PM Room defines a sequence A = {A
1, A
2,..., A
N}, each of which is either 0 or 1. In order to beat him, programmer Moor has to construct another sequence B = {B
1, B
2,... , B
N} of the same length, which satisfies that:
The input consists of multiple test cases. The number of test cases T(T<=100) occurs in the first line of input.
For each test case:
The first line contains a single integer N (1<=N<=100000), which denotes the length of A and B.
The second line consists of N integers, where the ith denotes A
i.
Output the minimal f (A, B) when B is optimal and round it to 6 decimals.