import core.thread; import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.range, std.regex; import core.bitop; // Input class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { tokens = readln.split; if (stdin.eof) throw new EOFException; } auto token = tokens[0]; tokens.popFront; return token; } int readInt() { return to!int(readToken); } long readLong() { return to!long(readToken); } real readReal() { return to!real(readToken); } // chmin/chmax void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } // Pair struct Pair(S, T) { S x; T y; int opCmp( const Pair p) const { return (x < p.x) ? -1 : (x > p.x) ? +1 : (y < p.y) ? -1 : (y > p.y) ? +1 : 0; } int opCmp(ref const Pair p) const { return (x < p.x) ? -1 : (x > p.x) ? +1 : (y < p.y) ? -1 : (y > p.y) ? +1 : 0; } string toString() const { return "(" ~ to!string(x) ~ ", " ~ to!string(y) ~ ")"; } } auto pair(S, T)(inout(S) x, inout(T) y) { return Pair!(S, T)(x, y); } // Array int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = as.length; for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) { return (a < val); }); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) { return (a <= val); }); } T[] unique(T)(in T[] as) { T[] bs; foreach (a; as) if (bs.empty || bs[$ - 1] != a) bs ~= a; return bs; } int root(int[] uf, int u) { return (uf[u] < 0) ? u : (uf[u] = uf.root(uf[u])); } bool conn(int[] uf, int u, int v) { u = uf.root(u); v = uf.root(v); if (u == v) return false; if (uf[u] > uf[v]) swap(u, v); uf[u] += uf[v]; uf[v] = u; return true; } int N, M, K; int[] A, B, C; int[] T; void main(string[] args) { try { for (; ; ) { N = readInt; M = readInt; K = readInt; A = new int[M]; B = new int[M]; C = new int[M]; foreach (i; 0 .. M) { A[i] = readInt - 1; B[i] = readInt - 1; C[i] = readInt; } T = new int[K]; foreach (k; 0 .. K) { T[k] = readInt - 1; } bool[] isT = new bool[N]; foreach (t; T) { isT[t] = true; } int[] nonTs; foreach (u; 0 .. N) if (!isT[u]) { nonTs ~= u; } int[][] D = new int[][](N, N); foreach (u; 0 .. N) { D[u][] = int.max / 2; D[u][u] = 0; } foreach (i; 0 .. M) { chmin(D[A[i]][B[i]], C[i]); chmin(D[B[i]][A[i]], C[i]); } foreach (w; 0 .. N) foreach (u; 0 .. N) foreach (v; 0 .. N) { chmin(D[u][v], D[u][w] + D[w][v]); } if (K == 1) { writeln(0); continue; } else if (K == 2) { writeln(D[T[0]][T[1]]); continue; } Pair!(int, Pair!(int, int))[] edges; foreach (u; 0 .. N) foreach (v; u + 1 .. N) { edges ~= pair(D[u][v], pair(u, v)); } edges.sort(); debug{ writeln("edges = ",edges); } int ans = int.max; foreach (L; 0 .. K - 1) if (L <= N - K) { bool[] flg = new bool[N - K]; flg[$ - L .. $] = true; do { bool[] on = isT.dup; foreach (j, u; nonTs) { if (flg[j]) { on[u] = true; } } int sum; int cnt = 1; int[] uf = new int[N]; uf[] = -1; foreach (e; edges) { if (ans <= sum + (K + L - cnt) * e.x) { goto failed; } if (on[e.y.x] && on[e.y.y]) { if (uf.conn(e.y.x, e.y.y)) { sum += e.x; if (++cnt == K + L) { break; } } } } if (cnt == K + L) { debug{ writeln(flg," ",sum); } chmin(ans, sum); } failed: } while (flg.nextPermutation); } writeln(ans); } } catch (EOFException) {} }