Road Network Connectivity

You are given a directed graph representing a network of intersections and one-way roads. The graph has n intersections numbered from 1 to n and m directed roads. Your task is to determine whether it is possible to visit every intersection starting from intersection 1 and, additionally, whether every intersection can reach intersection 1. In other words, the graph should be strongly connected with respect to node 1.

The input guarantees that the nodes are indexed from 1 to n. Use breadth-first search (BFS) or depth-first search (DFS) to check connectivity in the original graph and its reverse.

Note: When presenting a formula, use LaTeX formatting. For instance, the number of intersections and roads can be represented as \( n \) and \( m \), respectively.

inputFormat

The input is given from standard input in the following format:

 n m
 a1 b1
 a2 b2
 ...
 am bm

Where the first line contains two integers \( n \) and \( m \) — the number of intersections and the number of roads. Each of the next \( m \) lines contains two integers \( a_i \) and \( b_i \), indicating a directed road from intersection \( a_i \) to intersection \( b_i \).

outputFormat

Output a single line to standard output containing either YES if it is possible to travel from intersection 1 to every other intersection and back, or NO otherwise.

4 4
1 2
2 3
3 4
4 1

YES