Shoot the Target (Small1)

Kazuki is playing Worms. A target hangs above the ground and he has to hit it. The target is slanted, so it is not perpendicular to the ground. Kazuki may shoot from any point on the ground, and he wants to stand where the target looks widest. Find that maximum visible angle in degrees.

The world is a 2D plane with the $y$ axis pointing up toward the sky. The ground is the $x$ axis. You are given the coordinates of the two endpoints of the target, $(X_1, Y_1)$ and $(X_2, Y_2)$. The target is the line segment between those two points.

The visible angle Kazuki wants to maximize is the angle formed by the points $(X_1, Y_1)$, $(X, 0)$ and $(X_2, Y_2)$, with its vertex at $(X, 0)$. The optimal $X$ is not necessarily an integer.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains four integers $X_1$, $Y_1$, $X_2$ and $Y_2$ separated by spaces, where $(X_1, Y_1)$ and $(X_2, Y_2)$ are the coordinates of the two ends of the target.

Limits

• $1 \le T \le 100$
• $X_1 \ne X_2$
• $1 \le Y_1, Y_2 \le 10$
• $-10 \le X_1, X_2 \le 10$

For each test case, print one line in the form Case #t: Z, where $t$ is the test case number starting from 1 and $Z$ is the maximum visible angle in degrees that Kazuki can achieve. Round $Z$ to six decimal places and always print all six digits, so an angle of exactly 90 degrees prints as 90.000000.