Yuki is a careless girl and she is designing mazes.

A maze consists of \(n\) rooms and \(m\) passageways. The rooms are numbered from \(1\) to \(n\) and all the passageways are **unidirectional**, that is the passageway from room \(u\) to \(v\) **cannot** be passed from room \(v\) to \(u\). Besides, to avoid tourists being trapped in the maze, all the rooms should be connected, that is for every pair of integers \((u,v)\) such that \(1\leq u,v\leq n,u\neq v\), there should be a path from room \(u\) to room \(v\).

Yuki has already designed a "maze". However, due to her carelessness, you need to check whether the maze she designed is a **real** maze, that is all the rooms in her maze are **connected**.