#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } typedef long double ld; typedef pair LDP; const ld eps = 1e-8; const ld pi = acosl(-1.0); int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; //----------------------------------------- ///////////////////////////////// struct edge { int to, cost; }; ll dp[1 << 12][12][2]; void solve() { int n, m, k; cin >> n >> m >> k; assert(n <= 10000); assert(k <= 12); vector r(k); rep(i, k) { cin >> r[i]; r[i]--; } vector a(m), b(m), c(m); vector> G(n); rep(i, m) { cin >> a[i] >> b[i] >> c[i]; a[i]--; b[i]--; G[a[i]].push_back({ b[i],c[i] }); G[b[i]].push_back({ a[i],c[i] }); } vector vs; vs.push_back(0); vs.push_back(n - 1); rep(i, k) { int id = r[i]; vs.push_back(a[id]); vs.push_back(b[id]); } sort(all(vs)); vs.erase(unique(all(vs)), vs.end()); rep(i, vs.size()) { assert(vs[i] >= 0 && vs[i] < n); } vector> dist(vs.size(), vector(n)); vector> cost(vs.size(), vector(vs.size())); vector> loc(k, vector(2)); rep(i, k) { loc[i][0] = lower_bound(all(vs), a[r[i]]) - vs.begin(); loc[i][1] = lower_bound(all(vs), b[r[i]]) - vs.begin(); } rep(i, vs.size()) { fill(all(dist[i]), INF); priority_queue, greater> q; q.push({ 0,vs[i] }); dist[i][vs[i]] = 0; while (!q.empty()) { LP p = q.top(); q.pop(); if (p.first > dist[i][p.first])continue; for (edge e : G[p.second]) { ll nd = p.first + e.cost; if (nd < dist[i][e.to]) { dist[i][e.to] = nd; q.push({ nd,e.to }); } } } rep(j, vs.size())cost[i][j] = dist[i][vs[j]]; } rep(i, (1 << k))rep(j,k)rep(l, 2)dp[i][j][l] = INF; rep(i, k)rep(j,2) { dp[(1 << i)][i][j] = cost[0][loc[i][j^1]]+c[r[i]]; } rep(i, (1 << k))rep(j, k)rep(l,2) { if (dp[i][j][l] == INF)continue; rep(to, k)rep(y,2) { if (i & (1 << to))continue; int ni = i ^ (1 << to); int nj = to; int ny = y; ll sum = dp[i][j][l] + cost[loc[j][l]][loc[to][y ^ 1]] + c[r[to]]; chmin(dp[ni][nj][ny], sum); } } ll ans = INF; rep(j, k)rep(l,2) { ll sum = dp[(1 << k) - 1][j][l] + cost[loc[j][l]][vs.size()-1]; chmin(ans, sum); } cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(10); //init_f(); //init(); //while(true) //useexpr(); //int t; cin >> t; rep(i, t) solve(); return 0; }