The edit distance between two strings is the minimum number of operations required to transform one string into the other.

The allowed operations are:

• Add one character to the string.
• Remove one character from the string.
• Replace one character in the string.

For example, the edit distance between LOVE and MOVIE is 2, because you can first replace L with M, and then add I.

Your task is to calculate the edit distance between two strings.

Input

The first input line has a string that contains n characters between A–Z.

The second input line has a string that contains m characters between A–Z.

Output

Print one integer: the edit distance between the strings.

Constraints

• 1 \le n,m \le 5000

Example

Input:

LOVE
MOVIE

Output:

2