Polyhedron — Eolymp

Input

The first line contains the number of vertices, $n$ , of the polyhedron. For each $j$ from $1$ to $n$ , the ( $j$ + 1)-th line lists, in ascending order, the vertex numbers that are connected to the $j$ -th vertex by edges.

The following conditions are given:

The polyhedron has no more than $2000$ vertices.
There are no more than $4000$ edges.
Only one face has more than $8$ edges.

Output

Each line should list the vertex numbers of one face of the polyhedron. These lines should be organized in non-decreasing order based on the number of vertices in each face: starting with all $3$ -sided faces, followed by $4$ -sided faces, $5$ -sided faces, and so on.

For faces with the same number of vertices, the lists of vertex numbers $i_{1}$ i_1, $i_{2}$ i_2, $i_{3}$ i_3, … should be sorted first by $i_{1}$ i_1 in non-decreasing order, then by $i_{2}$ i_2 in non-decreasing order for constant $i_{1}$ i_1, and finally by $i_{3}$ i_3 in increasing order for constant $i_{1}$ i_1 and $i_{2}$ i_2.

Examples

Example 1

Loading