Strongly connected components

A directed graph $G = (V, A)$ consists of a set of vertices $V$ and a set of arcs $A$ . An arc is an ordered pair $(u, v)$ , where $u, v \in V$ . A path from a vertex $v_{i_1}$ to a vertex $v_{i_k}$ is a sequence of arcs $(v_{i_1}, v_{1_2}), (v_{i_2}, v_{i_3}), \dots, (v_{i_{k-1}}, v_{i_k})$ . By definition, there is always a path from every vertex to itself.

Consider the following equivalence relation: two vertices $u$ and $v$ of $G$ are related if, and only if, there is a path from $u$ to $v$ and a path from $v$ to $u$ . Every equivalence class resulting from this definition is called a strongly connected component of $G$ .

Given a directed graph, calculate how many strongly connected components it has.

Input

Input begins with the number of cases. Each case consists of the number of vertices $n$ and the number of arcs $m$ , followed by $m$ pairs $(u, v)$ . Vertices are numbered starting at 0. There are not repeated arcs, nor self-arcs $(v, v)$ . Assume $1 \le n \le 10^4$ .

Output

For every graph, print its number of strongly connected components.

Problem information

Author: Xavier Martínez

Generation: 2026-01-25T11:53:46.637Z