A nameless country consists of $$$n$$$ cities connected by $$$m$$$ bidirectional roads, such that it is possible to reach any city from any other.
There are three factions controlling this country: $$$i$$$-th faction occupies some connected set of cities $$$\{a_{i,j}\}$$$. That is, if we leave only the cities controlled by a specific faction, along with the roads between them, there will be a path between any two of them. It is also known that no city is controlled by more than one faction, meaning $$$a_{i,p} \neq a_{j,q}$$$ for $$$i \neq j$$$.
To celebrate the Equinox you need to mark some cities as main tourist attractions for the celebration. For all the factions so be satisfied, these cities along with factions' cities should form a connected set. Formally, it is necessary to choose a set of cities $$$B$$$ such that any two cities from the set $$$S = B \cup \{a_{i,j}\}$$$ are connected by a path that passes only through cities from $$$S$$$.
Of course, the most obvious way is to mark all the cities in the country, but the government will not be satisfied with such a solution. Find a suitable set $$$B$$$ of minimal size.
The first line contains two integers $$$n$$$ and $$$m$$$ — the number of cities and roads in the country ($$$1 \le n, m \le 2 \cdot 10^5$$$).
The next 6 lines describe the factions: two lines for each. The first line of the description of the $$$i$$$-th faction contains integer $$$k_i$$$ — the number of cities that it controls ($$$1 \le k_i \le n - 2$$$). The second line lists $$$k_i$$$ distinct integers $$$a_{i, j}$$$ — the cities controlled by the $$$i$$$-th faction ($$$1 \le a_{i,j} \le n$$$).
It is guaranteed that each number from $$$1$$$ to $$$n$$$ appears among $$$a_{i,j}$$$ no more than once.
In the next $$$m$$$ lines, the $$$i$$$-th line contains two integers $$$u_i$$$ and $$$v_i$$$ — the cities connected by the $$$i$$$-th road ($$$1 \le u_i, v_i \le n$$$).
It is guaranteed that it is possible to reach any city from any other using the given roads.
In the first line, output an integer $$$b$$$ — the minimum number of cities that you need to mark with for celebration. If the factions are already connected and no cities need to be marked, output $$$0$$$.
In the second line, output $$$b$$$ distinct integers from $$$1$$$ to $$$n$$$ — the numbers of these cities. No city controlled by a faction should be marked.
4 31112134 14 24 3
1 4
10 1231 2 324 5161 22 31 34 51 77 88 99 69 107 1010 54 9
3 9 7 10
An illustration for the second example from the statement is provided in the figure below. Suitable answers include cities $$$7$$$, $$$8$$$, $$$9$$$ or $$$7$$$, $$$9$$$, $$$10$$$.
