Score : $1400$ points

Problem Statement

You are given strings $s$ and $t$, both of length $N$. $s$ and $t$ consist of 0 and 1. Additionally, in these strings, the same character never occurs three or more times in a row.

You can modify $s$ by repeatedly performing the following operation:

• Choose an index $i$ ($1 \leq i \leq N$) freely and invert the $i$-th character in $s$ (that is, replace 0 with 1, and 1 with 0), under the condition that the same character would not occur three or more times in a row in $s$ after the operation.

Your objective is to make $s$ equal to $t$. Find the minimum number of operations required.

Constraints

• $1 \leq N \leq 5000$
• The lengths of $s$ and $t$ are both $N$.
• $s$ and $t$ consists of 0 and 1.
• In $s$ and $t$, the same character never occurs three or more times in a row.

Input

Input is given from Standard Input in the following format:

$N$

$s$

$t$

Output

Find the minimum number of operations required to make $s$ equal to $t$. It can be proved that the objective is always achievable in a finite number of operations.

4
0011
0101

4

One possible solution is 0011 → 1011 → 1001 → 1101 → 0101.

1
0
0

0

8
00110011
10101010

10