) * (gm[nG] - gm[nG -1]) > 0) -- nG ;            gm[++nG] = p[i] ;        }        //Print_GraHam() ; return ;     }}Point tmp_matrix[10] , matrix_p[10] ;namespace Matrix{    IL bool cmp_Sort_Matrix(Point a , Point b) {        return (a - matrix_p[0]) * (b - matrix_p[0]) >= 0 ;     }    IL void Print_Matrix() {        Point w = tmp_matrix[1] - tmp_matrix[0] , delta ;        double l , l1 , l2 , l3 ;        l = Dist(tmp_matrix[0] , tmp_matrix[1]) ;        l2 = (w ^ (tmp_matrix[2] - tmp_matrix[0])) / l ; delta = w * (l2 / l) ;        matrix_p[1] = tmp_matrix[0] + delta ;        l1 = (w ^ (tmp_matrix[4] - tmp_matrix[0])) / l ; delta = w * (l1 / l) ;        matrix_p[0] = tmp_matrix[0] + delta ;        Point up = w ; up = Rot(w , PI * 0.5) ; l3 = up.cal() ;        l = Dist(Line(tmp_matrix[0] , tmp_matrix[1]) , tmp_matrix[3]) ;         up = up * (l / l3) ;        matrix_p[2] = matrix_p[1] + up ;        matrix_p[3] = matrix_p[0] + up ;        int id = 0 ;        for(int i = 1; i <= 3; i ++)            if(matrix_p[i].x < matrix_p[id].x) id = i ;            else if(fabs(matrix_p[i].x - matrix_p[id].x) <= eps && matrix_p[i].y < matrix_p[id].y) id = i ;        swap(matrix_p[id] , matrix_p[0]) ;        sort(matrix_p + 1 , matrix_p + 3 + 1 , cmp_Sort_Matrix) ;         for(int i = 0; i <= 3; i ++)            printf("%.8Lf %.8Lf " , matrix_p[i].x , matrix_p[i].y) ;        puts("") ;        return ;     }    IL void main() {        ld now_C = 1e9 ;        ++ nG ;         for(int i = 0,lft,rg = 1,up = 2; i < nG; i ++) {            Point w = gm[(i+1)%nG] - gm[i] ;            while(w * (gm[up] - gm[i]) <= w * (gm[(up+1)%nG] - gm[i])) up = (up + 1) % nG ;            if(i == 0) lft = up ;            while((w ^ (gm[rg] - gm[i])) - eps <= (w ^ (gm[(rg+1)%nG] - gm[i]))) rg = (rg + 1) % nG ;            while((w ^ (gm[lft] - gm[i])) + eps >= (w ^ (gm[(lft+1)%nG] - gm[i]))) lft = (lft + 1) % nG ;            ld al = 0.0 , bh ;            bh = Dist(Line(gm[i] , gm[(i+1)%nG]) , gm[up]) ;            al += fabs((w ^ (gm[rg] - gm[i]))) ;            al += fabs((w ^ (gm[lft] - gm[i]))) ;            al /= Dist(gm[i] , gm[(i+1) % nG]) ;            if(2.0 * (al + bh) < now_C) {                tmp_matrix[0] = gm[i] , tmp_matrix[1] = gm[(i+1)%nG] , tmp_matrix[2] = gm[lft] ;                tmp_matrix[3] = gm[up] , tmp_matrix[4] = gm[rg] ;                now_C = 2.0 * (al + bh) ;            }        }        -- nG ;         Print_Matrix() ; return ;     }}Point tmp_triange[10] , triange_p[10] ;namespace Triange{    IL ld Calc_right(Point a , Point w , Point c , double lw) {        ld d = (w ^ (c - a)) / lw , h = Dist(Line(a , a + w) , c) ;        return h / sqrt(3.0) + d ;     }    IL ld Calc_left(Point a , Point w , Point c , double lw) {        ld d = (w ^ (c - a)) / lw , h = Dist(Line(a , a + w) , c) ;        return - h / sqrt(3.0) + d ;     }    IL bool cmp_Sort_Triange(Point a , Point b) {        return (a - triange_p[0]) * (b - triange_p[0]) >= 0 ;     }    IL void Print_Triange() {        ld l1 , l2 , l = Dist(tmp_triange[0] , tmp_triange[1]) , lg ;        Point w = tmp_triange[1] - tmp_triange[0] , delta ;        l1 = Calc_right(tmp_triange[0] , w , tmp_triange[2] , l) ;        triange_p[1] = tmp_triange[0] + w * (l1 / l) ;        l2 = Calc_left(tmp_triange[0] , w , tmp_triange[3] , l) ;        triange_p[0] = tmp_triange[0] + w * (l2 / l) ;        lg = fabs(l1) + fabs(l2) ;        Line al0 , al1 ;        delta = Rot(w , PI / 3.0) ; al0 = Line(triange_p[0] , triange_p[0] + delta * (lg / l)) ;        delta = Rot(delta , PI / 3.0) ; al1 = Line(triange_p[1] , triange_p[1] + delta * (lg / l)) ;        triange_p[2] = GetCross(al0 , al1) ;        int id = 0 ;        for(int i = 1; i <= 2; i ++)            if(triange_p[i].x < triange_p[id].x) id = i ;            else if(fabs(triange_p[i].x - triange_p[id].x) <= eps && triange_p[i].y < triange_p[id].y) id = i ;        swap(triange_p[id] , triange_p[0]) ;        sort(triange_p + 1 , triange_p + 2 + 1 , cmp_Sort_Triange) ;        for(int i = 0; i <= 2; i ++)            printf("%.8Lf %.8Lf " , triange_p[i].x , triange_p[i].y) ;        puts("") ; return ;     }    IL void main() {        ld now_C = 1e9 , al ;        ++ nG ;        for(int i = 0,lft = 1 , rgt = 1,up = 1; i < nG; i ++) {            Point w = gm[(i+1)%nG] - gm[i] ; ld lw = Dist(gm[(i+1)%nG] , gm[i]) ;            while(w * (gm[up] - gm[i]) <= w * (gm[(up+1)%nG] - gm[i])) up = (up + 1) % nG ;            if(i == 0) lft = up ;            while(Calc_right(gm[i] , w , gm[rgt] , lw) - eps <= Calc_right(gm[i] , w , gm[(rgt+1)%nG] , lw)) rgt = (rgt + 1) % nG ;            while(Calc_left(gm[i] , w , gm[lft] , lw) + eps >= Calc_left(gm[i] , w , gm[(lft+1)%nG] , lw)) lft = (lft + 1) % nG ;            al = 0.0 ;            al += fabs(Calc_left(gm[i] , w , gm[lft] , lw)) ;            al += fabs(Calc_right(gm[i] , w , gm[rgt] , lw)) ;            if(3.0 * al <= now_C) {                tmp_triange[0] = gm[i] ; tmp_triange[1] = gm[(i+1) % nG] ; tmp_triange[2] = gm[rgt] ; tmp_triange[3] = gm[lft] ;                now_C = 3.0 * al ;             }        }        -- nG ;         Print_Triange() ; return ;     }}Point gc[_] , tmp_gc[_] ; int nC ; namespace Divide_Cut{    IL void Print_Divide_Cut() {        for(int i = 1; i <= nC; i ++) {            gc[i].Print() ; putchar('-') ; putchar('-') ; putchar('>') ;         }        puts("") ; return ;    }    IL void Cut(Point a , Point b) {        gc[nC + 1] = gc[1] ;        tot = 0;  Point w = b - a ;        for(int i = 1; i <= nC; i ++) {            ld test1 = (a - gc[i]) * (b - gc[i]) ;            if(test1 >= 0.0) tmp_gc[++tot] = gc[i] ;            ld test2 = (a - gc[i+1]) * (b - gc[i+1]) ;            if(test2 * test1 < 0) tmp_gc[++tot] = GetCross(Line(a , b) , Line(gc[i] , gc[i + 1])) ;        }        for(int i = 1; i <= tot; i ++) gc[i] = tmp_gc[i] ;        nC = tot ;     }    IL void main() {        gc[++nC] = Point(-inf,-inf) ;        gc[++nC] = Point(inf,-inf) ;        gc[++nC] = Point(inf,inf) ;        gc[++nC] = Point(-inf,inf) ;         for(int i = 0; i <= 3; i ++) {            Cut(matrix_p[i] , matrix_p[(i+1)%4]) ;        }        for(int i = 0; i <= 2; i ++) Cut(triange_p[i] , triange_p[(i+1)%3]) ;        //Print_Divide_Cut() ;         return ;     }}ld circle_pl , circle_pr , polygon_pl , polygon_pr , Ans ;namespace Simpson_Int{    IL ld F(ld x) {        if(!(circle_p.x - circle_range - eps <= x && x <= circle_p.x + circle_range + eps)) return 0 ;        ld d = sqrt(Sqr(circle_range) - Sqr(fabs(x - circle_p.x))) ;        circle_pl = circle_p.y - d ; circle_pr = circle_p.y + d ;        polygon_pl = inf ; polygon_pr = -inf ;        tot = 0 ;        for(int i = 1; i <= nC; i ++)            if((gc[i].x - eps <= x && gc[i%nC + 1].x + eps >= x) || (gc[i%nC + 1].x - eps <= x && gc[i].x + eps >= x)  ) {                Point al = GetCross(Line(gc[i] , gc[i%nC+1]) , Line(Point(x,0) , Point(x,1))) ;                polygon_pl = min(polygon_pl , al.y) ;                polygon_pr = max(polygon_pr , al.y) ;            }        //cout << "circle: ["<
     
      <<","<
      
       <<"]" << endl ;        //cout << "polygon: ["<< polygon_pl<<","<
       
        <<"]" << endl ;         if(polygon_pl >= polygon_pr) return 0 ;        ld pl , pr ;        pl = max(circle_pl , polygon_pl) ;        pr = min(circle_pr , polygon_pr) ;        if(pl - eps <= pr) return pr - pl ; else return 0 ;     }    ld Calc(ld l , ld r) {return (r-l) * (F(l) + F(r) + 4.0 * F((l + r) * 0.5)) / 6.0 ; }    ld Simpson(ld l , ld r , ld ans) {        ld mid = (l + r) * 0.5 ;        ld x1 = Calc(l , mid) , x2 = Calc(mid , r) ;        ld al = x1 + x2 ;        if(fabs(al - ans) <= 1e-12) return al ;        return Simpson(l , mid , x1) + Simpson(mid , r , x2) ;    }    IL void main() {        ld pl = circle_p.x - circle_range ;        ld pr = circle_p.x + circle_range ;        for(int i = 1; i <= nC; i ++) {            pl = min(pl , gc[i].x) ;            pr = max(pr , gc[i].x) ;        }        Ans = Simpson(pl , pr , Calc(pl , pr)) ;        printf("%.8Lf\n" , Ans) ;        return ;    }}int main() {    freopen("adieu.in","r",stdin) ;    freopen("adieu.out","w",stdout) ;    n = gi() ;    for(int i = 1; i <= n; i ++) scanf("%Lf %Lf" , &p[i].x , &p[i].y) ;    CirCle::main() ;    GraHam::main() ;     Matrix::main() ;    Triange::main() ;    Divide_Cut::main() ;    Simpson_Int::main() ;     return 0 ;}