Simple calculations 

The Problem

There is a sequence of n+2 elements a0, a1,, an+1 (n <= 3000; -1000 <=  ai 1000). It is known that ai = (ai1 + ai+1)/2  ci for each i=1, 2, ..., n. You are given a0, an+1, c1, ... , cn. Write a program which calculates a1.

The Input

The first line is the number of test cases, followed by a blank line.

For each test case, the first line of an input file contains an integer n. The next two lines consist of numbers a0 and an+1 each having two digits after decimal point, and the next n lines contain numbers ci (also with two digits after decimal point), one number per line.

Each test case will be separated by a single line.

The Output

For each test case, the output file should contain a1 in the same format as a0 and an+1.

Print a blank line between the outputs for two consecutive test cases.

Sample Input

1

1
50.50
25.50
10.15

Sample Output

27.85