# Catch The Bus

Computer Science Level pending

The National University of Singapore is built on a hill, so even if the distance from A to B seems short from the map, walking over the steep ladder is very exhausting. Fortunately, there's a shuttle bus service.

Suppose that NUS has $$N$$ buildings and $$E$$ bidirectional roads. A shuttle bus starts moving from building X to building Y (the detailed path will be given). At the same time, Chris starts walking from building A and wants to go to building B. Chris is as fast as the shuttle bus, but walking $$k$$ meters requires $$k$$ amount of energy (in Joules) while no energy is spent if he travels by a shuttle bus. What is the minimum amount of energy will Chris need to arrive at his destination?

Input File

Details and Assumptions

• Chris walks as fast as the shuttle bus.
• Chris can choose to wait at a building to hop onto a bus; no energy is spent in this process.
• Chris can choose to drop by at any building the bus went through.
• Chris can choose not to hop onto the bus.
• The bus will not travel a building more than once.
• Moving to any buildings is possible.

Input Format

The first line consists of two integers $$N$$, $$E$$ - the number of buildings and the number of bidirectional roads.
The next $$E$$ lines each contains 3 integers $$u, v, t$$ describing a bidirectional road connecting building $$u$$ and $$v$$ of length $$t$$.
The next line contains an integer $$M$$, the number of buildings the shuttle bus go through.
The next line contains $$M$$ integers, describing the path of the shuttle bus in that order.
The last line contains two integers $$A$$ and $$B$$, the starting building and the destination respectively.

• $$N$$ and $$E$$ is as large as 82500 and 110000 respectively.
• The length of the road does not exceed 100.
• $$M$$ is as large as 1000.

Sample Input

 1 2 3 4 5 6 7 8 9 5 5 0 1 1 1 2 1 2 3 1 4 0 1 0 3 100 3 4 0 3 1 3

Sample Output

 1 1

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