Tree Transformation Cost

You are given two weighted rooted trees. For each vertex, the children are ordered from left to right. There are four elementary operations.

1. Growing: for a vertex $x$ with children $y_1, \ldots, y_m$, add a new vertex $z$ and an edge between $x$ and $z$, then insert $z$ at position $k$ of the children list, so the list becomes $y_1, \ldots, y_{k-1}, z, y_k, \ldots, y_m$. The cost is $c_1$ times the weight of the new edge $(x, z)$.

2. Expansion: for a vertex $x$ with children $y_1, \ldots, y_m$, choose an interval $[l, r]$ with $1 \le l \le r \le m$. Add a new vertex $z$ as the parent of $y_l, \ldots, y_r$, and add an edge between $x$ and $z$. The children list of $x$ becomes $y_1, \ldots, y_{l-1}, z, y_{r+1}, \ldots, y_m$, and the children list of $z$ is $y_l, \ldots, y_r$. Each edge $(z, y_i)$ keeps the weight of $(x, y_i)$ from the original tree. The cost is $c_1$ times the weight of the new edge $(x, z)$.

3. Contraction: for a vertex $x$, choose a child $y_k$ whose children list is $z_1, \ldots, z_p$, and contract the edge $(x, y_k)$. Vertex $y_k$ is removed, and the children list of $x$ becomes $y_1, \ldots, y_{k-1}, z_1, \ldots, z_p, y_{k+1}, \ldots, y_m$. Each edge $(x, z_i)$ keeps the weight of $(y_k, z_i)$. The cost is $c_2$ times the weight of the edge $(x, y_k)$ in the original tree.

4. Relabeling: for a vertex $x$ and its child $y$, change the weight of edge $(x, y)$ from $w_1$ to $w_2$. The cost is $c_3 \cdot |w_1 - w_2|$.

An edge $(x, z)$ added by growing or expansion cannot be relabeled. An edge that has been relabeled cannot be contracted.

You want to turn the first tree into the second tree. Output the minimum total cost. Two trees are the same if there is a bijection between their vertices that preserves the root and the order of children, and the weights of corresponding edges match.

The first line contains three integers $c_1$, $c_2$, and $c_3$ ($1 \le c_1, c_2, c_3 \le 10^6$). Then the two trees follow. For each tree, the first line contains $n$, the number of vertices. Each of the next $n$ lines starts with $k$, the number of children, followed by $2k$ integers $c_1, w_1, \ldots, c_k, w_k$ ($0 \le c_i \le 10^6$), which give the children list and the weights of the edges to the children.

The first tree has at most 50 vertices, and the second tree has at most 2000 vertices.

Print the answer.