Problem Statement

The country where Sayaka lives has $N$ cities.
There are also $D$ motorways and $W$ pedestrian roads connecting cities.
The $i$-th motorway allows travel in both directions between cities $a_i$ and $b_i$.
Similarly, the $i$-th pedestrian road allows travel in both directions between cities $c_i$ and $d_i$.

Find the number of pairs of integers $(u,v)\,(1 \le u,v \le N,u \ne v)$ satisfying the following condition.

• It is possible to move from city $u$ to city $v$ by traversing 0 or more motorways and then 0 or more pedestrian roads, in this order.

Input

$N \ D \ W$
$a_1\  b_1$
$\vdots$
$a_{D}\  b_{D}$
$c_1\  d_1$
$\vdots$
$c_{W} \ d_{W}$

• $2 \le N \le 10^5$
• $1 \le D,W \le \min\left(10^5,\frac{N(N-1)}{2}\right)$
• $1 \le a_i < b_i \le N$
• If $i \ne j$, then $(a_i,b_i) \ne (a_j,b_j)$
• $1 \le c_i < d_i \le N$
• If $i \ne j$, then $(c_i,d_i) \ne (c_j,d_j)$
• All inputs are integers

Output

Output the answer.
Print a newline at the end.

Sample

4 2 1
1 2
2 3
2 4

10

10 5 5
1 2
1 3
1 4
2 4
3 7
3 8
2 4
1 3
9 10
1 10

47