Given an ~a \times b~ rectangle, your task is to cut it into squares. On each move you can select a rectangle and cut it into two rectangles in such a way that all side lengths remain integers. What is the minimum possible number of moves?

Input

• The only input line has two integers ~a~ and ~b~.

Output

• Print one integer: the minimum number of moves.

Constraints

• ~1 \le a,b \le 500~

Example Input

3 5

Example Output

3