Constraint Relations: Acclerations of Blocks in System

ritwik06
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The system is given in the picture. I want to know the relation between the acclerations of each block.

My attempt:
suppose if the body in the middle moves up by x. the string will get loose by 2x. therefore, if a1, a2, a3 are the acclerations. -2*a2=a1+a3
am i correct?
 

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Sounds right to me.
 
But the thing is that my calculated accelerations of the three blocks differ from the answer in my book. Can you please just tell me the acclerations of each block? (in order that I may know if I am right)
 
Show what you did and I'll check it out.
 
Thanks for the help. I actaully was solving with the wrong sign.
 
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