Let B be a width-w balancing network of depth d in a quiescent states. Let n=2d. Prove that if n tokens enter the network on the same wire, pass through the network, and exit, then B will have the...

Let B be a width-w balancing network of depth d in a quiescent states. Let n=2d. Prove that if n tokens enter the network on the same wire, pass through the network, and exit, then B will have the same state after the tokens exit as it did before they entered.