import java.util.Random; // Random number module in Java

/* Author: Atul Prakash. */
/*
 * This code simulates a well-known game that is played as follows. 
 * You put in some 
 * unknown number of red and blue balls in a bag. You then take out two 
 * balls at random from the bag. If they are both the same color, you toss 
 * both of them and put in a blue ball  back in the bag (assume 
 * infinite supply of extra balls). If they are 
 * different colors, you toss the blue one aside and put in the red ball
 * back in the bag.

 * You keep repeating the above process till only one ball is left. Note 
 * that the # of balls reduces by one at every round, so eventually, you 
 * will end up with one ball.

 * If the final color of the ball is red, Reds win. Else Blues win
 * The goal is to discover a loop invariant that helps us precisely 
 * predict who will win, based on the initial counts of the balls.
*/



enum Color {RED, BLUE};
class BallGame {
	public static void main(String[] args) {
		// initialize the # of balls in the bag for each color
		// to random values
		//  between 0 and 99. Could be any random integers.
	
		Random r = new Random();
		int redcount = r.nextInt(100); 
		int bluecount = r.nextInt(100);
		System.out.println("redcount = " + redcount);
		System.out.println("bluecount = " + bluecount);
		/* as long as the number of balls in the bag is more than 1,
		 * keep taking out two balls. If they are both of the same
		 * color, toss them away and put a blue ball back in the bag. 
		 * If different, then toss away the blue ball. Put the red
		 * one back 
		 */
		Color firstballcolor;
		Color secondballcolor;
		assert (redcount >= 0 && bluecount >= 0);
		while (redcount + bluecount > 1) {
			// pick a value between 0 and the # of balls. If
			// the value is less than redcount, assume that a red
			// ball was taken out. Else, a blue ball.
			int pickone = r.nextInt(redcount + bluecount);
			if (pickone < redcount) { // red ball taken out
				firstballcolor = Color.RED;
				redcount--;
			} else { // blue ball taken out
				firstballcolor = Color.BLUE;
				bluecount--;
			}
			int picktwo = r.nextInt(redcount + bluecount);
			if (picktwo < redcount) { // red ball taken out
				secondballcolor = Color.RED;
				redcount--;
			} else { // blue ball taken out
				secondballcolor = Color.BLUE;
				bluecount--;
			}
			if (firstballcolor == secondballcolor) {
				// same colors. Put back a blue one
				bluecount++;
			} else { // different colors. Put back the red one.
				redcount++;
			}
		} // end of loop.
		// Exactly one ball must remain at the end. 
		assert ((redcount == 1 && bluecount == 0) || 
			(redcount == 0 && bluecount == 1));


		// Declare the winner.
		if (redcount == 1) {
			System.out.println("Reds win");
		} else {
			System.out.println("Blues win");
		}
	}

}