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 $B$.