You are given $n$ points on a line. The distance between the two points is defined as follows:

$dist(a, b) = sin(a + b) \times cos(a - b)$

Your task is to determine the sum of the distances between all the points, where the first distance is greater than the second.

Input format

• First line: $n$ denoting the number of points on a line
• Next line: $n$ space-separated numbers that correspond to $x_i$ denoting the points on the line

Output format

Print the number that represents the sum of the distance between all the points to exactly two decimal places.

Constraints

$2 \le n \le 5e^5\\ -1e^9 \le x_i \le 1e^9$