'if we know X, Y, Z and X=A^B,Y=B^C,Z=C^A, can we figure out the value of A,B,C?

If we know X, Y, Z and X=A^B,Y=B^C,Z=C^A, can we figure out the value of A,B,C? what's more, How about one more varible,W for input and D for output? W,X,Y,Z -> A,B,C,D



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