题目描述
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.
Examples
Input
4
2 1 3 0
0 2 3 1
Output
3
Input
10
0 4 5 3 7 8 2 1 9 6
3 8 5 6 4 0 2 1 7 9
Output
8
Input
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
Output
28
输入格式
见题面
输出格式
见题面