101854: [AtCoder]ABC185 E - Sequence Matching

Problem Statement

We have an integer sequence $A$ of length $N$ and an integer sequence $B$ of length $M$.
Takahashi will make a new sequence $A'$ by removing some elements (possibly zero or all) from $A$ and concatenating the remaining elements.
Similarly, he will make another new sequence $B'$ by removing some elements (possibly zero or all) from $B$ and concatenating the remaining elements.
Here, he will remove elements so that $|A'| = |B'|$. ($|s|$ denotes the length of $s$ for a sequence $s$.)
Let $x$ be the total number of elements removed from $A$ and $B$, and $y$ be the number of integers $i$ such that $1 \le i \le |A'|$ and ${A'}_i \neq {B'}_i$. Print the minimium possible value of $x + y$.

Constraints

• $1 \le N, M \le 1000$
• $1 \le A_i, B_i \le 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1 \hspace{7pt} A_2 \hspace{7pt} A_3 \hspace{5pt} \dots \hspace{5pt} A_N$
$B_1 \hspace{7pt} B_2 \hspace{7pt} B_3 \hspace{5pt} \dots \hspace{5pt} B_M$

Output

Print the minimum possible value of $x + y$.

Sample Input 1

4 3
1 2 1 3
1 3 1

Sample Output 1

2

If we make $A'$ by removing $A_4$ from $A$, and $B'$ by removing nothing from $B$, $x$ will be $1$.
Here, there is just one integer $i$ such that $1 \le i \le |A'|$ and ${A'}_i \neq {B'}_i$: $i = 2$, so $y$ will be $1$, and $x + y$ will be $2$, which is the minimum possible value.

Sample Input 2

4 6
1 3 2 4
1 5 2 6 4 3

Sample Output 2

3

If we remove nothing from $A$ and remove $B_4, B_6$ from $B$, we have $x = 2, y = 1$, and $x + y = 3$, which is the minimum possible value.

Sample Input 3

5 5
1 1 1 1 1
2 2 2 2 2

Sample Output 3

5

It is allowed to remove nothing from both $A$ and $B$.