In w-dimensional space, the solid sphere of radius r at point p is the set of points x such that Dist (x. p) Sr. Write a function VolumeSphere Intersect (P, Q, A,S, T, W) which uses a Monte Carlo method with T trials to compute the volume of the intersection of a sphere of radius R centered at P with a sphere of radius S centered at Q. The function should return a confidence interval with confidence W. Here P and Q are n-dimensional vectors; R. S are positive floating numbers, T is a positive integer: and W is an floating point number between 0 and 1. (It is possible to compute the exact answer, with some geometry and some calculus, but that is not the assignment.) To carry out the Monte Carlo method, use a uniform distribution within the box (B1, Ci] x [ Ba, Ca] x [B.. Ca] where By = max (P(K] - R. Q(K] - S) and Co = min P(K] + R, Q(K] + 5). Note that if the distance from P to Q is greater than R + S. then the two spheres do not intersect, and so the function should simply return [0, 0]