Problem Q. Half of a convex polygon ≡

Author:	T. Chistyakov, A. Klenin		Time limit:	2 sec
Input file:	input.txt		Memory limit:	24 Mb
Output file:	output.txt
Maximum points:	100

Statement

You need to divide a non-degenerate convex polygon with a horizontal line into two parts of equal area.

The polygon is specified by N vertices in the clockwise order.

Input file format

Input file contains integer N, then N pairs of floating-point numbers x_i y_i describing the vertices of the polygon.

Output file format

Output a single number — the ordinate of the horizontal line dividing the polygon as requested. The result must be rounded to 10^-2.

Constraints

3 ≤ N ≤ 1000000

1 ≤ x_i, y_i ≤ 1000000

Sample tests

No.	Input file (input.txt)	Output file (output.txt)
1	4 1 1 1 3 3 3 3 1 copy	2 copy

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