Problem Description

One day, zp, wangchaohui and snowingsea passed by Science Building on the way to have dinner, after their working on puzzle.

zp asks:”Do you know how high the building is?”, but none of them knew. "So let’s measure it!", snowingsea shouted out. Then they borrowed n theodolites（a tool used to measure angle of elevation）. The n theodolites were placed on the ground around the building, which formed an n-edge regular polygon. The building was inside the regular polygon. Each edge of the polygon is s meters, and the height of theodolite was h centimeters. They wrote down the angle of elevation in degrees from each theodolite to the top of the building. They wanted to calculate the building's height according to the data they measured. Can U help them.

Input

The input consists of several test cases. The first line contains an integer T representing the number of test cases. Each test case contains two lines. The first line contains three integers, they are n, s, h, ( described in problem's description ). The second line contains n float numbers, which are the angles of each elevation they wrote down. 3 ≤ n ≤ 100, 0 < s, h < 10 000.

Output

For each case, print the height of the science building in meters in a separate line. The answer should be rounded to four decimal digits.

1
3 100 100
60 60 60

101.0000