Practice Coding with the exercise "Tiling by Squares"

Statement

Goal

Given a rectangle of integer sides w and h, find the minimum number of squares with integer sides (the sides' sizes must be natural numbers) needed to fill the rectangle.

Example with w = 11 and h = 13:

 _ _ _ _ _ _ _ _ _ _ _
|       |             |
|   4   |             |
|       |             |
|_ _ _ _|      7      |
|       |             |
|   4   |             |
|       |_ _ _ _ _ _ _|
|_ _ _ _|1|           |
|         |           |
|         |     6     |
|    5    |           |
|         |           |
|_ _ _ _ _|_ _ _ _ _ _|

You can fill it with a minimum of 6 squares so the output should be 6.

Input

Two integers w, h separated by a space.

Output

The minimal number of squares.

Constraints

0 < w, h < 50

Example

Input

6 7

Output

Solve it

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