Problem Description

Given \( n \) non-intersecting polygons, where each polygon's edges are parallel or perpendicular to the coordinate axes. Define the depth \( d_i \) of polygon \( i \) as \( \max\{d_j\} + 1 \), where polygon \( j \) contains polygon \( i \). Specifically, if a polygon is not contained by any other polygon, its depth is \( 1 \). Determine the depth of the polygon with the maximum depth.

Input Format

The first line contains a positive integer \( n \).

Each subsequent line describes a polygon. First, an even number \( k \) \( (4 \leqslant k \leqslant 10000) \) is given, followed by \( k \) integers: \( x_1, x_2, \cdots, x_k \) \( (0 \leqslant x_i \leqslant 10^8) \). These coordinates are \( (x_1, x_2), (x_3, x_2), (x_3, x_4), (x_5, x_4), \cdots, (x_{k-1}, x_k), (x_1, x_k) \), forming the polygon in a counterclockwise order.

Output Format

Output a single integer representing the maximum depth.

Sample Input and Output

Sample Input #1

3
4 0 0 10 10
4 3 4 6 8
4 1 1 2 2

Sample Output #1

2

Sample Input #2

6
4 1 0 17 12
16 10 4 16 11 2 4 8 2 3 3 2 1 16 3 15 2
8 8 10 3 5 12 8 11 6
6 10 9 15 10 9 7
4 4 6 7 9
4 6 8 5 7

Sample Output #2

5

Notes

For \( 100\% \) of the data, \( n \leqslant 40000, \sum k \leqslant 200000 \).

见题面 Input 部分

见题面 Output 部分