Strongly Connected Components (SCC) Analysis

You are given a directed graph with N nodes and M edges. Your task is to compute two values:

• The number of strongly connected components (SCCs) in the graph.
• The size of the largest SCC.

A strongly connected component is a maximal set of vertices where every vertex is reachable from every other vertex in the same set via directed paths. In other words, for a directed graph \(G=(V,E)\), a subset \(S \subseteq V\) is strongly connected if for every pair \(u,v \in S\), there exists a path from \(u\) to \(v\) and a path from \(v\) to \(u\).

Input/Output through standard input/output.

inputFormat

The input is given from standard input and has the following format:

N M
u1 v1
u2 v2
...
 uM vM

Where:

• N is the number of nodes. The nodes are numbered from 1 to N.
• M is the number of directed edges.
• Each of the next M lines contains two integers u and v representing a directed edge from u to v.

outputFormat

Print two integers separated by a space on a single line:

• The number of strongly connected components (SCCs) in the graph.
• The size of the largest SCC.

## sample

5 5
1 2
2 3
3 1
4 5
5 4

2 3