ÖMO 2007 Problem 2

Find all tuples $(x_1,x_2,x_3,x_4,x_5,x_6)$ of non-negative integers, such that the following system of equations holds: $x_1x_2(1-x_3)=x_4x_5 x_2x_3(1-x_4)=x_5x_6 x_3x_4(1-x_5)=x_6x_1 x_4x_5(1-x_6)=x_1x_2 x_5x_6(1-x_1)=x_2x_3 x_6x_1(1-x_2)=x_3x_4$