CF707B.Bakery

普及/提高-

通过率:0%

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题目描述

Masha wants to open her own bakery and bake muffins in one of the nn cities numbered from 11 to nn . There are mm bidirectional roads, each of whose connects some pair of cities.

To bake muffins in her bakery, Masha needs to establish flour supply from some storage. There are only kk storages, located in different cities numbered a1,a2,...,aka_{1},a_{2},...,a_{k} .

Unforunately the law of the country Masha lives in prohibits opening bakery in any of the cities which has storage located in it. She can open it only in one of another nkn-k cities, and, of course, flour delivery should be paid — for every kilometer of path between storage and bakery Masha should pay 11 ruble.

Formally, Masha will pay xx roubles, if she will open the bakery in some city bb ( aiba_{i}≠b for every 1<=i<=k1<=i<=k ) and choose a storage in some city ss ( s=ajs=a_{j} for some 1<=j<=k1<=j<=k ) and bb and ss are connected by some path of roads of summary length xx (if there are more than one path, Masha is able to choose which of them should be used).

Masha is very thrifty and rational. She is interested in a city, where she can open her bakery (and choose one of kk storages and one of the paths between city with bakery and city with storage) and pay minimum possible amount of rubles for flour delivery. Please help Masha find this amount.

输入格式

The first line of the input contains three integers nn , mm and kk ( 1<=n,m<=1051<=n,m<=10^{5} , 0<=k<=n0<=k<=n ) — the number of cities in country Masha lives in, the number of roads between them and the number of flour storages respectively.

Then mm lines follow. Each of them contains three integers uu , vv and ll ( 1<=u,v<=n1<=u,v<=n , 1<=l<=1091<=l<=10^{9} , uvu≠v ) meaning that there is a road between cities uu and vv of length of ll kilometers .

If k>0 , then the last line of the input contains kk distinct integers a1,a2,...,aka_{1},a_{2},...,a_{k} ( 1<=ai<=n1<=a_{i}<=n ) — the number of cities having flour storage located in. If k=0k=0 then this line is not presented in the input.

输出格式

Print the minimum possible amount of rubles Masha should pay for flour delivery in the only line.

If the bakery can not be opened (while satisfying conditions) in any of the nn cities, print 1-1 in the only line.

输入输出样例

  • 输入#1

    5 4 2
    1 2 5
    1 2 3
    2 3 4
    1 4 10
    1 5
    

    输出#1

    3
  • 输入#2

    3 1 1
    1 2 3
    3
    

    输出#2

    -1

说明/提示

Image illustrates the first sample case. Cities with storage located in and the road representing the answer are darkened.

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