The pulleys move

The pulley block system is shown in the figure. All strings and pulleys are ideal. The relation between a1,a2,a3a_{1},a_{2} , a_{3} is given as xa1+ya2+za3=0xa_{1}+ya_{2}+za_{3}=0 where x,y,zx,y,z are co prime integers. Find x+y+z|x+y+z|.

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