Two Permutations

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

inputFormat

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}

outputFormat

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

样例

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