E. Reachability from the Capitaltime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere are n cities and m roads in Berland. Each road connects a pair of cities. The roads in Berland are one-way.What is the minimum number of new roads that need to be built to make all the cities reachable from the capital?New roads will also be one-way.InputThe first line of input consists of three integers n, m and s (1 \le n \le 5000, 0 \le m \le 5000, 1 \le s \le n) — the number of cities, the number of roads and the index of the capital. Cities are indexed from 1 to n.The following m lines contain roads: road i is given as a pair of cities u_i, v_i (1 \le u_i, v_i \le n, u_i \ne v_i). For each pair of cities (u, v), there can be at most one road from u to v. Roads in opposite directions between a pair of cities are allowed (i.e. from u to v and from v to u).OutputPrint one integer — the minimum number of extra roads needed to make all the cities reachable from city s. If all the cities are already reachable from s, print 0.ExamplesInput9 9 11 21 32 31 55 66 11 89 87 1Output3Input5 4 51 22 33 44 1Output1NoteThe first example is illustrated by the following:  For example, you can add roads (6, 4), (7, 9), (1, 7) to make all the cities reachable from s = 1.The second example is illustrated by the following:  In this example, you can add any one of the roads (5, 1), (5, 2), (5, 3), (5, 4) to make all the cities reachable from s = 5.
Input9 9 11 21 32 31 55 66 11 89 87 1
Output3
['dfs and similar', 'graphs', 'greedy', '*2000']