Artificial Neural Network

In 2020, the Seoul Metropolitan Office of Education designated Sunlin Internet High School as a high school specializing in artificial intelligence.

Jeong-hwi decided to write neural network problems to check whether his juniors had received good AI education over the past two years.

An artificial neural network is a net-shaped structure made of several artificial neurons. The $i$-th artificial neuron has weights $W_{i,1}, W_{i,2}, \cdots, W_{i,C_i}$ and a bias $B_i$. When it receives $C_i$ inputs $X_{i,1}, X_{i,2}, \cdots, X_{i,C_i}$, it outputs the following value.

$Y_i = \sum_{k=1}^{C_i} X_{i,k}W_{i,k} + B_i$

The figure below shows the structure of an artificial neuron.

For example, take a neuron with weights $\{3, 1\}$ and bias $2$. If the inputs are $\{1, 2\}$, the output is $1\times3+2\times1+2=7$.

The neural network Jeong-hwi prepared has an input layer, a hidden layer, and an output layer.

The input layer consists of $N$ inputs $A_1, A_2, \cdots, A_N$, and the hidden layer consists of $M$ artificial neurons. The $i$-th hidden neuron takes $A_{P_{i,1}}, A_{P_{i,2}}, \cdots, A_{P_{i,C_i}}$ as inputs and computes its output. The output layer is a single artificial neuron. It takes the outputs of hidden neurons $1, 2, \cdots, M$ in that order as inputs and computes its output. For convenience, the output layer neuron is called the $M+1$-th artificial neuron.

For example, suppose the weights are $W = \{\{1,2\}, \{3,4\}, \{5,6\}, \{10,20,30\}\}$, the biases are $B = \{7, 8, 9, 100\}$, and the hidden neurons take the input layer values at positions $P = \{\{1, 2\}, \{2, 3\}, \{4, 5\}\}$ as inputs. If the input is $A = \{2, 7, 6, 8, 4\}$, the network can be drawn as in the figure below.

Given the structure of a neural network and its input data, write a program that computes the output of the network.

The first line contains three integers $N$, $M$, and $Q$, separated by spaces. $N$ is the size of the input layer, $M$ is the number of hidden neurons, and $Q$ is the number of times the output must be computed. $(1 \leq N,M,Q \leq 2\,000)$

From the second line through the $M$-th line, each line gives one hidden neuron in order. Each line contains the number of inputs $C_i$, the input positions $P_{i,1}, P_{i,2}, \cdots, P_{i,C_i}$, the weights $W_{i,1}, W_{i,2}, \cdots, W_{i,C_i}$, and the bias $B_i$, separated by spaces. ($1 \leq C_i \leq N$, $1 \leq P_{i,j} \leq N$, and the $P_{i,j}$ are distinct for each $i$)

The next line gives the output neuron. It contains the weights $W_{M+1,1}, W_{M+1,2}, \cdots, W_{M+1,M}$ and the bias $B_{M+1}$, separated by spaces. ($1 \leq W_{i,j}, B_i \leq 100$)

Each of the next $Q$ lines contains one set of input data, which is $N$ integers $A_1, A_2, \cdots, A_N$. ($1 \leq A_i \leq 100$)

All input numbers are integers.

Print $Q$ lines. Each line contains the answer for one input.

Python users are recommended to submit with PyPy.

The answer can exceed the range of a 32-bit integer.