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Problem 1914 Funny Positive Sequence

## Problem Description

There are n integers a1,a2,…,an-1,an in the sequence A, the sum of these n integers is larger than zero. There are n integers b1,b2,…,bn-1,bn in the sequence B, B is the generating sequence of A and bi = a1+a2,+…+ai (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): a1,a2,…,an-1,an

A(1): a2,a3,…,an,a1

A(n-2): an-1,an,…,an-3,an-2

A(n-1): an,a1,…,an-2,an-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) }.

## Input

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.

## Output

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

## Sample Input

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

## Sample Output

Case 1: 1 Case 2: 4

## Source

2010年全国大学生程序设计邀请赛（福州）

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