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1626. Interfering Segment

Time limit: 5.0 second
Memory limit: 64 MB
A triangulation of a polygon P is its partition into non-overlapping triangles whose union is P. In this problem, we put some restrictions on triangulations: all vertices of a triangle must coincide with some vertices of P and no vertex of P must lie on a boundary of a triangle (except for triangle's vertices). We call a segment interfering with a triangulation if it intersects (or touches) a boundary of some triangle of the triangulation.
Your task is, given the polygon P and segment S, to determine whether there exists a triangulation that S does not interfere with. Since it is well-known that all simple polygons can be triangulated, you have only to output the triangle that belongs to some triangulation and contains S strictly inside.


In the first line there is N (3 ≤ N ≤ 800) — the number of vertices in P.
The following N lines contain pairs of integers (XiYi) — the coordinates of vertices of P in the order of traversal. All points are distinct, and no three consecutive points lie on the same line.
The last line contain four integers Xs, Ys, Xf, Yf — the coordinates of endpoints of S.
All coordinates do not exceed 104 by absolute value. The segment S is guaranteed to lie strictly inside the polygon P. S is also guaranteed to have non-zero length.


If the solution does exist, output the one-based indices of vertices of triangle that belongs to some triangulation and contains S strictly inside. The indices must be output in a single line and separated by single spaces.
If the solution does not exist, output the word "Impossible" in a single line.


0 0
0 3
4 3
1 2 2 2
1 2 3
0 0
2 0
2 3
0 3
1 1 1 2
Problem Source: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.