This is a problem I was given back when I'm training for APIO Vietnam team selection.

"There are n (n ≤ 600) factory that is planned to be built on a line, number from 1 to n. There are m (m ≤ 100000) restriction, each restriction has form uv, meaning that if both factory u and v is built, x_u + 1 = x_v. There are another p (p ≤ 100000) restriction, each restriction has form uv, meaning that if both factory u and v is built, x_u ≤ x_v. (x_i mean coordinate of factory i, if it's going to be built)

Your task is to choose a set of factories to build, and pick an appropriate coordinate for each factory, such that no restriction is violated, and the number of different coordinate is maximum."

I didn't understand the solution to this problem well back then. And now I'm trying to solve this again, but I can't think of any good idea. Can anyone give me a hint? Thanks in advance.

UDP1: Sorry about the mistaken objective. The correct objective is "the number of distinct point", not "factory".