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.

小阿特约姆决定学习概率论。他找到一本习题丰富的书，现在希望你能帮他解决其中一道题目。

考虑两个骰子。每次投掷时，每个骰子均显示一个从 $1$ 到 $n$（含端点）的整数。对每个骰子，各面朝上的概率均已知（显然，这些概率之和为 $1$），且两个骰子的概率分布可能不同。

我们同时投掷这两个骰子，然后计算 $\max(a,\,b)$ 和 $\min(a,\,b)$ 的值，其中 $a$ 表示第一个骰子的投掷结果，$b$ 表示第二个骰子的投掷结果。你并不知道每个骰子上各个具体数值对应的确切概率分布，但你知道 $\max(a,\,b)$ 和 $\min(a,\,b)$ 的概率分布。也就是说，对每个从 $1$ 到 $n$ 的整数 $x$，你已知 $\max(a,\,b) = x$ 的概率，以及 $\min(a,\,b) = x$ 的概率。请找出任意一组满足条件的、两个骰子各自面上数值的概率分布。题目保证输入数据是自洽的，即至少存在一个解。

First line contains the integer n (1 ≤ n ≤ 100 000) — 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.

第一行包含整数 $n$（$1 \leq n \leq 100\,000$）—— 表示两个骰子各自可能取到的不同数值的个数。

第二行包含一个由 $n$ 个实数组成的数组，每个实数最多保留小数点后 8 位——该数组表示 $\max(a,\,b)$ 的概率分布，其中第 $i$ 个值等于 $\max(a,\,b) = i$ 的概率。保证该数组所有元素之和为 1。第三行以相同格式给出 $\min(a,\,b)$ 的概率分布。

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.

第一行输出关于 a 的概率分布描述，第二行输出关于 b 的概率分布描述。

若对于每个 max(a, b) 和 min(a, b) 的概率分布值，其与输入中给定值的差均不超过 $10^{-6}$，则答案视为正确。此外，所有概率值应为非负数，且其总和与 1 的差值不应超过 $10^{-6}$。