Score : $1600$ points

Problem Statement

Snuke has permutations $(P_0,P_1,\cdots,P_{N-1})$ and $(Q_0,Q_1,\cdots,Q_{N-1})$ of $(0,1,\cdots,N-1)$.

Now, he will make new permutations $A$ and $B$ of $(0,1,\cdots,N-1)$, under the following conditions:

• For each $i$ ($0 \leq i \leq N-1$), $A_i$ should be $i$ or $P_i$.
• For each $i$ ($0 \leq i \leq N-1$), $B_i$ should be $i$ or $Q_i$.

Let us define the distance of permutations $A$ and $B$ as the number of indices $i$ such that $A_i \neq B_i$. Find the maximum possible distance of $A$ and $B$.

Constraints

• $1 \leq N \leq 100000$
• $0 \leq P_i \leq N-1$
• $P_0,P_1,\cdots,P_{N-1}$ are all different.
• $0 \leq Q_i \leq N-1$
• $Q_0,Q_1,\cdots,Q_{N-1}$ are all different.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$P_0$ $P_1$ $\cdots$ $P_{N-1}$

$Q_0$ $Q_1$ $\cdots$ $Q_{N-1}$

Output

Print the maximum possible distance of $A$ and $B$.

4
2 1 3 0
0 2 3 1

3

For example, if we make $A=(0,1,2,3)$ and $B=(0,2,3,1)$, the distance will be $3$, which is the maximum result possible.

10
0 4 5 3 7 8 2 1 9 6
3 8 5 6 4 0 2 1 7 9

8

32
22 31 30 29 7 17 16 3 14 9 19 11 2 5 10 1 25 18 15 24 20 0 12 21 27 4 26 28 8 6 23 13
22 3 2 7 17 9 16 4 14 8 19 26 28 5 10 1 25 18 15 13 11 0 12 23 21 20 29 24 27 6 30 31

28