312. 43 King
Time limit per test: 0.25
second(s)
Memory limit: 65536
kilobytes
input: standard
output: standard
The king of the Quadroland (or was it Triland?..) has died. After four or three days of mourning, his will was declared: all his kingdom was to be divided into four or three parts, one for each son. The kingdom itself can be represented as a quadrangle or a triangle on a plane, with each side associated with one of the sons. After the division is performed, each son should get a quadrangle or a triangle, one of the sides coinciding with his associated side of the original kingdom. The required ratio between areas of their parts is given. You are to perform such a division.
Input
The first line of the input file contains the number
N (3 ≤
N ≤ 4) of sons (equal to the number of sides of the kingdom).
The next
N lines contain the coordinates of the vertices of the kingdom. The vertices are given in either clockwise or counterclockwise order. No two consecutive sides of the kingdom lie on the same line. Each coordinate is an integer not exceeding 100 by its absolute value.
The last, (
N+2)th line contains the required ratio formatted like
K_{1}:K_{2}:...:K_{N}
, where
K_{1} corresponds to the side between 1st and 2nd vertices,
K_{2} — between 2nd and 3rd vertices, etc,
K_{N} — between
Nth and 1st vertices. Each
K_{i} is an integer, 1 ≤
K_{i} ≤ 100.
Output
The first line of the output file should contain the description of the part corresponding to the side between 1st and 2nd vertices, the second line — between 2nd and 3rd vertices, etc.
Each description should consist of the number of vertices in the polygon (3 or 4), followed by their coordinates, in either clockwise or counterclockwise order. Two ends of each side should be some neighbouring vertices of the corresponding polygon. The coordinates can be real numbers; if this is the case, print as many digits after the decimal point as possible.
In case the division is impossible, output 1 on the only line of output.
Example(s)
sample input

sample output

3
0 0
10 0
0 10
4:2:4

3 0 0 10 0 4 4
3 10 0 0 10 4 4
3 0 10 0 0 4 4

sample input

sample output

4
0 0
0 30
100 30
100 0
1:3:1:3

3 0 0 0 30 25.0 15.0
4 0 30 100 30 75.0 15.0 25.0 15.0
3 100 30 100 0 75.0 15.0
4 0 0 100 0 75.0 15.0 25.0 15.0
