#1207AGTC

Let x and y be two strings over some finite alphabet A. We would like to transform x into y allowing only operations given below:

• Deletion: a letter in x is missing in y at a corresponding position.
• Insertion: a letter in y is missing in x at a corresponding position.
• Change: letters at corresponding positions are distinct

Certainly, we would like to minimize the number of all possible operations.

Illustration

A   G   T   A   A   G   T   *   A   G   G   C
|   |   |               |       |       |   |
A   G   T   *   C   *   T   G   A   C   G   C

• Deletion: * in the bottom line
• Insertion: * in the top line
• Change: when the letters at the top and bottom are distinct

This tells us that to transform x = AGTCTGACGC into y = AGTAAGTAGGC we could be required to perform 5 operations (2 changes, 2 deletions and 1 insertion).

If we want to minimize the number operations, we should do it like

A   G   T   A   A   G   T   A   G   G   C
|   |   |           |       |       |   |
A   G   T   C   T   G   *   A   C   G   C

and 4 moves would be required (3 changes and 1 deletion).

In this problem we would always consider strings x and y to be fixed, such that the number of letters in x is m and the number of letters in y is n where n ≥ m.

Assign 1 as the cost of an operation performed. Otherwise, assign 0 if there is no operation performed.

Write a program that would minimize the number of possible operations to transform any string x into a string y.

Input

Input contains several datasets. Each dataset consists of the strings x and y prefixed by their respective lengths, one in each line.

Output

For each dataset, an integer representing the minimum number of possible operations to transform any string x into a string y.

10 AGTCTGACGC
11 AGTAAGTAGGC

4