There have been reports of cheating in the ICPC (Interdisciplinary Course for Programming and Cooking) at ETH Zürich! After checking all submitted assignments, a list of cheating reports has been made.

Each report is a pair $$$(X, Y)$$$, meaning that the student with legi $$$X$$$ and the student with legi $$$Y$$$ shared some of their homework. For simplicity, we assume that legi are consecutively indexed, starting with $$$1$$$ (if there are $$$5$$$ students taking the course, they will have a legi of $$$1, 2, 3, 4$$$, and $$$5$$$).

The general consensus is that most ETH students follow the code of conduct, and the current hypothesis is that the students can be divided into 2 types:

• Cheaters, who cheat whenever they can and with whoever they can.
• Non-cheaters, who generally don't cheat but might be influenced by cheaters to share some solutions.

Specifically, the hypothesis is that the set $$$V = \{ 1, 2, \dots, N \}$$$ of students can be partitioned into the sets $$$A$$$ and $$$B$$$ such that:

• For any $$$2$$$ students $$$x$$$ and $$$y$$$ in $$$A$$$, a report with the pair $$$(x, y)$$$ or $$$(y, x)$$$ has been made.
• For any $$$2$$$ students $$$x$$$ and $$$y$$$ in $$$B$$$, no report with the pair $$$(x, y)$$$ or $$$(y, x)$$$ has been made.

Your task is to verify if such a division of $$$V$$$ into $$$A$$$ and $$$B$$$ exists.