시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

한동이는 경상도내를 돌아다니면서 열심히 일하는 영업사원이다. 예전에는 자기가 원하는 도시만 골라서 다닐 수 있었지만 시대가 바뀌어서 이제 그렇게는 하지 못하게 되었다. 시대가 바뀜에 따라, 한동이는 회사에서 돌아야 할 도시의 목록을 받고, 그 목록대로 도시를 여행한다. 회사에서 주는 여행지 목록은 정말 안타깝게도 최적화되어 있지가 않다. 여행을 떠나기 전에 한동이는 모든 도시를 방문하는데 걸리는 최소의 시간을 알고싶어하는데, 한동이는 경영학과라 컴퓨터를 하지 못 하기 때문에 여러분이 한동이를 도와주자.

포항 시내의 도시들은 1부터 n까지 번호 지어져 있다. 한동이는 항상 포항시청에서 여행을 시작하고, 포항시청의 번호는 항상 1번이다. 모든 도시들은 양방향 도로로 연결되어있는데 한 도시에서 바로 길이 이어져있는 다른 도시로 이동하는데는 항상 1의 시간이 걸린다. 포항시청에서는 어떤 도시든지 갈 수 있다. 또한 포항의 도로는 굉장히 잘 되어있어서 도로끼리 사이클을 만들지 않는다.

여러분의 목표는 한동이가 모든 도시를 방문하는데 걸리는 최소의 시간을 출력하는 것이다.

입력

입력의 첫 줄에는 포항에 있는 도시의 숫자 n이 주어진다. 1 ≤ n ≤ 30,000. 

다음 n-1줄에는 도시를 잇는 도로가 주어진다. 각 줄에는 정수 a와 b가 주어진다. 이는 a도시와 b도시를 잇는 도로가 존재한다는 의미이다. (1 ≤ a,b ≤ n; a≠b)

n+1번째 줄에는 정수 m이 주어지는데, 이는 한동이가 방문해야 할 도시의 숫자를 의미한다. 1 ≤ m ≤ 5,000 그 후 m개의 줄에는 한 줄에 하나씩 한동이가 방문해야 할 도시의 숫자가 순서대로 주어진다.

출력

첫 줄에 한동이가 방문해야 할 모든 도시를 방문 할 수 있는 최소 시간을 출력한다.

예제 입력 1

5
1 2
1 5
3 5
4 5
4
1
3
2
5

예제 출력 1

7
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In past times travelling salesmen could choose on their own towns they wanted to visit and order to do so, but those times are now gone forever. From the time the Central Controlling Office for Travelling Salesmen was established every salesman gets from the Office a list of towns to visit and the order of his tour. As it usually happens with central offices, the imposed order of visiting towns has not much in common with an optimal order. Before leaving for his tour Byteasar would like to know at least how much time it will take him to visit all the towns. It is your task to compute this.<\/p>\r\n\r\n<p>The towns of Byteotia are numbered from 1 to n. The capital of Byteotia has the number 1, and this is the place Byteasar starts on his journey from. The towns are connected by a network of two-way roads. A trip between two towns directly connected by a road always takes 1 unit of time. From the capital one can reach any other Byteotian town. 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