XiaoXin has a kingdom with the infinite area.
He has n soldiers guarding the kingdom.
The i-th soldier stands at the position (xi,yi), and his walking speed is vi.
If a point can be reached by a soldier, and the time this soldier walking to this point is strictly less than other soldiers, this point is in the charge of this soldier.
For every soldier, XiaoXin wants to know if the area in the charge of him is infinite.
For each test case, the first line contains one integer n(1<=n<=500).
In following n lines, each line contains three integers xi,yi,vi(0<=|xi|,|yi|,vi<=10^4).
For each case, output "Case #k: s", where k is the case number counting from 1, and s is a string consisting of n character. If the area in the charge of the i-th soldier isn\'t infinite, the i-th character is "0", else it\'s "1".
3 0 0 3 1 1 2 2 2 1 0
Case #1: 100