The author of the previous problem is half a psycho, half a freak.
He is well know for his lengthy and weird statements,
although *a few* of his problems are not that hard.
Consider for instance the following adaptation of an old problem of the same author.

The rules of *Snakes and Ladders* (see the board below) are simple:

- Players red and blue start with their counters on cell number 1, and take turns in rolling a six-sided die, with red going first.
- The counter for the current player moves forward the number of cells rolled in the die (e.g., rolling a 5 when on cell 4 takes the counter to 9).
- The goal is to reach the cell 100. An exact roll is
needed: in case of excess, the counter
*bounces*and moves the extra count backwards (e.g., rolling a 5 when on cell 97 takes the counter to 98).

- If the landing cell (after potential bouncing) is the bottom of a ladder, the counter is moved to its top, which will be a higher-numbered cell (e.g., rolling a 1 when on cell 1 takes the counter to 38). Nothing happens when the counter directly lands on a top.
- If the landing cell (after potential bouncing) is the head of a snake, the counter is moved to its tail, which will be a lower-numbered one (e.g., rolling a 3 when on cell 98 takes the counter to 80). Nothing happens when the counter directly lands on a tail.
- If the rolled number was six, the player keeps the turn; otherwise, it passes to the other player (irrespective of whether bouncing, snakes, or ladders were involved).

You must simulate several of these games using pseudo-random numbers. In particular, include the <random> library, and declare a global

mt19937 rng;

variable. Every game will be defined by a seed s. Just do

rng.seed(s);

to reset rng before every game. Afterwards, every time that you need the result d of the next rolling of the die, use this code:

unsigned int r = rng(); int d = r%6 + 1;

For instance, with the initial seed 42, we get these values for r: 1608637542, 3421126067, 4083286876, 787846414, …Therefore, the values for d are 1, 6, 5, 5, …In this game, red goes to 2 (and then to 38), blue goes to 7 (and then to 14), blue moves again (he got a 6) and goes to 19, red goes to 43, …, and eventually blue wins.

Input

Input consists of several games,
each one defined by an integer seed s between 1 and 10^{9}.

Output

For each game, print “RED” or “BLUE” depending on the winner.

Public test cases

**Input**

42 1 999999999 1000000000

**Output**

BLUE BLUE RED BLUE

Information

- Author
- Edgar Gonzàlez
- Language
- English
- Official solutions
- C++
- User solutions
- C++