Rectangle Cutting

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

Output

3