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

\(2 \le n \le 5e^5\\ -1e^9 \le x_i \le 1e^9\)