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Changing a list with the information of other


Good morning

I have the following (possibly very simple) problem.
I have a list, created using a Table

{{0, 1}, {1, w}, {2, 1 + w}, {3, 1 + 2 w}, {4, 2}, {5, 2 w}, {6, 2 + 2 w}, {7, 2 + w}}.

Then, using another Table, I created the list

{1, 1 + w, 2 + w, 2 w, 2, 2 + 2 w, 1 + 2 w, w}

Note that all these elements appear always in second place, in the ordered pairs of the first list. What I want is an instruction that allows to replace all these elements by the ones that appear first in the ordered pairs above. That is, I would like to replace this list by the new one

{0, 2, 7, 5, 4, 6, 3, 1}.

As you may guess this is only of interest when the lists are very big (with thousands of elements).

Thank you



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