Minas had a box of marble which is lost last week. About that box Minas only know that length and height of the box was L and H, and box contains K marbles. But he forget the width of the box. But he remember that width = 2 * radius of marble and width is also an integer. You can assume that all marble are same.

Now, Minas will give you L, H and K. You need to tell him the width of the box. If the width is less than 1 then print -1.

Input

Input starts with an integer T (1<=T<=1000), denoting the number of test cases.
Each case contains 3 integer L (1 ≤ L ≤ 10^9), H (1 ≤ H ≤ 10^9) and K (1 ≤ K ≤ 10^9).

Output

For each case of input, print the case number as "Case #: x", # is replaced by the case number starting from 1 and x is replaced by the maximum possible width of the box.

Example

Input:
1
2 2 4

Output:
Case 1: 1