Bishwock

Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states:

XX   XX   .X   X.  
X.   .X   XX   XX  

Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square.

Vasya has a board with 2× n squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.

Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.

Input

The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols "0" (zero) that denote the empty squares and symbols "X" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed 100.

Output

Output a single integer — the maximum amount of bishwocks that can be placed onto the given board.

Examples

Input

00 00

Output

1

Input

00X00X0XXX0 0XXX0X00X00

Output

4

Input

0X0X0 0X0X0

Output

0

Input

0XXX0 00000

Output

2

inputFormat

Input

The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols "0" (zero) that denote the empty squares and symbols "X" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed 100.

outputFormat

Output

Output a single integer — the maximum amount of bishwocks that can be placed onto the given board.

Examples

Input

00 00

Output

1

Input

00X00X0XXX0 0XXX0X00X00

Output

4

Input

0X0X0 0X0X0

Output

0

Input

0XXX0 00000

Output

2

样例

0XXX0
00000

2

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