Time Limit: 1000 mSec Memory Limit : 32768 KB

There are n integers a_{1},a_{2},…,a_{n-1},a_{n} in the sequence A, the sum of these n integers is larger than zero. There are n integers b_{1},b_{2},…,b_{n-1},b_{n} in the sequence B, B is the generating sequence of A and bi = a_{1}+a_{2},+…+a_{i} (1≤i≤n). If the elements of B are all positive, A is called as a positive sequence.

We left shift the sequence A 0,1,2,…,n-1 times, and get n sequences, that is showed as follows:

A(0): a_{1},a_{2},…,a_{n-1},a_{n}

A(1): a_{2},a_{3},…,a_{n},a_{1}

…

A(n-2): a_{n-1},a_{n},…,a_{n-3},a_{n-2}

A(n-1): a_{n},a_{1},…,a_{n-2},a_{n-1}

Your task is to find out the number of positive sequences in the set { A(0), A(1), …, A(n-2), A(n-1) }.

The first line of the input contains an integer T (T <= 20), indicating the number of cases. Each case begins with a line containing one integer n (1 <= n <= 500,000), the number of elements in the sequence. The next line contains n integers ai(-2,000,000,000≤ai≤2,000,000,000,1≤i≤n), the value of elements in the sequence.

For each test case, print a line containing the test case number (beginning with 1) and the number of positive sequences.

2
3
1 1 -1
8
1 1 1 -1 1 1 1 -1

Case 1: 1
Case 2: 4