#include using namespace std; typedef long long signed int LL; typedef long long unsigned int LU; #define incID(i, l, r) for(int i = (l) ; i < (r); i++) #define incII(i, l, r) for(int i = (l) ; i <= (r); i++) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); i--) #define decII(i, l, r) for(int i = (r) ; i >= (l); i--) #define inc(i, n) incID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec(i, n) decID(i, 0, n) #define dec1(i, n) decII(i, 1, n) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define FI first #define SE second #define PQ priority_queue #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define FOR(it, v) for(auto it = v.begin(); it != v.end(); ++it) #define RFOR(it, v) for(auto it = v.rbegin(); it != v.rend(); ++it) template bool setmin(T & a, T b) { if(b < a) { a = b; return true; } else { return false; } } template bool setmax(T & a, T b) { if(b > a) { a = b; return true; } else { return false; } } template bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } } template bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } } template T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); } template T lcm(T a, T b) { return a / gcd(a, b) * b; } // ---- ---- void mat_inv3(double z[3][3], double x[3][3]) { // z = x ^ -1 double d = + x[0][0] * x[1][1] * x[2][2] + x[0][1] * x[1][2] * x[2][0] + x[0][2] * x[1][0] * x[2][1] - x[0][2] * x[1][1] * x[2][0] - x[0][1] * x[1][0] * x[2][2] - x[0][0] * x[1][2] * x[2][1] ; // assert(abs(d) > 0.00001); double y[3][3] = { { x[1][1]*x[2][2] - x[1][2]*x[2][1], x[0][2]*x[2][1] - x[0][1]*x[2][2], x[0][1]*x[1][2] - x[0][2]*x[1][1] }, { x[1][2]*x[2][0] - x[1][0]*x[2][2], x[0][0]*x[2][2] - x[0][2]*x[2][0], x[0][2]*x[1][0] - x[0][0]*x[1][2] }, { x[1][0]*x[2][1] - x[1][1]*x[2][0], x[0][1]*x[2][0] - x[0][0]*x[2][1], x[0][0]*x[1][1] - x[0][1]*x[1][0] } }; inc(i, 3) { inc(j, 3) { z[i][j] = y[i][j] / d; } } } template void mat_prod(double a[N][N], double b[N][N], double c[N][N]) { // a = b * c; double d[N][N]; inc(i, N) { inc(j, N) { d[i][j] = 0; } } inc(i, N) { inc(j, N) { inc(k, N) { (d[i][j] += b[i][k] * c[k][j]); } } } inc(i, N) { inc(j, N) { a[i][j] = d[i][j]; } } return; } double norm3(double x, double y, double z) { return sqrt(x * x + y * y + z * z); } double distance_of_triangle_to_point(double p[4][3]) { dec(i, 4) { inc(j, 3) { p[i][j] -= p[0][j]; } } double a[3][3] = { { p[1][0], p[2][0], p[1][1] * p[2][2] - p[1][2] * p[2][1] }, { p[1][1], p[2][1], p[1][2] * p[2][0] - p[1][0] * p[2][2] }, { p[1][2], p[2][2], p[1][0] * p[2][1] - p[1][1] * p[2][0] } }; double d[3][3] = { { p[3][0], 0, 0 }, { p[3][1], 0, 0 }, { p[3][2], 0, 0 } }; double b[3][3]; mat_inv3(b, a); mat_prod(b, b, d); return abs(b[2][0]) * norm3(a[0][2], a[1][2], a[2][2]); } // ---- int n; double p[301][3]; double f(array a) { double q[4][3]; inc(i, 4) { inc(j, 3) { q[i][j] = p[a[i]][j]; } } return distance_of_triangle_to_point(q); } int main() { cin >> n; inc(i, n + 1) { inc(j, 3) { cin >> p[i][j]; } } double ans = 0.0; incII(k, 1, n) { incID(j, 1, k) { incID(i, 1, j) { ans += f({ i, j, k, 0 }); } } } printf("%.12f\n", ans); return 0; }