TW-TST 1995 Problem 2

Given a sequence of eight integers $x_{1},x_{2},...,x_{8}$ in a single operation one replaces these numbers with $|x_{1}-x_{2}|,|x_{2}-x_{3}|,...,|x_{8}-x_{1}|$ . Find all the eight-term sequences of integers which reduce to a sequence with all the terms equal after finitely many single operations.