Give a $2*2$ 01-matrix A, which can deal with the following $2$ kinds of transformation:
**Rotation transformation**: clockwise rotation. Move $A(i, j)$ to $A(j,1- i)$
**Replace**: replace the matrix $A$ into matrix $B$.
Given a tree, there is a matrix $A_i$ in every node of the tree, Baby Ming likes to play the matrix in the tree. Every time, Baby Ming choose two node $a, b$ in the tree and change all the matrixes in the path from $a$ to $b$ into matrix $B$ by the above two kinds of transformation.
Suppose rotation transformation takes $2$ seconds every time while replace takes $10$. Baby Ming wants to know the minimum time it costs.
Input
In the first line contains a single positive integer $T$, indicating number of test case.
For every test case:
In the first line there is a number $n$ to show the tree has $n$ nodes.
In the next $n-1$ lines, each line contains $2$ integer $a, b$, indicate the edge between $a$ and $b$.
In the next $n*2$ lines, each line contains $2$ numbers $01$, indicate the matrix $A_i$ in the node $i$.
Input a positive integer $q$, indicate the number of queries.
For each query:
In the first line there is two positive numbers $a, b$.
In the second line and third line there is a $2*2$ 01-matrix B, It represents select two nodes $a, b$, transform all the matrix $A_i$ in the path from $a$ to $b$ into matrix $B$
**(matrix $A_i, B$ consist by $2$ zeros and $2$ ones)**
$1 \leq T \leq 30, 1 < n \leq 20000, 1 \leq q \leq 20000, 1 \leq a, b \leq n$
Output
For each of $Q$ operation, print one line to show minimum time the change needed.
