Less than 3

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.

Examples

Input

4 0011 0101

Output

4

Input

1 0 0

Output

0

Input

8 00110011 10101010

Output

10

inputFormat

Input

Input is given from Standard Input in the following format:

N s t

outputFormat

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.

Examples

Input

4 0011 0101

Output

4

Input

1 0 0

Output

0

Input

8 00110011 10101010

Output

10

样例

1
0
0

0