// Enjoy your stay. #include #define EPS 1e-9 #define INF 1070000000LL #define MOD 1000000007LL #define fir first #define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++) #define ite iterator #define mp make_pair #define mt make_tuple #define rep(i,n) rep2(i,0,n) #define rep2(i,m,n) for(int i=m;i<(n);i++) #define pb push_back #define sec second #define sz(x) ((int)(x).size()) using namespace std; typedef istringstream iss; typedef long long ll; typedef pair pi; typedef stringstream sst; typedef vector vi; // geometry library from hos const double PI = acos(-1); int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; } struct PT { double x, y, z; PT() {} PT(double x, double y, double z) : x(x), y(y), z(z) {} PT operator+(const PT &a) const { return PT(x + a.x, y + a.y, z + a.z); } PT operator-(const PT &a) const { return PT(x - a.x, y - a.y, z - a.z); } PT operator-() const { return PT(-x, -y, -z); } PT operator*(const double &k) const { return PT(x * k, y * k, z * k); } PT operator/(const double &k) const { return PT(x / k, y / k, z / k); } double abs() const { return sqrt(x * x + y * y + z * z); } double abs2() const { return x * x + y * y + z * z; } double dot(const PT &a) const { return x * a.x + y * a.y + z * a.z; } PT cross(const PT a) const { return PT(y * a.z - z * a.y, z * a.x - x * a.z, x * a.y - y * a.x); } bool operator<(const PT &a) const { return (x != a.x) ? (x < a.x) : (y != a.y) ? (y < a.y) : (z < a.z); } bool operator==(const PT &a) const { return (sig(x - a.x) == 0) && (sig(y - a.y) == 0) && (sig(z - a.z) == 0); } }; ostream &operator<<(ostream &os, const PT &a) { os << "(" << a.x << ", " << a.y << ", " << a.z << ")"; return os; } PT tri(PT a, PT b, PT c) { return (b - a).cross(c - a); } double tet(PT a, PT b, PT c, PT d) { return (b - a).cross(c - a).dot(d - a); } double dLP(PT a, PT b, PT c) { return tri(a, b, c).abs() / (b - a).abs(); } double dSP(PT a, PT b, PT c) { if (sig((b - a).dot(c - a)) <= 0) return (c - a).abs(); if (sig((a - b).dot(c - b)) <= 0) return (c - b).abs(); return tri(a, b, c).abs() / (b - a).abs(); } // end of library double triangle(double a,double b,double c){ double s = (a+b+c)/2; return sqrt(s*(s-a)*(s-b)*(s-c)); } int main(){ int N; PT p,q[333]; cin>>N; cin>>p.x>>p.y>>p.z; rep(i,N){ cin>>q[i].x>>q[i].y>>q[i].z; } double ans = 0; rep(i,N)rep2(j,i+1,N)rep2(k,j+1,N){ double V = tet(p,q[i],q[j],q[k]); double t = triangle((q[i]-q[j]).abs(),(q[j]-q[k]).abs(),(q[k]-q[i]).abs()); ans += abs(V/t); } cout<