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 $B$.

> $N$ > $P_0$ $P_1$ $\cdots$ $P_{N-1}$ > $Q_0$ $Q_1$ $\cdots$ $Q_{N-1}$

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

- $1 \leq N \leq 100000$ - $0 \leq P_i \leq N-1$ - $P_0,P_1,\cdots,P_{N-1}$ 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.