CUTPOLY

A polygonal line with ~N~ points in the plane is given. The points are sorted by ~x~-coordinate, i.e., ~x_i + 1 > x_i~, and also the polygonal line is strictly increasing with respect to ~y~-coordinate, i.e., ~y_{i+1} > y_i~.

Let ~y = y_1~, and ~y = y_N~ be lines parallel to the ~x~-axis. We can bring a line ~x =~ λ parallel to the ~y~-axis, which intersects the polygonal line at a point (~x_1~ ~\le~ λ ~\le~ ~x_N~). It may intersect at any of the ~N~ points given or it may intersect any of the ~N - 1~ line segments formed. Let ~L~(λ) be the area enclosed by the polygonal line, the line ~y = y_1~, and the line ~x =~ λ. Let ~U~(λ) be the area enclosed by the polygonal line, the line ~y = y_N~, and the line ~x =~ λ.

The task is to determine the minimum value of ~L~(λ) ~+~ ~U~(λ).

Input

The first line of the input contains only the integer ~N~, the number of points of the polygonal line. Each of the next ~N~ lines contains a pair of integers separated by a space, corresponding to the ~x~ and ~y~ coordinates respectively of each point of the line. The points will be given sorted by the ~x~ dimension.

Output

The output should consist of a real number, the minimum possible value of ~L~(λ) + ~U~(λ), with an accuracy of ~6~ decimal places. Attention! Be sure to print with "%0.6lf\n" or something similar.

Constraints

~2 \le N \le 1.000.000~.
Execution time limit: 1 sec.
Memory limit: 64 MB.

Example of Input - Output

STDIN (cutpoly.in)

4
1 1
3 2
8 5
9 7

STDOUT (cutpoly.out)

12.833333