【CodeForces 707B】Bakery（暴力）



B. Bakery

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Masha wants to open her own bakery and bake muffins in one of the n cities numbered from 1 to n. There are m 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 onlyk storages, located in different cities numbereda₁, a₂, ..., 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 anothern - k cities, and, of course, flour delivery should be paid — for every kilometer of path between storage and bakery Masha should pay1 ruble.

Formally, Masha will pay x roubles, if she will open the bakery in some cityb (a_i ≠ b for every1 ≤ i ≤ k) and choose a storage in some citys (s = a_j for some1 ≤ j ≤ k) and b and s are connected by some path of roads of summary lengthx (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 ofk 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.

Input

The first line of the input contains three integers n,m and k (1 ≤ n, m ≤ 10⁵,0 ≤ 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 m lines follow. Each of them contains three integersu, v andl (1 ≤ u, v ≤ n,1 ≤ l ≤ 10⁹,u ≠ v) meaning that there is a road between citiesu and v of length ofl kilometers .

If k > 0, then the last line of the input containsk distinct integers a₁, a₂, ..., a_k (1 ≤ a_i ≤ n) — the number of cities having flour storage located in. Ifk = 0 then this line is not presented in the input.

Output

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 n cities, print  - 1 in the only line.

Examples

Input

5 4 21 2 51 2 32 3 41 4 101 5

Output

3

Input

3 1 11 2 33

Output

-1

Note

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

题目大意：有n个城市，m条城市间的双向路，在k个城市上建立仓库，找一个没有仓库的城市使它到其中一个仓库的距离最小

思路：解一定是与仓库直接相连的，暴力一下。思路很简单，写法挺神奇的，值得记下来

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#define manx 100005#define INF 0x3f3f3f3fusing namespace std;int main(){    int n,m,k,x;    int u[manx]={0},v[manx]={0},l[manx]={0};    bool f[manx];    memset(f,true,sizeof(f));    scanf("%d%d%d",&n,&m,&k);    for (int i=0; i<m; i++)        scanf("%d%d%d",&u[i],&v[i],&l[i]);    for (int i=0; i<k; i++){        scanf("%d",&x);        f[x]=false;    }    int ans=INF;    for (int i=0; i<m; i++){        if(!f[u[i]] && f[v[i]] || f[u[i]] && !f[v[i]])            ans=min(ans,l[i]);    }    if(ans==INF) printf("-1\n");    else printf("%d\n",ans);    return 0;}