A network of size $N$
contains $N$ computers
connected by $N1$ cables,
so that there is exactly $1$ path between any pair of
computers.
The transmission cost between $2$ computers is equal to the square
of the number of cables on the path connecting the $2$ computers.
The transmission cost of a network is equal to the sum of
the transmission cost between all unordered pair of computers.
Given network $A$ with
$N$ computers and network
$B$ with $M$ computers, the administrator wants
to create a new network $C$, by adding exactly one cable
connecting one computer in $A$ and one computer in $B$.
Your task is to minimize the transmission cost of the new
network $C$.
Input

The first line contains an integer $N$  the number of computers in
the network $A$
($1 \leq N \leq 50\,
000$).

In the next $N1$
lines, each line contains two distinct integers
$u$ and $v$, representing a cable
connecting computers $u$ and $v$ in network $A$ ($1 \leq u,v \leq N$).

The next line contains an integer $M$  the number of computers in
the network $B$
($1 \leq M \leq 50\,
000$).

In the next $M1$
lines, each line contains two distinct integers
$u$ and $v$, representing a cable
connecting computers $u$ and $v$ in network $B$ ($1 \leq u,v \leq M$).
It is guaranteed that each network is a tree.
Output
Write in one line the minimum transmission cost of the
resulting network $C$.
Sample clarification
In the first sample below, connecting computer $2$ of network $A$ and computer $1$ of network $B$ will minimize the transmission
cost of the network.
In the second sample below, connecting computer $4$ of network $A$ and computer $1$ of network $B$ will minimize the transmission
cost of the network.
Sample Input 1 
Sample Output 1 
3
1 2
2 3
4
1 2
1 3
1 4

96

Sample Input 2 
Sample Output 2 
7
1 2
2 3
2 4
4 5
5 6
5 7
5
1 2
1 3
1 4
1 5

551
