Problem: Snap Dragons II

Want to try solving this problem? You can submit your code online if you log in or register.

Snap Dragons II

Input File: snapin.txt
Output File: snapout.txt
Time Limit: 1 second

Have you ever heard of Melodramia, my friend? It is a land of magic forests and mysterious swamps, of sprinting heroines and dashing heroes. And it is home to two dragons, Rose and Scarlet, who, despite their competitive streak, are the best of friends.

Rose and Scarlet love playing snap tag, a game for two players on an grid. The game goes as follows:

The two dragons start on different squares.
It's Rose's turn first. On her turn she must move to an adjacent square (i.e. she must make one step left, right, up, or down).
It's Scarlet's turn next. On her turn she must move to an adjacent square.
The two dragons continue alternating turns...
...until one dragon lands on the same square as another. When this happens, the dragon who moved last shouts `Snap tag!' and wins the game.

Rose and Scarlet are both snap tag experts and always find a winning strategy if one exists. If it is not possible for either player to gain the upper hand, then the game goes on forever.

In this task, you are given the size of the grid and the starting locations of both dragons. You must write a program to determine how the game ends: Does Rose win? Does Scarlet win? Does the game go on forever?

Input

The input file will contain six space separated integers on a single line, in the format: R C r_ROSE c_ROSE r_SCARLET c_SCARLET where:

R and C are the number of rows and columns in the grid, respectively;
r_ROSE and c_ROSE are the row and column of Rose's starting square (rows are numbered 1 to R from top to bottom; columns are numbered 1 to C from left to right); and
r_SCARLET and c_SCARLET are the row and column of Rose's starting square.

Output

Output should consist of a single upper-case word with no punctuation.

If Rose can guarantee herself a win, output ROSE.
If Scarlet can guarantee herself a win, output SCARLET.
If neither player can guarantee a win, output DRAW.

Sample Input 1

2 3 1 1 2 3

Sample Output 1

ROSE

Explanation

In the first example, Rose can guarantee herself a win if she is clever and cautious.

On her first move, Rose steps to the right. Then, no matter whether Scarlet goes up or left on her turn, Rose can tag her the next turn.

Sample Input 2

5 1 2 1 4 1

Sample Output 2

SCARLET

Explanation

In the second example, Scarlet can guarantee herself a win if she is clever and cautious.

If Rose moves down, then Scarlet will tag her on her very next turn. Otherwise, if Rose moves up, then Scarlet moves up and Rose will be forced to move down next to Scarlet, who will tag her the next turn.

Sample Input 3

15 15 3 5 12 13

Sample Output 3

ROSE

Explanation

In the third example, Rose can guarantee herself a win if she is clever and cautious.

Subtasks & Constraints

For Subtask 1 (25 marks), R = 2 and C = 2. In other words, if your program always produces the correct solution for a 2 by 2 grid, you will receive at least 25 marks for this problem.
For Subtask 2 (25 marks), 1 ≤ R ≤ 100 and C = 1.
For Subtask 3 (40 marks), 1 ≤ R, C ≤ 100.
For Subtask 4 (10 marks), 1 ≤ R, C ≤ 1,000,000,000.