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

• \(1 \leq a,b \leq 500\)

Example

Sample input

3 5

Sample output

3