Polygon Intersection

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Given \(n\) convex polygons.

For all \(k\) from 1 to \(n\), compute the total area covered by exactly \(k\) polygons.

Input

The first line contains an integer \(n\) — the number of polygons.

The next \(n\) blocks define \(n\) polygons.

A block starts with a line containing an integer \(m_i\) — the number of vertices of the \(i\)-th polygon.

The following lines of the block contain pairs of integers \(x_{i j}\), \(y_{i j}\) separated by a space — the coordinates of the vertices of the \(i\)-th polygon in counterclockwise order.

Output

In a single line, output \(n\) real numbers — the answer to the problem.

The answer will be considered correct if the absolute or relative error of each output number does not exceed \(10^{-7}\).

Constraints

\(1 \le n \le 50\),

\(3 \le m_i\),

\(3 \le \sum_{i=1} ^n m_i \le 10^3\),

\(|x_{i j}|, |y_{i j}| \le 10^5\).

Samples