Given a binary string $S$ consisting of characters 0, 1, and ?. In one operation, you can:

• Change the character 0 to 1.
• Change the character ? to 0 or 1.
• Swap two characters.

Determine the minimum number of operations required to transform the string $S$ into a binary string $T$.

Input

• The first line contains the string $S$.
• The second line contains the string $T$.

Output

• Print an integer representing the minimum number of operations. It is guaranteed that the answer exists.

Constraints

• $1 \le |S| \le 300$.

Sample test

Input:

0?1?
1001

Output:

3