CF641D Little Artem and Random Variable

Little Artyom decided to study probability theory. He found a book with a lot of nice exercises and now wants you to help him with one of them. Consider two dices. When thrown each dice shows some integer from $ 1 $ to $ n $ inclusive. For each dice the probability of each outcome is given (of course, their sum is $ 1 $ ), and different dices may have different probability distributions. We throw both dices simultaneously and then calculate values $ max(a,b) $ and $ min(a,b) $ , where $ a $ is equal to the outcome of the first dice, while $ b $ is equal to the outcome of the second dice. You don't know the probability distributions for particular values on each dice, but you know the probability distributions for $ max(a,b) $ and $ min(a,b) $ . That is, for each $ x $ from $ 1 $ to $ n $ you know the probability that $ max(a,b) $ would be equal to $ x $ and the probability that $ min(a,b) $ would be equal to $ x $ . Find any valid probability distribution for values on the dices. It's guaranteed that the input data is consistent, that is, at least one solution exists.

First line contains the integer $ n $ ( $ 1

Output two descriptions of the probability distribution for $ a $ on the first line and for $ b $ on the second line. The answer will be considered correct if each value of max( $ a,b $ ) and min( $ a,b $ ) probability distribution values does not differ by more than $ 10^{-6} $ from ones given in input. Also, probabilities should be non-negative and their sums should differ from $ 1 $ by no more than $ 10^{-6} $ .