Lasers#5161
Never before had special agent Ivan Okhotnichii been so close to failure. It had seemed that getting into a secret laboratory through a ventilation hatch in the ceiling and hacking the computer would be no trouble. However, from above, Ivan noticed that the laboratory was crisscrossed by laser beams. Touching any of them would trigger the alarm system. The -th beam is generated by an emitter located at the point (X_i, Y_i, Z_i) and is directed along the vector (u_i, v_i, w_i). Ivan has determined the numbers X_i and Y_i, and, by analyzing the direction of the beams, has calculated the vectors (u_i, v_i, w_i). However, to plan his next steps, Ivan needs to know the -coordinates of the emitters as well.
Luckily, for some pairs of laser beams, Ivan managed to determine which one is above the other (that is, there exist , , Z_1, and Z_2 such that the point (X, Y, Z_1) belongs to the first beam, the point (X, Y, Z_2) belongs to the second beam, and Z_1 > Z_2). Help Ivan find one possible arrangement of the lasers in space.
The first line contains the number of lasers (1 \le N \le 100). Each of the following lines contains five integers X_i, Y_i, u_i, v_i, and w_i, which describe the -th laser; all these numbers are integers in the range . The next line contains the number of pairs for which their relative positions are known (0 \le M \le 10000). Each of the following lines contains two different integers and , indicating that the -th laser is above the -th laser (1 \le i, j \le N). No laser beam is parallel to the axis, and no two beams lie in the same vertical plane.
Output real numbers, one per line: the coordinates Z_i. Their absolute values should not exceed 10^6. The numbers must be given with the maximum possible precision. At least one arrangement of lasers that satisfies the input data is guaranteed to exist.
Example 1