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What factors must one consider choosing an NN structure?

Suppose we have a classification problem and we wish to solve the problem by Neural Network. What factors must one consider choosing an NN structure? e.g Feed Forward, Recurrent and other available ...
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How many layers should a neural network have?

Are there any advantages of having more than 2 hidden layers in a Neural Network? I've seen some places that recommend it, others prove that there is no advantage. Which one is right?