A10330 | 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 $n$ ( $1<=n<=100000$ ) — the number of different values for both dices.

Second line contains an array consisting of $n$ real values with up to 8 digits after the decimal point — probability distribution for $max(a,b)$ , the $i$ -th of these values equals to the probability that $max(a,b)=i$ . It's guaranteed that the sum of these values for one dice is $1$ . The third line contains the description of the distribution $min(a,b)$ in the same format.

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 $10^{-6}$ .