Non-negative Partial Sums 

You are given a sequence of n numbers a₀,..., a_n-1. A cyclic shift by k positions ( 0$\le$k$\le$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 first i numbers is greater than or equal to zero for all i with 1$\le$i$\le$n?

Input 

Each test case consists of two lines. The first contains the number n ( 1$\le$n$\le$10⁶), the number of integers in the sequence. The second contains n integers a₀,..., a_n-1 ( -1000$\le$a_i$\le$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