Question

Best Restaurant

In order to become the best restaurant of the area, Issac(The Owner) wants to make as many of his customers happy.

There are N customers C0, C1,. . Cn-1 seating in a circular manner and ith of the N customers has dish Di in front of them.

The ith customer (Ci) will be happy if the dish i is in front of customer C(i+1)%N or Ci or C(i-1)%N

To maximise the happiness Issac can rotate the table anticlockwise so that the dish which was in front of customer Ci is now in front of customer C(i+1)%N

Calculate the maximum happiness that Issac can achieve.

There are N customers C0, C1,. . Cn-1 seating in a circular manner and ith of the N customers has dish Di in front of them.

The ith customer (Ci) will be happy if the dish i is in front of customer C(i+1)%N or Ci or C(i-1)%N

To maximise the happiness Issac can rotate the table anticlockwise so that the dish which was in front of customer Ci is now in front of customer C(i+1)%N

Calculate the maximum happiness that Issac can achieve.

Input

The first line of the input contains a single integer N

The second line contains N integers D0, D1,. . Dn-1 representing the initial arrangement of the dishes.

Constraints:

3 <= N <= 2 x 105

0 <= Ci <= N-1. All Ci are distinct.

0 <= Di <= N-1. All Di are distinct.

All values are integers.

The second line contains N integers D0, D1,. . Dn-1 representing the initial arrangement of the dishes.

Constraints:

3 <= N <= 2 x 105

0 <= Ci <= N-1. All Ci are distinct.

0 <= Di <= N-1. All Di are distinct.

All values are integers.

Output

Output the maximum happiness that is possible.

Example

Sample Input 1:

4

1 2 0 3

Sample Output 1:

4

Explanation 1:

Initial arrangement - > 1 2 0 3

Final arrangement - > 3 1 2 0

Person 0 is happy because Dish 0 is in front of Person 3 (=(0−1)mod4).

Person 1 is happy because Dish 1 is in front of Person 1 (=1).

Person 2 is happy because Dish 2 is in front of Person 2 (=2).

Person 3 is happy because Dish 3 is in front of Person 0 (=(3+1)mod4).

Sample Input 2:

3

0 1 2

Sample Output 2:

3

Sample Input 3:

10

3 9 6 1 7 2 8 0 5 4

Sample Output 3:

5

4

1 2 0 3

Sample Output 1:

4

Explanation 1:

Initial arrangement - > 1 2 0 3

Final arrangement - > 3 1 2 0

Person 0 is happy because Dish 0 is in front of Person 3 (=(0−1)mod4).

Person 1 is happy because Dish 1 is in front of Person 1 (=1).

Person 2 is happy because Dish 2 is in front of Person 2 (=2).

Person 3 is happy because Dish 3 is in front of Person 0 (=(3+1)mod4).

Sample Input 2:

3

0 1 2

Sample Output 2:

3

Sample Input 3:

10

3 9 6 1 7 2 8 0 5 4

Sample Output 3:

5