Edit Distance

• Time limit: 1.00 s
• Memory limit: 512 MB

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