#!/usr/bin/env pypy3 import itertools import math NUM_AXES = 3 def compute_sum_of_dist(n, ps): # psを破壊的に変更 for i, j in itertools.product(range(1, n), range(NUM_AXES)): # P (Q_0) が原点になるように移動 ps[i][j] -= ps[0][j] for j in range(NUM_AXES): ps[0][j] = 0.0 # 二点間距離を前計算 dist = [[0.0 for _ in range(n)] for _ in range(n)] for p1, p2 in itertools.combinations(range(n), 2): dist[p1][p2] = math.sqrt(sum((ps[p1][a] - ps[p2][a]) ** 2 for a in range(NUM_AXES))) dist[p2][p1] = dist[p1][p2] # 三角形の面積 def area_of_triangle(p1, p2, p3): a = dist[p1][p2] b = dist[p2][p3] c = dist[p3][p1] s = (a + b + c) / 2.0 return math.sqrt(s * (s - a) * (s - b) * (s - c)) # 四面体の体積 def volume_of_tetrahedron(p1, p2, p3): x1, y1, z1 = ps[p1] x2, y2, z2 = ps[p2] x3, y3, z3 = ps[p3] vol = y1 * z2 * x3 + z1 * x2 * y3 + x1 * y2 * z3 vol = vol - z1 * y2 * x3 - x1 * z2 * y3 - y1 * x2 * z3 vol = abs(vol) / 6.0 return vol # 高さ def height(p1, p2, p3): vol = volume_of_tetrahedron(p1, p2, p3) area = area_of_triangle(p1, p2, p3) height = vol / area * 3 return height g = itertools.combinations(range(1, n), 3) res = sum(height(*qs) for qs in g) return res def main(): n = int(input()) + 1 ps = [[0.0 for _ in range(NUM_AXES)] for _ in range(n)] for i in range(n): ws = tuple(float(w) for w in input().split()) for j in range(NUM_AXES): ps[i][j] = ws[j] res = compute_sum_of_dist(n, ps) print("{:.12f}".format(res)) if __name__ == '__main__': main()