CF638D Three-dimensional Turtle Super Computer

A super computer has been built in the Turtle Academy of Sciences. The computer consists of $ n·m·k $ CPUs. The architecture was the paralellepiped of size $ n×m×k $ , split into $ 1×1×1 $ cells, each cell contains exactly one CPU. Thus, each CPU can be simultaneously identified as a group of three numbers from the layer number from $ 1 $ to $ n $ , the line number from $ 1 $ to $ m $ and the column number from $ 1 $ to $ k $ . In the process of the Super Computer's work the CPUs can send each other messages by the famous turtle scheme: CPU $ (x,y,z) $ can send messages to CPUs $ (x+1,y,z) $ , $ (x,y+1,z) $ and $ (x,y,z+1) $ (of course, if they exist), there is no feedback, that is, CPUs $ (x+1,y,z) $ , $ (x,y+1,z) $ and $ (x,y,z+1) $ cannot send messages to CPU $ (x,y,z) $ . Over time some CPUs broke down and stopped working. Such CPUs cannot send messages, receive messages or serve as intermediates in transmitting messages. We will say that CPU $ (a,b,c) $ controls CPU $ (d,e,f) $ , if there is a chain of CPUs $ (x_{i},y_{i},z_{i}) $ , such that $ (x_{1}=a,y_{1}=b,z_{1}=c) $ , $ (x_{p}=d,y_{p}=e,z_{p}=f) $ (here and below $ p $ is the length of the chain) and the CPU in the chain with number $ i $ ( $ i<p $ ) can send messages to CPU $ i+1 $ . Turtles are quite concerned about the denial-proofness of the system of communication between the remaining CPUs. For that they want to know the number of critical CPUs. A CPU $ (x,y,z) $ is critical, if turning it off will disrupt some control, that is, if there are two distinctive from $ (x,y,z) $ CPUs: $ (a,b,c) $ and $ (d,e,f) $ , such that $ (a,b,c) $ controls $ (d,e,f) $ before $ (x,y,z) $ is turned off and stopped controlling it after the turning off.

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In the first sample the whole first layer of CPUs is malfunctional. In the second layer when CPU $ (2,1,2) $ turns off, it disrupts the control by CPU $ (2,1,3) $ over CPU $ (2,1,1) $ , and when CPU $ (2,2,2) $ is turned off, it disrupts the control over CPU $ (2,2,3) $ by CPU $ (2,2,1) $ . In the second sample all processors except for the corner ones are critical. In the third sample there is not a single processor controlling another processor, so the answer is $ 0 $ .