시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
300 초 512 MB 0 0 0 0.000%

## 문제

You are steering a boat from the coordinates (-10, A) to the coordinates (10, B). The coordinates are measured in kilometers, and your boat travels at a constant speed of 1 kilometer per hour. You have full control over the path the boat takes. We model the boat as a single point.

There are N islands in the area; we model them as single points. The i-th island is at the coordinates (0, Ci).

The area is radioactive, and you constantly receive 1 microsievert per hour of radiation from the general environment, no matter where you are. Moreover, the islands themselves are radioactive, and you constantly receive additional radiation at a rate of (Di)-2microsieverts per hour from the i-th island, where Di is your current distance (in kilometers) from the i-th island. (Formally: let Di(t) be your distance from the i-th island as a function of time t, and X be the total time your journey takes. Then the total radiation received from the i-th island is the definite integral from 0 to X of Di(t)-2.) You can get as close to an island as you would like, as long as you do not match its exact coordinates.

## 입력

The first line of the input gives the number of test cases, TT test cases follow. Each test cases consists of two lines. The first line of a test case consists of three values: an integer N, and two floating-point numbers A and B, as described in the statement above. The second line of a test case consists of N floating-point numbers Ci; the i-th of these numbers gives the y coordinate of the i-th island.

All floating-point numbers are specified to exactly two decimal places.

### Limits

• -10.00 ≤ A ≤ 10.00.
• -10.00 ≤ B ≤ 10.00.
• -10.00 ≤ Ci ≤ 10.00, for all i.
• Ci ≠ Cj, for all i ≠ j.
• 1 ≤ T ≤ 50;
• 1 ≤ N ≤ 2.

## 출력

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the minimum radiation dose (in microsieverts) received while completing the journey.

y will be considered correct if it is within an absolute or relative error of 10-3 of the correct answer. See the FAQ for an explanation of what that means, and what formats of real numbers we accept.

## 예제 입력

2
1 1.00 -2.00
0.00
2 0.00 0.00
3.00 -3.00


## 예제 출력

Case #1: 21.81
Case #2: 21.71



## 힌트

Here is a diagram of the optimal path for sample case #1. We have enlarged the island to make it more visible, but remember to treat it as a single point.