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 first 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 first 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.

Output

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

Example

Input:
3
2 2 1
3
-1 1 1
1
-1
0

Output:
3
2
0

Problem setter: Adrian Kuegel