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There are cities in Byteland (numbered from to ), connected by bidirectional roads. The king of Byteland is not very generous, so there are only roads, but they connect the cities in such a way that it is possible to travel from each city to any other city.
One day, a traveller Byterider arrived in the city number . He was planning to make a journey starting in the city and visiting on his way cities , , ..., (not necessarily in this order) - the numbers are all different and they are also different from . Byterider - like every traveller - has only a limited amount of money, so he would like to visit all the cities that he has planned to visit using the shortest possible path (starting in the city ). A path is one road or a sequence of roads, where every next road begins in the city where the previous one ends. Help Byterider to determine the length of the shortest path for his journey.
The first line of the standard input contains two integers and separated by a single space (, ), is the number of cities in Byteland and is the number of the first city on Byterider's path. Each of the following lines contains the description of one road in Byteland. Line (for ) contains three integers , and separated by single spaces (, ), and are the cities connected by the road, and is the length of the road. Line contains one integer - the number of cities which Byterider would like to visit (). The next line contains different integers separated by single spaces - the numbers of the cities that Byterider would like to visit (, ).
The first and only line of the standard output should contain exactly one integer: the length of the shortest path for Byterider's journey.
For the input data:
4 2 1 2 1 4 2 2 2 3 3 2 1 3
the correct result is:
Task author: Jakub Radoszewski.