CF1749A.Cowardly Rooks

There's a chessboard of size $n \times n$ . $m$ rooks are placed on it in such a way that:

• no two rooks occupy the same cell;
• no two rooks attack each other.

A rook attacks all cells that are in its row or column.

Is it possible to move exactly one rook (you can choose which one to move) into a different cell so that no two rooks still attack each other? A rook can move into any cell in its row or column if no other rook stands on its path.

The first line contains a single integer $t$ ( $1 \le t \le 2000$ ) — the number of testcases.

The first line of each testcase contains two integers $n$ and $m$ ( $1 \le n, m \le 8$ ) — the size of the chessboard and the number of the rooks.

The $i$ -th of the next $m$ lines contains two integers $x_i$ and $y_i$ ( $1 \le x_i, y_i \le n$ ) — the position of the $i$ -th rook: $x_i$ is the row and $y_i$ is the column.

No two rooks occupy the same cell. No two rooks attack each other.

For each testcase, print "YES" if it's possible to move exactly one rook into a different cell so that no two rooks still attack each other. Otherwise, print "NO".

In the first testcase, the rooks are in the opposite corners of a $2 \times 2$ board. Each of them has a move into a neighbouring corner, but moving there means getting attacked by another rook.

In the second testcase, there's a single rook in a middle of a $3 \times 3$ board. It has $4$ valid moves, and every move is fine because there's no other rook to attack it.