Daltons (Daida, Alhar, Tara, and Reyton) love playing games. One of their favorite games is ’Battle II’. In order to play this game, first, one of them is chosen as a problem-setter. The problem-setter starts drawing some bombs on a piece of paper (each bomb is a circle: has a center and a radius). She then associates to each bomb a destruction range. There are three rules defined in this game:

- If a bomb explodes, all the bombs in its destruction range will also explode. A bomb b1 is in destruction range of another bomb b2 if distance of b2 from the perimeter of b1 is less than the range of b1. (i.e. b2.range + b1.radius + b2.radius ≥ Distance(b1.center, b2.center))
- A bomb may explode due to either being affected by explosion of another bomb according to the first rule or manually being fired.
- Firing a bomb manually has a cost which is equal to the range of it. She finally gives the configuration of the bombs to the others and asks them to find a sequence of bombs to fire which should satisfy the following conditions:
- All the bombs should be exploded as a result of firing and explosion of the bombs in this sequence. 2. The i-th bomb in the sequence should not result explosion of the j-th bomb where j > i.
- The average cost of firing the bombs that are in the sequence must be minimum. You should help the players find the solution to this problem by writing a program which is able to find such a sequence given the specifications and configuration of the bombs in the paper. Input The first line of input gives the number of cases, N. N test cases will follow. Each one starts with a line containing the number of bombs (0 < n ≤ 300). Each of the next n lines contains four integers Xi, Yi, Ri, Ei, meaning that the i-th bomb is located at (Xi, Yi), has a radius of Ri, and has a range of Ei. There will be a blank line after each block of test case. Output For each test case, output the line containing ‘Case #x:’, followed by list of bombs in the order that should be fired, seperated by a single space. Follow the output format used in sample output. If there are more than one solution, any of them is acceptable. “Marriage, in life, is like a duel in the midst of the battle” Edmond About

2/2 Sample Input 1 3 4722 8510 3 -3 1 1 Sample Output Case #1: 1 0 2