Non-negative Partial Sums

You are given a sequence of n numbers a₀,..., a_n-1. A cyclic shift by k positions (0<=k<=n-1) results in the following sequence: a_k a_k+1,..., a_n-1, a₀, a₁,..., a_k-1. How many of the n cyclic shifts satisfy the condition that the sum of the first i numbers is greater than or equal to zero for all i with 1<=i<=n?

Each test case consists of two lines. The first contains the number n (1<=n<=10⁶), the number of integers in the sequence. The second contains n integers a₀,..., a_n-1 (-1000<=a_i<=1000) representing the sequence of numbers. The input will finish with a line containing 0.

For each test case, print one line with the number of cyclic shifts of the given sequence which satisfy the condition stated above.

3
2 2 1
3
-1 1 1
1
-1
0

3
2
0

SWERC 2011