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 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 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 nish 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.