#define _CRT_SECURE_NO_WARNINGS #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; typedef vector vl; typedef pair pll; typedef vector > vpll; typedef vector vs; typedef long double ld; template inline void amin(T &x, U y) { if(y < x) x = y; } template inline void amax(T &x, U y) { if(x < y) x = y; } int main() { int N, M, T; scanf("%d%d%d", &N, &M, &T); vector > g(N, vector(N, INF)); rep(i, N) g[i][i] = 0; rep(i, M) { int a, b, c; scanf("%d%d%d", &a, &b, &c), -- a, -- b; amin(g[a][b], c); amin(g[b][a], c); } rep(k, N) rep(i, N) rep(j, N) amin(g[i][j], g[i][k] + g[k][j]); vi required(T); vector important(N, false); rep(i, T) { int v; scanf("%d", &v), -- v; required[i] = v; important[v] = true; } if(T == 1) { puts("0"); return 0; } vi steiners; rep(i, N) if(!important[i]) steiners.push_back(i); int X = steiners.size(); int ans = INF; if(T >= 16) { vector vertices; rep(use, 1 << X) { vertices = required; rep(i, X) if(use >> i & 1) vertices.push_back(steiners[i]); int V = vertices.size(); vector vis(V, false); vector cost(V, INF); int totalcost = 0; cost[0] = 0; rep(k, V) { pii p(INF, -1); rep(i, V) if(!vis[i]) amin(p, mp(cost[i], i)); int i = p.second, v = vertices[i]; vis[i] = true; totalcost += cost[i]; rep(j, V) amin(cost[j], g[v][vertices[j]]); } amin(ans, totalcost); } }else { vector dp((1 << T) * N, INF); rep(p, T) rep(q, N) dp[(1 << p) * N + q] = g[required[p]][q]; rep(S, 1 << T) { if(!(S & (S-1))) continue; rep(p, N) for(int E = (S-1) & S; E > 0; (-- E) &= S) { amin(dp[S * N + p], dp[E * N + p] + dp[(S - E) * N + p]); } rep(p, N) rep(q, N) amin(dp[S * N + p], dp[S * N + q] + g[p][q]); } int U = (1 << T) - 1; rep(S, 1 << T) rep(q, N) amin(ans, dp[S * N + q] + dp[(U - S) * N + q]); } printf("%d\n", ans); return 0; }