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.

Sample Input 1

4
0011
0101

Sample Output 1

4

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

Sample Input 2

1
0
0

Sample Output 2

0

Sample Input 3

8
00110011
10101010

Sample Output 3

10