For every pair of triplets, Ta = (Ia, Ja, Ka) and Tb = (Ib, Jb, Kb), we define the difference value between Ta and Tb as follows: D(Ta, Tb) = max {Ia - Ib, Ja - Jb, Ka - Kb} - min {Ia - Ib, Ja - Jb, Ka - Kb} Now you are given N triplets, could you write a program to calculate the sum of the difference values between every unordered pair of triplets?


The input consists of several test cases. Each test case begins with a line containing an integer N, denotes the number of triplets. Assume that we number the triplets as T1, T2, ... , TN. Then, there are following N lines, each line contains three integers, giving the elements of each triplet. A case with N = 0 indicates the end of the input.


For each case, output a line with the sum of difference values between every unordered pair of triplets.

Sample Input

2 1 2 3 3 2 1 3 1 3 2 4 0 7 2 2 9 0

Sample Output

4 20


Case 1: D(T1,T2)=4 Case 2: D(T1,T2)+D(T1,T3)+D(T2,T3)=8+8+4=20 You can assume that N, the number of triplets in each case, will not exceed 200,000 and the elements in triplets fit into [-10^6,10^6].


POJ Monthly--2007.07.08, Yuan, Xinhao