(10%) Consider a neural network with $n$ layers of fully connected layers, where the first layer is the input layer, the $n$th layer is the output layer, and the rest are hidden layers. The $i$th layer has $P_i$ neurons, where $1 \le i \le n$. Each neuron in the $i$th layer is connected to every neuron in the $(i+1)$th layer, where $1 \le i < n$. Let $w_{j,k}^{i}$ represent the weight of the connection from the $j$th neuron in the $i$th layer to the $k$th neuron in the $(i+1)$th layer. Let $[v_1^i\ v_2^i\ \cdots\ v_{P_i}^i]^T$ be the values of neurons in the $i$th layer, where $1 \le i \le n$. Then, we can obtain $v_k^{i+1} = \sum_{j=1}^{P_i} w_{j,k}^{i} v_j^{i}$, where $1 \le k \le P_{i+1}$.

Given that $\langle P_1, P_2, P_3, P_4, P_5, P_6 \rangle = \langle 10, 6, 12, 5, 50, 3 \rangle$, we want to achieve the result from the input layer to the output layer in the fastest possible way. Please determine the minimum number of multiplications required for this neural network.