Taco's One-Way Street Connectivity

You are given a directed graph representing one-way streets between intersections. The graph has n intersections labelled from 1 to n and m one-way streets. Each street connects two intersections and is given as a directed edge from a to b.

Your task is to determine if it is possible to travel from any intersection to any other intersection. In other words, the graph must be strongly connected. Formally, a directed graph \(G=(V,E)\) is strongly connected if for every pair of vertices \(u,v\in V\) there exists a path from \(u\) to \(v\).

Note that when there is only one intersection (i.e. \(n=1\)), the answer is trivially YES.

Input/Output via standard input and output.

inputFormat

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

n m
a1 b1
a2 b2
... 
am bm

Where:

• n is the number of intersections.
• m is the number of one-way streets.
• Each of the next m lines contains two integers a and b indicating a one-way street from intersection a to intersection b.

outputFormat

Output a single line containing either YES if the graph is strongly connected, or NO otherwise. Output is via standard output.

## sample

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

YES