Two Chessboards

Two $N \times N$ chessboards each have $N$ rooks on them. A rook can attack another rook in the same row or the same column of the same board.

Swap rooks between the two boards so that no rook on either board attacks another rook.

A swap works as follows. Write a square in row $r$ and column $c$ as $(r, c)$. If the rook at $(a,b)$ on board 1 is swapped with the rook at $(c,d)$ on board 2, then board 1 gets a rook at $(c,d)$, board 2 gets a rook at $(a,b)$, and the two rooks at their original squares are removed.

Each square holds at most one rook. So if a square already has a rook where a swapped rook would land, that existing rook cannot be swapped. For example, if board 1 has a rook at $(a,b)$, then the rook at $(a,b)$ on board 2 cannot be swapped with any rook on board 1 except the one at $(a,b)$ on board 1.

What is the minimum number of swaps needed so that no rook on either board can attack another rook?

The first line contains an integer $N$. ($1\leq N\leq 100\ 000$)

The next $N$ lines each contain the row number $x_i$ and the column number $y_i$ of a rook on board 1, separated by a space. ($1\leq x_i,y_i\leq N$)

The next $N$ lines each contain the row number $x_i$ and the column number $y_i$ of a rook on board 2, separated by a space. ($1\leq x_i,y_i\leq N$)

No coordinate is given twice on the same board.

Print the minimum number of swaps needed so that no rook on either board can attack another rook.

If no sequence of swaps can reach a state where no rook on either board can attack another rook, print $-1$ instead.