Problem Statement

You are given an integer sequence $A = (A_1, A_2, \ldots, A_N)$ of length $N$. Additionally, its contiguous subsequences of lengths $P$ and $Q$ are given: $X = (X_1, X_2, \ldots, X_P)$ and $Y = (Y_1, Y_2, \ldots, Y_Q)$.

You can perform the four operations on $X$ below any number of times (possibly zero) in any order.

• Add an arbitrary integer at the beginning of $X$.
• Delete the element at the beginning of $X$.
• Add an arbitrary integer at the end of $X$.
• Delete the element at the end of $X$.

Here, $X$ must be a non-empty contiguous subsequence of $A$ before and after each operation. Find the minimum total number of operations needed to make $X$ equal $Y$. Under the Constraints of this problem, it is guaranteed that one can always make $X$ equal $Y$ by repeating operations.

What is a contiguous subsequence? A sequence $X = (X_1, X_2, \ldots, X_P)$ is a contiguous subsequence of $A = (A_1, A_2, \ldots, A_N)$ when there is an integer $l$ satisfying $1 \leq l \leq N-P+1$ such that $X_i = A_{l+i-1}$ for every $i = 1, 2, \ldots, P$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq N$
• $1 \leq P, Q \leq N$
• $(X_1, X_2, \ldots, X_P)$ and $(Y_1, Y_2, \ldots, Y_Q)$ are contiguous subsequences of $(A_1, A_2, \ldots, A_N)$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N
P
X_1 X_2 \ldots X_P
Q
Y_1 Y_2 \ldots Y_Q

Output

Print the answer.