Walk

Alice would like to visit Bob. However, they live in a hilly landscape, and Alice does not like to walk in hills. She has a map of the area, showing the height curves. You have to calculates the total altitude climbed, and the total altitude descended, for the route which minimizes these numbers. It does not matter how far she has to walk to achieve this.

Since you do not know what the landscape looks like in between the height curves, you cannot know exactly how much climb and descent she will actually get in practice, but you should calculate the minimum possible under optimal conditions based on what you can deduce from the map.

The map is represented as an $xy$ grid. Alice lives in $(0, 0)$, and Bob lives in $(100\, 000, 0)$. The height curves are represented as polygons, where a polygon cannot intersect itself or another polygon. Furthermore, neither Alice nor Bob lives exactly on a height curve.

\includegraphics[width=0.8\textwidth ]{walk}
Figure 1: Second sample input (compressed).

Input

  • One line with $0 \le N \le 2\, 500$, the number of height curves.

  • One line for each height curve, with integers $1 \le H_ i \le 1\, 000$ being the height of the curve, $3 \le P_ i \le 2\, 000$ the number of vertices in the polygon, and the vertices $x_1, y_1, \ldots , x_{P i}, y_{P i}$ having integral values $-300\, 000 \le x_ j, y_ j \le 300\, 000$.

There will be no more than $100\, 000$ polygon vertices in total in all the height curves.

Output

One line with two numbers: the total altitude climbed and the total altitude descended.

Sample Input 1 Sample Output 1
2
20 3 10 10 0 -10 -10 10
25 3 20 20 0 -20 -20 20
5 0
Sample Input 2 Sample Output 2
3
100 4 -1 1 1 1 1 -1 -1 -1
300 8 -2 2 2 2 2 -2 5 -2 5 1 6 1 6 -3 -2 -3
50 8 3 3 100001 3 100001 -1 7 -1 7 2 4 2 4 -1 3 -1
200 250