When John and Brus were high school students, they liked to investigate integer sequences.
Once, John wrote down a sequence containing only positive integers.
Brus wanted to change the sequence so it contained only "lucky" numbers.
Brus considered a number lucky only if it was evenly divisible by 4 or 7 (or both).
(Note that 0 is a lucky number by this definition.)
For each number x in John's sequence, Brus did the following.
If x was lucky, he did not change it.
Otherwise, he replaced x with a lucky number y (not necessarily positive) such that the absolute value of the difference between x and y was minimal.
If there were two such values for y, he chose the smaller one.
You are given an int sequence containing John's original sequence.
Return the sequence after Brus made all his changes.