Minimum Swaps

You are given arrays $A$ and $B$. Each one holds the numbers $1$ through $N$ exactly once, but the two orders may differ.

One operation swaps two numbers inside $A$.

Find the minimum number of operations that makes $A$ equal to $B$.

• The first line contains $N$, the size of arrays $A$ and $B$. ($1 \le N \le 1{,}000{,}000$)
• The second line contains the elements of $A$, separated by single spaces.
• The third line contains the elements of $B$, separated by single spaces.

Print on the first line the minimum number of operations that makes $A$ equal to $B$.

For $A = [1, 4, 2, 3]$ and $B = [4, 3, 1, 2]$, swapping $1$ with $4$, then $2$ with $3$, then $1$ with $3$ turns $A$ into $B$ in three operations.

For $A = [3, 6, 4, 7, 1, 2, 5]$ and $B = [4, 3, 7, 6, 1, 5, 2]$, swapping $2$ with $5$, then $3$ with $6$, then $4$ with $6$, then $6$ with $7$ takes four operations.