As a radio engineer at the Balanced Audio Podcast © your job is to deliver an equal listening experience at all times. You did a poll among the listeners and they are especially concerned about fluctuations in loudness. To resolve this you bought a transformer to equalise the audio, but alas, its software got corrupted during transport.
Your job is to rewrite the equalising software. As input the transformer gets $$$n$$$ amplitudes $$$a_1, \ldots, a_n$$$, with an average perceived loudness of $$$\frac{1}{n}\sum_{i=1}^n a_i^2$$$. The output should contain the same amplitudes, but renormalised by some constant positive factor, such that the average perceived loudness is $$$x$$$. There is one exception: total silence should always be preserved.
The input consists of:
Output one line containing $$$n$$$ numbers, the renormalised amplitudes with an average perceived loudness of $$$x$$$.
Your answers should have an absolute or relative error of at most $$$10^{-6}$$$.
5 6 0 1 -2 3 -4
0 1 -2 3 -4
4 1 1 3 3 7
0.242535625 0.7276068751 0.7276068751 1.697749375
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