import heapq as hq import sys input = sys.stdin.readline INF = 10 ** 18 """ Union-Find from : https://github.com/customaddone/beginPython/blob/master/cgi-bin/library/unionfind/unionfind.py ref : https://algo-logic.info/union-find-tree/ """ class UnionFind(): #Uni = UnionFind(n) のようにする def __init__(self, n): self.n = n self.parents = [-1] * n #xの親(親がいないときは自身の番号を返す) def find(self, x): if self.parents[x] < 0: return x else: self.parents[x] = self.find(self.parents[x]) return self.parents[x] #xとyを関係付ける def union(self, x, y): x = self.find(x) y = self.find(y) if x == y: return if self.parents[x] > self.parents[y]: x, y = y, x # if x > y: # よりrootのインデックスが小さい方が親 # x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x #xとyが同じ組に属するかどうか def same(self, x, y): return self.find(x) == self.find(y) #xが属する組の大きさ def size(self, x): return -self.parents[self.find(x)] #xが属する組の全要素をリストとして取得 def members(self, x): root = self.find(x) return [i for i in range(self.n) if self.find(i) == root] #Union-Find木の根に当たる要素全てをリストとして取得 def roots(self): return [i for i, x in enumerate(self.parents) if x < 0] #Union-Find木の根とそれに属する組の全要素 def all_group_members(self): return {r: self.members(r) for r in self.roots()} N,M,K = map(int, input().split()) if not(2 <= N <= 10 ** 4 and N - 1 <= M <= min(2 * 10 ** 4, N * (N - 1) // 2) and 1 <= K <= min(12, M)): exit(1) R = [i - 1 for i in map(int, input().split())] S = set(R) if any(not(1 <= i + 1 <= M) for i in S): exit(1) if not(len(S) == len(R) == K): exit(1) edge = [[] for _ in [0] * M] route = [[] for _ in [0] * N] abst = set([]) uni = UnionFind(N) for i in range(M): a,b,c = map(int, input().split()) if((a,b) in abst): exit(1) abst.add((a,b)); abst.add((b,a)) if not(1 <= a <= N and 1 <= b <= N and a != b and 1 <= c <= 10 ** 4): exit(1) a -= 1; b -= 1 uni.union(a,b) route[a].append((b,c)) route[b].append((a,c)) if(i in S): edge[i] = [a,b,c] if not(uni.size(0) == N): exit(1) def dijkstra(s,route): que = [(0,s)] dist = [INF] * N while(que): d,v = hq.heappop(que) if(dist[v] < INF): continue dist[v] = d for nv,nd in route[v]: hq.heappush(que,(d + nd, nv)) return dist dist = [[] for _ in [0] * N] T = set([0,N - 1]) for i in S: T.add(edge[i][0]) T.add(edge[i][1]) for i in T: dist[i] = dijkstra(i,route) dp = [[[INF] * 2 for _ in [0] * K] for _ in [0] * (1 << K)] for i in range(K): for j in range(2): dp[1 << i][i][j] = dist[0][edge[R[i]][j ^ 1]] + edge[R[i]][2] for bit in range(1, 1 << K): for s in range(K): if not(bit & (1 << s)): continue for t in range(K): if(bit & (1 << t)): continue b = bit | (1 << t); c = edge[R[t]][2] for x in range(2): for y in range(2): p = edge[R[s]][x]; q = edge[R[t]][y ^ 1] d = dp[bit][s][x] + dist[p][q] + c if(dp[b][t][y] > d): dp[b][t][y] = d ans = INF for i in range(K): for j in range(2): d = dp[-1][i][j] + dist[edge[R[i]][j]][N - 1] if(ans > d): ans = d print(ans)