import sys,bisect,string,math,time,functools,random,fractions from heapq import heappush,heappop,heapify from collections import deque,defaultdict,Counter from itertools import permutations,combinations,groupby rep=range def Golf():n,*t=map(int,open(0).read().split()) def I():return int(input()) def S_():return input() def IS():return input().split() def LS():return [i for i in input().split()] def LI():return [int(i) for i in input().split()] def LI_():return [int(i)-1 for i in input().split()] def NI(n):return [int(input()) for i in range(n)] def NI_(n):return [int(input())-1 for i in range(n)] def StoLI():return [ord(i)-97 for i in input()] def ItoS(n):return chr(n+97) def LtoS(ls):return ''.join([chr(i+97) for i in ls]) def RA():return map(int,open(0).read().split()) def GI(V,E,ls=None,Directed=False,index=1): org_inp=[];g=[[] for i in range(V)] FromStdin=True if ls==None else False for i in range(E): if FromStdin: inp=LI() org_inp.append(inp) else: inp=ls[i] if len(inp)==2: a,b=inp;c=1 else: a,b,c=inp if index==1:a-=1;b-=1 aa=(a,c);bb=(b,c);g[a].append(bb) if not Directed:g[b].append(aa) return g,org_inp def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1): #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage mp=[boundary]*(w+2);found={} for i in range(h): s=input() for char in search: if char in s: found[char]=((i+1)*(w+2)+s.index(char)+1) mp_def[char]=mp_def[replacement_of_found] mp+=[boundary]+[mp_def[j] for j in s]+[boundary] mp+=[boundary]*(w+2) return h+2,w+2,mp,found def TI(n):return GI(n,n-1) def accum(ls): rt=[0] for i in ls:rt+=[rt[-1]+i] return rt def bit_combination(n,base=2): rt=[] for tb in range(base**n):s=[tb//(base**bt)%base for bt in range(n)];rt+=[s] return rt def gcd(x,y): if y==0:return x if x%y==0:return y while x%y!=0:x,y=y,x%y return y def show(*inp,end='\n'): if show_flg:print(*inp,end=end) YN=['YES','NO'];Yn=['Yes','No'] mo=10**9+7 inf=float('inf') FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb)) l_alp=string.ascii_lowercase #sys.setrecursionlimit(10**7) read=sys.stdin.buffer.read readline=sys.stdin.buffer.readline input=lambda: sys.stdin.readline().rstrip() class Tree: def __init__(self,inp_size=None,ls=None,init=True,index=1): self.LCA_init_stat=False self.ETtable=[] if init: if ls==None: self.stdin(inp_size,index=index) else: self.size=len(ls)+1 self.edges,_=GI(self.size,self.size-1,ls,index=index) return def stdin(self,inp_size=None,index=1): if inp_size==None: self.size=int(input()) else: self.size=inp_size self.edges,_=GI(self.size,self.size-1,index=index) return def listin(self,ls,index=0): self.size=len(ls)+1 self.edges,_=GI(self.size,self.size-1,ls,index=index) return def dfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0): q=deque([x]) v=[None]*self.size v[x]=root_v while q: c=q.pop() for nb,d in self.edges[c]: if v[nb]==None: q.append(nb) v[nb]=func(c,v[c],nb,d) return v def bfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0): q=deque([x]) v=[None]*self.size v[x]=root_v while q: c=q.popleft() for nb,d in self.edges[c]: if v[nb]==None: q.append(nb) v[nb]=func(c,v[c],nb,d) return v def parent(self,x): return self.dfs(0,func=lambda pr,prv,nx,dist:pr,root_v=-1) def topological_sort(self,x): # return topological sort of the tree tps=[] q=deque([x]) v=[None]*self.size v[x]=0 while q: c=q.popleft() tps.append(c) for nb,d in self.edges[c]: if v[nb]==None: q.append(nb) v[nb]=0 return tps def EulerTour(self,x): q=deque() q.append(x) self.depth=[None]*self.size self.depth[x]=0 self.ETtable=[] self.ETdepth=[] self.ETin=[-1]*self.size self.ETout=[-1]*self.size cnt=0 while q: c=q.pop() if c<0: ce=~c else: ce=c for nb,d in self.edges[ce]: if self.depth[nb]==None: q.append(~ce) q.append(nb) self.depth[nb]=self.depth[ce]+1 self.ETtable.append(ce) self.ETdepth.append(self.depth[ce]) if self.ETin[ce]==-1: self.ETin[ce]=cnt else: self.ETout[ce]=cnt cnt+=1 return def LCA_init(self,root): self.EulerTour(root) self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf) #self.st=SegTree(self.size*2-1,self.ETdepth,function=min,ide=inf) self.LCA_init_stat=True return def LCA(self,root,x,y): if self.LCA_init_stat==False: self.LCA_init(root) xin,xout=self.ETin[x],self.ETout[x] yin,yout=self.ETin[y],self.ETout[y] a=min(xin,yin) b=max(xout,yout,xin,yin) id_of_min_dep_in_et=self.st.query_id(a,b+1) return self.ETtable[id_of_min_dep_in_et] def __str__(self): return str(self.edges) def show(self): if all([all([d==1 for nd,d in edge]) for edge in self.edges]): print( [[nd for nd,d in edge] for edge in self.edges] ) else: print(self) class SparseTable: # O(N log N) for init, O(1) for query(l,r) def __init__(self,ls,init_func=min,init_idl=float('inf')): self.func=init_func self.idl=init_idl self.size=len(ls) self.N0=self.size.bit_length() self.table=[ls[:]] self.index=[list(range(self.size))] self.lg=[0]*(self.size+1) for i in range(2,self.size+1): self.lg[i]=self.lg[i>>1]+1 for i in range(self.N0): tmp=[self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) for j in range(self.size)] tmp_id=[self.index[i][j] if self.table[i][j]==self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) else self.index[i][min(j+(1<<i),self.size-1)] for j in range(self.size)] self.table+=[tmp] self.index+=[tmp_id] # return func of [l,r) def query(self,l,r): if r>self.size:r=self.size #N=(r-l).bit_length()-1 N=self.lg[r-l] return self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))]) # return index of which val[i] = func of v among [l,r) def query_id(self,l,r): if r>self.size:r=self.size #N=(r-l).bit_length()-1 N=self.lg[r-l] a,b=self.index[N][l],self.index[N][max(0,r-(1<<N))] if self.table[0][a]==self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))]): b=a return b # return boundary index of r such that func({table[i]} =< x , i in [pos,r] def right_bound(self,pos,x): k=(self.size-pos).bit_length() for j in range(k)[::-1]: nx=pos+(1<<j) if nx<n and self.query(pos,nx+1)<=x: pos+=(1<<j) return pos # return boundary index of l such that func({table[i]} =< x , i in [l,pos] def left_bound(self,pos,x): k=pos.bit_length() for j in range(k)[::-1]: nx=pos-(1<<j) if 0<=nx and self.query(nx,pos+1)<=x: pos-=(1<<j) return pos def __str__(self): return str(self.table[0]) def print(self): for i in self.table: print(*i) class UnionFind: def __init__(self, n): # 負 : 根であることを示す。絶対値はランクを示す # 非負: 根でないことを示す。値は親を示す self.table = [-1] * n def _root(self, x): if self.table[x] < 0: return x else: # 経路の圧縮 self.table[x] = self._root(self.table[x]) return self.table[x] def find(self, x, y): return self._root(x) == self._root(y) def union(self, x, y): r1 = self._root(x) r2 = self._root(y) if r1 == r2: return # ランクの取得 d1 = self.table[r1] d2 = self.table[r2] if d1 <= d2: self.table[r2] = r1 if d1 == d2: self.table[r1] -= 1 else: self.table[r1] = r2 def __str__(self): rt=[i if j<0 else j for i,j in enumerate(self.table)] return str(rt) show_flg=False show_flg=True ans=0 n,m,k=LI() e=[] for i in range(m): a,b,c=LI_() c+=1 e+=[(c,(a,b))] f=set(NI_(k)) uf=UnionFind(n) g=[] for i in range(m): c,(a,b)=e[i] if i in f: uf.union(a,b) else: g+=[(c,(a,b))] heapify(g) while g: c,(a,b)=heappop(g) if uf._root(a)==uf._root(b): ans+=c else: uf.union(a,b) print(ans)