A12406. Be Positive

You are given an array of $n$ integers: $a_1, a_2, \ldots, a_n$ . Your task is to find some non-zero integer $d$ ( $-10^3 \leq d \leq 10^3$ ) such that, after each number in the array is divided by $d$ , the number of positive numbers that are presented in the array is greater than or equal to half of the array size (i.e., at least $\lceil\frac{n}{2}\rceil$ ). Note that those positive numbers do not need to be an integer (e.g., a $2.5$ counts as a positive number). If there are multiple values of $d$ that satisfy the condition, you may print any of them. In case that there is no such $d$ , print a single integer $0$ .

Recall that $\lceil x \rceil$ represents the smallest integer that is not less than $x$ and that zero ( $0$ ) is neither positive nor negative.

The first line contains one integer $n$ ( $1 \le n \le 100$ ) — the number of elements in the array.

The second line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$ ( $-10^3 \le a_i \le 10^3$ ).

Print one integer $d$ ( $-10^3 \leq d \leq 10^3$ and $d \neq 0$ ) that satisfies the given condition. If there are multiple values of $d$ that satisfy the condition, you may print any of them. In case that there is no such $d$ , print a single integer $0$ .

In the first sample, $n = 5$ , so we need at least $\lceil\frac{5}{2}\rceil = 3$ positive numbers after division. If $d = 4$ , the array after division is $[2.5, 0, -1.75, 0.5, 1.5]$ , in which there are $3$ positive numbers (namely: $2.5$ , $0.5$ , and $1.5$ ).

In the second sample, there is no valid $d$ , so $0$ should be printed.