Convex hull of the 3D - 3

Input

The first line contains the number $n$ (4 \leq n \leq 100). The following $n$ lines each contain three numbers — the coordinates of the points. All coordinates are integers and do not exceed $500$ in absolute value.

Output

Print, in the first line, the number of faces $m$. In the next $m$ lines, output the description of the faces: the number of vertices and the indices of the points in the original set. The points are numbered in the order in which they are given in the input file. Within each face, the points must be listed in counterclockwise order relative to the outer normal of the face.

Examples