In 2037, a detachment of robots landed on Mars to create a research base, one of which went to collect information about the area of deployment. At the moment, due to the failure of some nodes, the robot urgently needs to return to the place of laying the future base.
The surface of Mars in the landing area can be conditionally represented as a plane with a coordinate system introduced on it, such that the base is at the point (0, 0). The robot stopped at the point (x
0, y
0). It can move in four directions:
x "R" — to the right, while the x-coordinate of the robot increases by 1;
x "L" — to the left, while the x-coordinate of the robot decreases by 1;
x "U" — up, while the y-coordinate of the robot increases by 1;
x "D" — down, while the y-coordinate of the robot decreases by 1.
Due to a malfunction, the robot cannot make two consecutive movements in the same direction.
Help the robot return to base. The robot must make no more than 10,000 movements, otherwise it is discharged and will not reach the base!
Input
The only line of the input contains two integers x0 and y0 — initial coordinates of the robot (−1000 ≤ x0, y0 ≤ 1000).
Imprint
In the first line print an integer not greater than 10000 — the number of operations that the robot must do. In the second line print the operations themselves. Each operation is defined by a single letter:
right — "R" left — "L", up — "U", down — "D" Characters must be printed without spaces between them.
Examples
| # |
Input |
Output |
| 1 |
2 1 |
5
DLULD |
Remark
You are not required to output the shortest route. For example, in the above example, the shortest
the route consists of 3 movements: left, down, left.
Example test illustration:
