list_evenlyOdd()--Mr. Guidry is a little odd about even and odd things in his lists. He dosen't like when he has odd values at even indexes, and even values at odd indexes.
This method iterates through a given integer list to remove all items that meet the following criteria: odd indexes with an even value, or even indexes with an odd value.

IMPORTANT NOTE: This method only removes the first item meeting the removal criteria during each pass of the list.

Write a method that will accomplish this and return the corrected list to Mr. Guidry's approval.