A feed$-$forward neural network $($shown above$)$ has four input nodes, $5$ nodes in the first hidden layer, $10$ nodes in the second hidden layer, and three output nodes. How many weights does this neural network $1$ contain in total? Suppose that we increase the number of nodes in the first hidden layer to $20.$ How many weights does this neural network $2$ contain? What about a neural network $3$ that has three hidden layers with $5$ nodes in each? $($Input and output layers unchanged.$)$

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