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* ≤ 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.
none
2
0.25 0.75
0.75 0.25
0.5 0.5 
0.5 0.5 
3
0.125 0.25 0.625
0.625 0.25 0.125
0.25 0.25 0.5 
0.5 0.25 0.25 
10
0.01 0.01 0.01 0.01 0.01 0.1 0.2 0.2 0.4 0.05
1.0 0 0 0 0 0 0 0 0 0
0.010000000000000009 0.010000000000000009 0.010000000000000009 0.009999999999999953 0.010000000000000009 0.10000000000000003 0.2 0.1999999999999999 0.39999999999999825 0.05000000000000182 
1.0 0.0 0.0 0.0 0.0 -1.1102230246251565E-16 1.1102230246251565E-16 0.0 1.9984014443252818E-15 -1.9984014443252818E-15 
10
0 0 0 0 0 0 0 0 0 1.0
1.0 0 0 0 0 0 0 0 0 0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 
1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 
1
1.0
1.0
1.0 
1.0 
2
0.00001 0.99999
0.5 0.5
2.000040002400616E-5 0.999979999599976 
0.4999899995999759 0.5000100004000241 
3
0.1 0.1 0.8
0.6 0.2 0.2
0.20000000000000004 0.07639320225002103 0.7236067977499789 
0.4999999999999999 0.22360679774997905 0.27639320225002106 
8
0.09597231 0.11315755 0.32077119 0.22643005 0.03791746 0.04296694 0.10284494 0.05993956
0.52402769 0.19814245 0.20452881 0.06686995 0.00468254 0.00103306 0.00055506 0.00016044
0.29869999999999886 0.07920000000000116 0.32760000000000133 0.0734999999999989 0.02229999999999943 0.039699999999999847 0.10169999999999968 0.057299989463288625 
0.32130000000000125 0.23209999999999875 0.19769999999999854 0.219800000000001 0.020300000000000762 0.0043000000000001926 0.0017000000000002569 0.002800010536711417 
print("_RANDOM_GUESS_1689348529.3950982")# 1689348529.395118