You have a zero-indexed array, \(A\), containing positive integers, and a permutation of the indexes for that array, \(D\). You plan to go through \(D\) in order, and mark the corresponding element in \(A\) as deleted. Note that you won't then move elements of \(A\) down after deletion, so elements keep their original indexes throughout this process. For example, consider \(A = \{ 2, 1, 8, 3 \}\) and \(D = \{ 1, 3, 0, 2 \}\).

We start with,

2, 1, 8, 3

Then index 1 is marked as deleted,

2, x, 8, 3

Then index 3,

2, x, 8, x

Then 0,

x, x, 8, x

Finally 2,

x, x, x, x

After which deletion is \(A\) first sorted in monotonically ascending order? In our example, it is sorted after the second deletion, since (ignoring deleted elements) 2, 8 is sorted.

Input Specification

The first line contains a single integer, the size of \(A\) (\(1 \leq |A| \leq 10^5\)). The next line contains \(|A|\) space separated integers in the inclusive range from \(1\) to \(10^9\). The next line also contains \(|A|\) space separated integers, these are the elements of \(D\), and are a permutation of \(\{ 0, 1, \dots , |A|-1 \}\).

Output Specification

Output a single integer. The minimum number of deletions after which \(A\) is sorted.

Sample Input 1

4
2 1 8 3
1 3 0 2

Sample Output 1

2