using System; using System.Linq; using System.Linq.Expressions; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = System.Int32; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var m = sc.Integer(); var k = sc.Integer(); var g = new SteinerTreeMaker(n); for (int i = 0; i < m; i++) { var f = sc.Integer() - 1; var t = sc.Integer() - 1; var c = sc.Integer(); g.AddEdge(f, t, c); } for (int i = 0; i < k; i++) g.AddVertex(sc.Integer() - 1); IO.Printer.Out.WriteLine(g.Get()); } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region Edge public struct Edge : IComparable { public int from, to, id; public long cost; public Edge(int f, int t) : this() { from = f; to = t; cost = 0; id = -1; } public Edge(int f, int t, long v) : this() { from = f; to = t; cost = v; id = -1; } public Edge(int f, int t, long v, int idx) : this() { from = f; to = t; cost = v; id = idx; } public override string ToString() { return string.Format("{0}->{1}:{2} id:{3}", from, to, cost, id); } public int CompareTo(Edge other) { var cmp = cost.CompareTo(other.cost); if (cmp != 0) return cmp; return id.CompareTo(other.id); } } #endregion public class SteinerTreeMaker { int n; int[][] g; List s; List es; const int INF = 1000000000; public SteinerTreeMaker(int n) { this.n = n; g = new int[n][]; s = new List(); es = new List(); for (int i = 0; i < n; i++) g[i] = new int[n]; for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (i != j) g[i][j] = INF; } public void AddEdge(int f, int t, int c) { g[f][t] = Math.Min(g[f][t], c); g[t][f] = Math.Min(g[t][f], c); es.Add(new Edge(f, t, c)); } public void AddVertex(int v) { s.Add(v); } bool ok = false; public void Build() { s = s.Distinct().ToList(); s.Sort(); for (int k = 0; k < n; k++) for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) g[i][j] = Math.Min(g[i][j], g[i][k] + g[k][j]); es.Sort(); ok = true; } public long Get() { if (!ok) Build(); var k = s.Count; if (k <= 12) return GetKSmall(); return GetKLarge(); } /// /// O(n*3^k+n^2*2^k+n^3) /// /// long GetKSmall() { var k = s.Count; if (k <= 1) return 0; var opt = new int[1 << k][]; for (int i = 0; i < 1 << k; i++) { opt[i] = new int[n]; for (int j = 0; j < n; j++) opt[i][j] = INF; } for (int i = 0; i < k; i++) for (int j = 0; j < n; j++) opt[1 << i][j] = g[s[i]][j]; for (int i = 1; i < 1 << k; i++) { if ((i & (i - 1)) == 0) continue; for (int p = 0; p < n; p++) { for (var sub = i; sub != 0; sub = (sub - 1) & i) opt[i][p] = Math.Min(opt[i][p], opt[sub][p] + opt[i - sub][p]); } for (int p = 0; p < n; p++) for (int q = 0; q < n; q++) opt[i][p] = Math.Min(opt[i][p], opt[i][q] + g[p][q]); } long ans = long.MaxValue; for (int i = 0; i < 1 << k; i++) for (int j = 0; j < n; j++) ans = Math.Min(ans, opt[i][j] + opt[((1 << k) - 1) - i][j]); return ans; } public long GetKLarge() { var rem = new List(); for (int i = 0; i < n; i++) { if (!s.Contains(i)) rem.Add(i); } var k = rem.Count; long ans = long.MaxValue; var ea = es.ToArray(); for (int i = 0; i < 1 << k; i++) { var use = new bool[n]; foreach (var x in s) use[x] = true; for (int j = 0; j < k; j++) if ((i >> j & 1) == 1) use[rem[j]] = true; var set = new DisjointSet(n); long val = 0; var cnt = 0; for (int j = 0; j < n; j++) if (use[j]) cnt++; foreach (var e in ea) { if (use[e.from] && use[e.to]) if (set.Unite(e.from, e.to)) val += e.cost; } if (set.Size(s[0]) == cnt) ans = Math.Min(ans, val); } return ans; } } #region DisjointSet public class DisjointSet { public int[] par, ranks, count; public DisjointSet(int n) { par = new int[n]; count = new int[n]; for (int i = 0; i < n; i++) { par[i] = i; count[i] = 1; } ranks = new int[n]; } public int this[int id] { get { return (par[id] == id) ? id : this[par[id]]; } } public bool Unite(int x, int y) { x = this[x]; y = this[y]; if (x == y) return false; if (ranks[x] < ranks[y]) { par[x] = y; count[y] += count[x]; } else { par[y] = x; count[x] += count[y]; if (ranks[x] == ranks[y]) ranks[x]++; } return true; } public int Size(int x) { return count[this[x]]; } public bool IsUnited(int x, int y) { return this[x] == this[y]; } } #endregion