You are given an array of ~N~ integers ~a_1, a_2, \dots, a_N~. Suppose ~b_1, b_2, \dots, b_N~ is any array of ~N~ integers. Find the minimum possible positive value of ~X = \sum_{i=1}^N a_i \times b_i~.

Constraints

~1 \le N \le 2 \times 10^5~

~-10^9 \le a_i \le 10^9~

At least one ~a_i \ne 0~.

Input Specification

The first line contains an integer, ~N~.

The next line contains ~N~ space-separated integers, ~a_1, a_2, \dots, a_N~.

Output Specification

Output the minimum positive value of ~X~.

Sample Input

3
2 -1 3

Sample Output

1

Explanation for Sample

One possible value for array ~b~ is ~[-2, 4, 3]~. Then, ~X = (2)(-2) + (-1)(4) + (3)(3) = 1~. This is the minimum positive value of ~X~ amongst all values of ~b~.