Poilog who got a 4.0 grade in mathematical analysis, invented a game called Poilogtopia. Today he invites his friend Vltava, a master in game theory, to play Poilogtopia with him.
There are )
castles on the map of Poilogtopia, the 
of which has gained )
coins. The castles are initially connected with )
undirected weighted roads, the of which connects castle )
with weight )
. At the beginning of the game, Poilog is given )
additional roads, in which he can choose the first )
roads to construct. Constructing the road would cost Poilog )
coins, which must be taken into account.
After
Poilog determines the map,
Vltava can choose a set of castles as his territory and take over the coin accounts of these castles. Yet for all the roads which connect one castle inside
Vltava's territory and the other castle outside,
Poilog can collect
coins as toll fees. Both players' final scores equals to the coins they own at last, and both would like to maximize the value of his own score minus his opponent's score.
Simply putting, if
Poilog chooses the first
roads and then
Vltava chooses a castle set
as his territory,
Vltava's score
Poilog's score %5C%3B%20or%20%5C%3B(x_j%20%5Cnotin%20S%2C%20y_j%20%5Cin%20S)%5D)
Vltava would like to maximize 
, while Poilog would like to minimize .
Smart as Vltava and Poilog are, they would both choose the optimal strategy. As you are a huge fan of the two experts, please compute the final result .
The first line contains three integers 
.
The second line contains
integers
.
The third line contains
integers
.
The next 
lines each contain three integers 
, each describing a weighted road. Notice that the first 
roads are initially placed on the map, and the following roads are additional roads which Poilog would choose to add with certain costs.
It is guaranteed that for all roads, no two roads connect the same set of castles.
Note that the castles do not have to be connected.
