Last Casino

The movie The Last Casino is about a professor who exploits probabilities to beat the casino and win often at blackjack. This has terrified Lucy, the owner of the new casino in town, The Little Epsilon (TLE), so she has banned blackjack in her casino.

To bring people into TLE, she has invented a new game called bins-and-balls. Two players, Alice and Britney, play it. There are $n$ bins, and each bin is red, black, or white. There are $B$ balls. Each ball is placed independently and at random into one of the $n$ bins, and every bin is equally likely. If all of the balls end up in red bins, Alice wins. If there is at least one ball in a white bin and at least one ball in a black bin, Britney wins. In every other case, the casino wins.

The government has placed these restrictions on the game:

1. The casino can choose the number of bins.
2. The casino must choose how many balls to use (an integer from 1 to $10^6$ inclusive) and how to color the bins, so that the absolute difference between the probability of Alice winning and the probability of Britney winning is minimized.
3. If more than one choice satisfies restriction 2, the casino must choose the one that minimizes the casino's probability of winning.

Restriction 2 keeps the game fair for the players. Restriction 3 keeps the casino from gaining too large an advantage. Lucy has already decided on the number of bins. You must decide the color of each bin and the number of balls so that the government's restrictions are met.

The input consists of a single line with one integer $n$ ($1 \le n \le 10^6$), the number of bins the casino will use.

Print the number of balls to use. On the next line, print the number of bins to color black and the number of bins to color white. The remaining bins are colored red. If there are multiple solutions, any one of them is accepted.