Non-negative Partial Sums

Problem Description
You are given a sequence of n numbers a0,..., an-1. A cyclic shift by k positions (0<=k<=n-1) results in the following sequence: ak ak+1,..., an-1, a0, a1,..., ak-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?

Input
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,..., an-1 (-1000<=ai<=1000) representing the sequence of numbers. The input will finish with a line containing 0.

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

Sample Input
3
2 2 1
3
-1 1 1
1
-1
0

Sample Output
3
2
0