Task Completion with Dependency Constraints

You are given n tasks labelled from 0 to n-1 and a list of d dependency pairs. Each dependency is described by two integers a and b which means that task b cannot be started until task a is completed. Determine if it is possible to complete all tasks while satisfying these dependency constraints.

This problem can be solved using topological sorting. In a dependency graph, if a valid topological ordering exists then all tasks can be completed. In other words, if the graph does not contain any cycle, the answer is YES; otherwise, the answer is NO.

The mathematical condition can be stated as follows: A valid ordering exists if and only if \( |\text{sorted_order}| = n \), where \( n \) is the total number of tasks.

inputFormat

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

n d
a1 b1
a2 b2
... 
ad bd

Here, the first line contains two integers n (the number of tasks) and d (the number of dependency pairs). Each of the following d lines contains two integers a and b representing a dependency: task b depends on task a.

outputFormat

The output is a single line to the standard output: YES if it is possible to complete all tasks following the dependency constraints, or NO if it is not possible.

4 4
1 0
2 0
3 1
3 2

YES