You just landed a job as a machine learning engineer! As a ramp-up exercise, Boss Rob tasked you with modeling the watering wells in his yard, which can be represented on a Cartesian plane.

Boss Rob has a primary well at point ((A_x, A_y)) and a backup well at a different point ((B_x, B_y)), each able to water trees within an (R) unit radius. Using (A_x), (A_y), (B_x), (B_y), and (R) (unknown integers to you), Rob plants (N) happy little trees at real number points obtained by (N) calls to the function:

def gen_one_tree(A_x, A_y, B_x, B_y, R):
    while True:
        r = random.uniform(0, R)
        theta = random.uniform(0, 2*math.pi)
        x = A_x + r*math.cos(theta)
        y = A_y + r*math.sin(theta)
        if (x - B_x)**2 + (y - B_y)**2 <= R*R:
            return (x, y)

Here, random.uniform(L, H) returns a real number in ([L, H)) uniformly at random.

In other words, he picks a point ((x, y)) in the circular range of the primary well using the special method above. If ((x, y)) happens to be in range of the backup well, he plants a tree there (else he discards it and tries again with a new ((x, y))). This repeats until Rob has planted (N) trees.

Given only the planted tree coordinates ((X_1, Y_1), \ldots, (X_N, Y_N)), you are tasked to predict the exact values of (A_x), (A_y), (B_x), (B_y), and (R). As you are new, Boss Rob will accept your solution if it correctly predicts at least (80%) of the test cases.

Constraints

(1 \le T \le 1{,}000) (500 \le N \le 1{,}000{,}000) (0 \le A_x, A_y, B_x, B_y \le 50) ((A_x, A_y) \ne (B_x, B_y)) (1 \le R \le 50) The sum of (N) across all test cases is at most (2{,}000{,}000).

The intersection area of the two circular regions is strictly positive.

Tree coordinates in the data were truly generated using the randomized algorithm as described above. The secret parameters (A_x), (A_y), (B_x), (B_y), and (R) have also been chosen uniformly at random for each case (rejecting cases where the circles are identical or do not have positive overlap).

Input Format

Input begins with a single integer (T), the number of test cases. For each case, there is first a line containing a single integer (N), the number of planted trees. Then, (N) lines follow, the (i)th of which contains two space-separated real numbers (X_i) and (Y_i), each given to (6) decimal places.

Output Format

For the (i)th test case, print a line containing "Case #i: ", followed by the five space-separated integers (A_x), (A_y), (B_x), (B_y), and (R), in that order.

Sample Explanation

The first sample case is pictured below, with the primary well's range in red, the backup well's range in blue, and the (500) randomly-generated trees in green: