Kian is trapped in a room and cannot see anything. We know that the floor of this room is an $n \times n$ square tiled with square tiles. Each tile has a unique number, and the tiles are numbered in a spiral pattern. For example, the figure below shows the numbering of the tiles for $n = 5$.

Kian knows there is a candle in the room and wants to reach it, but since the room is dark, he cannot see anything. He asks you to guide him on how much he needs to move in each direction to reach the candle, given the number of the tile Kian is standing on and the number of the tile the candle is on.

Input

The only line of input contains three space-separated integers $n$, $s$, and $d$, representing the side length of the room, the tile number Kian is standing on, and the tile number where the candle is located, respectively.

Output

On the first line of output, print a number and a character separated by a space. The number is the distance Kian must move horizontally, and the character is L if he must move to the left, or R if he must move to the right. If Kian does not need to move horizontally, this line is omitted.

On the second line of output, print a number and a character separated by a space. The number is the distance Kian must move vertically, and the character is U if he must move up, or D if he must move down. If Kian does not need to move vertically, this line is omitted.

Constraints

• $1 \le n \le 2000$
• $1 \le s \neq d \le n^2$

Examples

Input 1

5 1 25

Output 1

2 R
2 U

Input 2

5 3 22

Output 2

3 U

Input 3

15 67 24

Output 3

3 R
8 U