using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ProgrammingContest { class MainClass : IDisposable { Scanner sc; Writer wr; string backPath = ".."; char dirSep = System.IO.Path.DirectorySeparatorChar; string inFilePath = null; string outFilePath = null; public MainClass() { this.inFilePath = this.backPath + this.dirSep + this.backPath + this.dirSep + "in.txt"; this.outFilePath = this.backPath + this.dirSep + this.backPath + this.dirSep + "out.txt"; } static void Main(string[] args) { using (var mainClass = new MainClass()) { //mainClass.MakeTestCase(); mainClass.Solve(); } } public void Dispose() { if (this.sc != null) { this.sc.Dispose(); this.sc = null; } if (this.wr != null) { this.wr.Dispose(); this.wr = null; } } void MakeTestCase() { Random rand = new Random(); this.wr = new Writer(inFilePath); } void Solve() { this.wr = new Writer(this.isReactive); //this.wr = new Writer(this.outFilePath); #if DEBUG if (!this.isReactive) this.sc = new Scanner(this.inFilePath); else this.sc = new Scanner(); #else this.sc = new Scanner(); #endif Point st = new Point(sc.NextInt, sc.NextInt, -1); int n = sc.NextInt; Point[] p = new Point[n].Select( e => new Point(sc.NextInt, sc.NextInt, sc.NextDouble) ).ToArray(); double[,] dp = new double[1 << n, n]; double[] weights = new double[1 << n]; for (int i = 0; i < 1 << n; i++) { for (int j = 0; j < n; j++) { if ((i & (1 << j)) == 0) { weights[i] += p[j].w; } } } double inf = 1e18; for (int i = 0; i < 1 << n; i++) { for (int j = 0; j < n; j++) { dp[i, j] = inf; } } for (int i = 0; i < n; i++) { dp[1 << i, i] = CalcDist(st, p[i]) * CalcSpeed(weights[0]) + p[i].w; } for (int i = 0; i < 1 << n; i++) { for (int j = 0; j < n; j++) { if (dp[i, j] < inf) { for (int k = 0; k < n; k++) { if ((i & (1 << j)) != 0 && (i & (1 << k)) == 0) { dp[i | (1 << k), k] = Math.Min( dp[i | (1 << k), k], dp[i, j] + CalcDist(p[j], p[k]) * CalcSpeed(weights[i]) + p[k].w); } } } } } double ans = inf; for (int i = 0; i < n; i++) { ans = Math.Min(ans, dp[(1 << n) - 1, i] + CalcDist(p[i], st) * CalcSpeed(0)); } wr.WriteLine(ans); } double CalcDist(Point p1, Point p2) => Math.Abs(p1.x - p2.x) + Math.Abs(p1.y - p2.y); double CalcSpeed(double weight) => (weight + 100) / 120; bool isReactive = false; // TODO: reactive check !! } class Point { public int x, y; public double w; public Point(int x, int y, double w) { this.x = x; this.y = y; this.w = w; } } class Writer : IDisposable { private System.IO.TextWriter writer; private StringBuilder sb; private bool isReactive; public Writer(string path) : this(new System.IO.StreamWriter(path)) { } public Writer(bool isReactive) : this(null, isReactive) { } public Writer(System.IO.TextWriter writer = null, bool isReactive = false) { this.writer = (writer ?? Console.Out); this.isReactive = isReactive; if (!this.isReactive) this.sb = new StringBuilder(); } public void Dispose() { if (!this.isReactive) this.writer.Write(sb.ToString()); if (!this.writer.Equals(Console.Out)) this.writer.Dispose(); } public void Write(object val) { if (this.isReactive) { this.writer.Write(val.ToString()); this.writer.Flush(); } else this.sb.Append(val.ToString()); } public void Write(string format, params object[] vals) { if (this.isReactive) { this.writer.Write(format, vals); this.writer.Flush(); } else this.sb.AppendFormat(format, vals); } public void WriteLine(object val) { this.Write(val.ToString() + System.Environment.NewLine); } public void WriteLine(string format, params object[] vals) { this.Write(format + System.Environment.NewLine, vals); } } class Scanner : IDisposable { private Queue buffer; private char[] sep; private System.IO.TextReader reader; public Scanner(string path) : this(new System.IO.StreamReader(path)) { } public Scanner(System.IO.TextReader reader = null) { this.buffer = new Queue(); this.sep = new char[] { ' ' }; this.reader = (reader ?? Console.In); } private void CheckBuffer() { if (this.buffer.Count == 0) { string str = string.Empty; while (string.IsNullOrEmpty(str)) str = this.reader.ReadLine(); str.Split(this.sep).ToList() .ForEach(el => this.buffer.Enqueue(el)); } } public void Dispose() { if (!this.reader.Equals(Console.In)) this.reader.Dispose(); } public string Next { get { this.CheckBuffer(); return this.buffer.Dequeue(); } } public int NextInt { get { return int.Parse(this.Next); } } public double NextDouble { get { return double.Parse(this.Next); } } public long NextLong { get { return long.Parse(this.Next); } } public bool IsEnd { get { this.CheckBuffer(); return this.buffer.Count == 0; } } } }