I am currently designing a simple pneumatic circuit but am having trouble and need some assistance as i am not very familiar with the design of pneumatic systems.

I need to design a system which contains 3 double actuating cylinders. 2 of the cylinders are controlled from an electrically actuated 5/2 solenoid.  I need to use these two solenoids to control the third cylinder. it must be designed without being electrically actuated due to the environment it sits in. The positional chart requirements are below: (- is retracted + is extended)

State 1 = C1 (-)  C2 (-)  C3 (-)

State 2 = C1 (+) C2(-)  C3(+)

State 3 = C1 (-)  C2(+) C3(+) 

The normal resting position for all of the cylinders is retracted as seen in state 1. C1 and C2 will never open at the same time. Any help would be greatly appreciated. see a horrendously drawn schematic of the system below: 

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