You are given $n$ points in a plane. You would like choose a number $k$ and partition the points into disjoint sets $P_1, P_2, \ldots, P_k$.

The score of your partition will be as follows. Let $P$ be a point set, and let $h(P)$ denote the convex hull of the point set. Let $A(x)$ denote the area of polygon $x$. Your score is equal to $\sum_{i} A(h(P_i))$. You would like to maximize this score. Note that the convex hulls are allowed to overlap.

Note that the convex hull can contain 1 or 2 points, in which case, its area is zero.

Test Data Generation

First, a number $n$ is chosen randomly from $20$ to $100$.
Next, the coordinates of each point is chosen uniformly at random from $0$ to $10^3$. Note that it is possible two points can coincide.
Note that the sample will not appear in the main tests, it is only to show the input/output format.

Input Format

The first line will contain a single integer $n$ ($20 \leq n \leq 100$).
The next $n$ lines will contain two integers $x_i, y_i$ ($0 \leq x_i, y_i \leq 10^3$), denoting a point with coordinates $(x_i, y_i)$. Note that points are not guaranteed to be distinct.

Output Format

On the first line, output a single integer $k$ ($1 \leq k \leq n$), the number of sets in your partition.
On the next $k$ lines, print the elements of the partition. On the $i$-th of these $k$ lines, first print the integer $l_i$ ($1 \leq l_i \leq n$), and then $l_i$ indices of points forming the $i$-th set. Points are numbered starting from $1$. Each index from $1$ to $n$ must appear in exactly one set.