Hidden triangles

Input

In the first line, the number $N$ is the amount of triangles. Then in $N$ lines triangles are listed in the order they were put to the plane. Each triangle is defined with $6$ integers x_{i1}, y_{i1}, x_{i2}, y_{i2}, x_{i3}, y_{i3}, which are the coordinates of its vertices. All the triangles are not degenerated. Any edge of a triangle has no more than one common point with any edge of another triangle.

Output

Output the amount of visible triangles in the first line. List their numbers in any order in the second line.

Constraints

$1$ ≤ $N$ ≤ $500$

$-1000$ ≤ x_{ij}, y_{ij} ≤ $1000$, for $1$ ≤ $i$ ≤ $N$, $1$ ≤ $j$ ≤ $3$.

Examples