using System; using System.IO; using System.Collections.Generic; using System.Linq; using System.Numerics; using System.Runtime.CompilerServices; using System.Text; using System.Globalization; using System.Threading; using static System.Math; namespace FertiLib.Contest.E { public class Solver { Scanner sr; StreamWriter sw; bool isMultipleTestCases = false; public void Solve() { var (n, m) = sr.ReadValue<int, int>(); var (s, t, d) = sr.ReadValueArray<int, int, long>(m); var dic = new SortedDictionary<long, List<int>>(); for (int i = 0; i < m; i++) { d[i] *= -1; if (!dic.ContainsKey(d[i])) dic.Add(d[i], new List<int>()); dic[d[i]].Add(i); } var uf = new UnionFind(n); var ok = 0L; foreach (var (key, value) in dic) { foreach (var edge in value) { uf.Unite(s[edge] - 1, t[edge] - 1); } if (uf.IsSame(0, n - 1)) ok.Chmax(key * -1); } var g = new Graph.DirectedWeightedGraph(n); for (int i = 0; i < m; i++) { if (-1 * d[i] >= ok) { g.AddEdge(s[i] - 1, t[i] - 1, 1); g.AddEdge(t[i] - 1, s[i] - 1, 1); } } var dijkstra = new Graph.Dijkstra(g); Console.WriteLine($"{ok} {dijkstra.GetDistanceFrom(0)[n - 1]}"); } public Solver(Scanner cin, StreamWriter cout) { this.sr = cin; this.sw = cout; } public void Start() { int _t = 1; if (isMultipleTestCases) _t = sr.ReadInt(); while (_t-- > 0) Solve(); } public static void YESNO(bool condition) => Console.WriteLine(condition ? "YES" : "NO"); public static void YesNo(bool condition) => Console.WriteLine(condition ? "Yes" : "No"); public static void yesno(bool condition) => Console.WriteLine(condition ? "yes" : "no"); } public class PriorityQueue<T> : IEnumerable<T> { private readonly List<T> heap; private readonly IComparer<T> comparer; public PriorityQueue(IComparer<T> comparer) { this.comparer = comparer; this.heap = new List<T>(); } public PriorityQueue(Comparison<T> comparison) : this(Comparer<T>.Create(comparison)) { } public PriorityQueue() : this(Comparer<T>.Default) { } public void Enqueue(T item) { this.heap.Add(item); int index = this.Count - 1; while (index > 0) { var par = Parent(index); if (comparer.Compare(heap[index], heap[par]) >= 0) break; Swap(index, par); index = par; } } public T Dequeue() { var ret = this.Peek; var last = this.Count - 1; heap[0] = heap[last]; heap.RemoveAt(last--); var index = 0; while (true) { var (r, l) = Child(index); int child; if (l <= last) { if (comparer.Compare(heap[l], heap[r]) < 0) child = l; else child = r; } else if (r <= last) child = r; else break; if (comparer.Compare(heap[index], heap[child]) <= 0) break; Swap(index, child); index = child; } return ret; } public T Peek => heap[0]; public int Count => heap.Count; private void Swap(int a, int b) { var t = heap[a]; heap[a] = heap[b]; heap[b] = t; } private int Parent(int index) => (index - 1) / 2; private (int l, int r) Child(int index) => (2 * index + 1, 2 * index + 2); public IEnumerator<T> GetEnumerator() { var ret = new List<T>(); while (this.Count > 0) { ret.Add(this.Dequeue()); } for (int i = 0; i < ret.Count; i++) { this.Enqueue(ret[i]); } foreach (var e in ret) { yield return e; } } System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); } public static partial class Graph { public class Dijkstra { private DirectedWeightedGraph graph; public Dijkstra(DirectedWeightedGraph graph) => this.graph = graph; public long[] GetDistanceFrom(int index) { const long Inf = long.MaxValue / 5; var distances = Enumerable.Repeat(Inf, graph.NodeCount).ToArray(); distances[index] = 0; var queue = new PriorityQueue<(long distance, int index)>(); queue.Enqueue((0, index)); while (queue.Count > 0) { var cur = queue.Dequeue(); if (cur.distance > distances[cur.index]) continue; foreach (var edge in graph[cur.index]) { var nextDistance = cur.distance + edge.Weight; if (distances[edge.To] > nextDistance) { distances[edge.To] = nextDistance; queue.Enqueue((nextDistance, edge.To)); } } } return distances; } } } public static partial class Graph { public interface IEdge { int To { get; } } public interface IWeightedEdge : IEdge { long Weight { get; } } public interface IGraph<TEdge> where TEdge : IEdge { public List<TEdge> this[int index] { get; } public int NodeCount { get; } public List<TEdge> Next(int x); } public interface IWeightedGraph<TEdge> : IGraph<TEdge> where TEdge : IWeightedEdge { } public struct BasicEdge : IEdge { public int To { get; private set; } public BasicEdge(int to) { this.To = to; } public override string ToString() => $"{To}"; public static implicit operator BasicEdge(int edge) => new BasicEdge(edge); public static implicit operator int(BasicEdge edge) => edge.To; } public struct WeightedEdge : IWeightedEdge { public int To { get; private set; } public long Weight { get; private set; } public WeightedEdge(int to, long weight) { To = to; Weight = weight; } public WeightedEdge(int to) : this(to, 1) { } public override string ToString() => $"[{Weight}] -> {To}"; public void Deconstruct(out int to, out long weight) => (to, weight) = (To, Weight); } public class UndirectedGraph : IGraph<BasicEdge> { public readonly List<List<BasicEdge>> g; public List<BasicEdge> this[int index] => g[index]; public int NodeCount => g.Count; public UndirectedGraph(int nodeCount) => g = Enumerable.Repeat(0, nodeCount).Select(_ => new List<BasicEdge>()).ToList(); public UndirectedGraph(int nodeCount, int[] u, int[] v) : this(nodeCount) { if (u.Length != v.Length) throw new ArgumentException($"The arrays {nameof(u)} and {nameof(v)} must have the same length."); for (var i = 0; i < u.Length; i++) { AddEdge(u[i], v[i]); } } public void AddEdge(int u, int v) { g[u].Add(v); g[v].Add(u); } public void AddNode() => g.Add(new List<BasicEdge>()); public List<BasicEdge> Next(int x) => g[x]; } public class DirectedGraph : IGraph<BasicEdge> { public readonly List<List<BasicEdge>> g; public List<BasicEdge> this[int index] => g[index]; public int NodeCount => g.Count; public DirectedGraph(int nodeCount) => g = Enumerable.Repeat(0, nodeCount).Select(_ => new List<BasicEdge>()).ToList(); public DirectedGraph(int nodeCount, int[] from, int[] to) : this(nodeCount) { if (from.Length != to.Length) throw new ArgumentException($"The arrays {nameof(from)} and {nameof(to)} must have the same length."); for (var i = 0; i < from.Length; i++) { AddEdge(from[i], to[i]); } } public void AddEdge(int from, int to) => g[from].Add(to); public void AddNode() => g.Add(new List<BasicEdge>()); public List<BasicEdge> Next(int x) => g[x]; } public class UndirectedWeightedGraph : IWeightedGraph<WeightedEdge> { public readonly List<List<WeightedEdge>> g; public List<WeightedEdge> this[int index] => g[index]; public int NodeCount => g.Count; public UndirectedWeightedGraph(int nodeCount) => g = Enumerable.Repeat(0, nodeCount).Select(_ => new List<WeightedEdge>()).ToList(); public UndirectedWeightedGraph(int nodeCount, int[] u, int[] v, long[] weight) : this(nodeCount) { if (u.Length != v.Length) throw new ArgumentException($"The arrays {nameof(u)} and {nameof(v)} must have the same length."); if (u.Length != weight.Length) throw new ArgumentException($"The arrays {nameof(u)} and {nameof(weight)} must have the same length."); if (weight.Length != v.Length) throw new ArgumentException($"The arrays {nameof(v)} and {nameof(weight)} must have the same length."); for (var i = 0; i < u.Length; i++) { AddEdge(u[i], v[i], weight[i]); } } public void AddEdge(int u, int v, long w) { g[u].Add(new WeightedEdge(v, w)); g[v].Add(new WeightedEdge(u, w)); } public void AddNode() => g.Add(new List<WeightedEdge>()); public List<WeightedEdge> Next(int x) => g[x]; } public class DirectedWeightedGraph : IWeightedGraph<WeightedEdge> { public readonly List<List<WeightedEdge>> g; public List<WeightedEdge> this[int index] => g[index]; public int NodeCount => g.Count; public DirectedWeightedGraph(int nodeCount) => g = Enumerable.Repeat(0, nodeCount).Select(_ => new List<WeightedEdge>()).ToList(); public DirectedWeightedGraph(int nodeCount, int[] from, int[] to, long[] weight) : this(nodeCount) { if (from.Length != to.Length) throw new ArgumentException($"The arrays {nameof(from)} and {nameof(to)} must have the same length."); if (from.Length != weight.Length) throw new ArgumentException($"The arrays {nameof(from)} and {nameof(weight)} must have the same length."); if (weight.Length != to.Length) throw new ArgumentException($"The arrays {nameof(to)} and {nameof(weight)} must have the same length."); for (var i = 0; i < from.Length; i++) { AddEdge(from[i], to[i], weight[i]); } } public void AddEdge(int from, int to, long w) { g[from].Add(new WeightedEdge(to, w)); } public void AddNode() => g.Add(new List<WeightedEdge>()); public List<WeightedEdge> Next(int x) => g[x]; } } public class UnionFind { public int Count { get; private set; } int[] parent; int[] rank; int[] size; public UnionFind(int n) { parent = Enumerable.Range(0, n).ToArray(); rank = Enumerable.Repeat(0, n).ToArray(); size = Enumerable.Repeat(1, n).ToArray(); } public void Unite(int x, int y) { x = Find(x); y = Find(y); if (x == y) return; if (rank[x] > rank[y]) { parent[y] = x; size[x] += size[y]; } else { parent[x] = y; if (rank[x] == rank[y]) rank[x]++; size[y] += size[x]; } } public int Find(int x) { if (parent[x] == x) return x; else return parent[x] = Find(parent[x]); } public bool IsSame(int x, int y) => Find(x) == Find(y); public int Size(int x) => size[Find(x)]; } public static class Program { public static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); var cin = new Scanner(); var solver = new Solver(cin, sw); solver.Start(); Console.Out.Flush(); } } public static class Extention { public static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x); public static int UpperBound<T>(this IList<T> list, T value) => list.BinarySearch(value, true, 0, list.Count, Comparer<T>.Default); public static int LowerBound<T>(this IList<T> list, T value) => list.BinarySearch(value, false, 0, list.Count, Comparer<T>.Default); public static int BinarySearch<T>(this IList<T> list, T value, bool isUpperBound, int index, int length, Comparer<T> comparer) { var ng = index - 1; var ok = index + length; while (ok - ng > 1) { var mid = ng + (ok - ng) / 2; var res = comparer.Compare(list[mid], value); if (res < 0 || (isUpperBound && res == 0)) ng = mid; else ok = mid; } return ok; } public static bool Chmax<T>(ref this T a, T b) where T : struct, IComparable<T> { if (a.CompareTo(b) >= 0) return false; a = b; return true; } public static bool Chmin<T>(ref this T a, T b) where T : struct, IComparable<T> { if (a.CompareTo(b) <= 0) return false; a = b; return true; } } public class Scanner { string[] s; int i; char[] separator = new char[] { ' ' }; public Scanner() { s = new string[0]; i = 0; } public string Read() => ReadString(); public string ReadString() { if (i < s.Length) return s[i++]; string st = Console.ReadLine(); while (st == "") st = Console.ReadLine(); s = st.Split(separator, StringSplitOptions.RemoveEmptyEntries); if (s.Length == 0) return ReadString(); i = 0; return s[i++]; } public string[] ReadStringArray(int N) { string[] Array = new string[N]; for (int i = 0; i < N; i++) { Array[i] = ReadString(); } return Array; } public int ReadInt() => int.Parse(ReadString()); public int[] ReadIntArray(int N, int add = 0) { int[] Array = new int[N]; for (int i = 0; i < N; i++) { Array[i] = ReadInt() + add; } return Array; } public long ReadLong() => long.Parse(ReadString()); public long[] ReadLongArray(int N, long add = 0) { long[] Array = new long[N]; for (int i = 0; i < N; i++) { Array[i] = ReadLong() + add; } return Array; } public double ReadDouble() => double.Parse(ReadString()); public double[] ReadDoubleArray(int N, double add = 0) { double[] Array = new double[N]; for (int i = 0; i < N; i++) { Array[i] = ReadDouble() + add; } return Array; } public T1 ReadValue<T1>() => (T1)Convert.ChangeType(ReadString(), typeof(T1)); public (T1, T2) ReadValue<T1, T2>() { var inputs = ReadStringArray(2); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); return (v1, v2); } public (T1, T2, T3) ReadValue<T1, T2, T3>() { var inputs = ReadStringArray(3); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); return (v1, v2, v3); } public (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>() { var inputs = ReadStringArray(4); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); return (v1, v2, v3, v4); } public (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>() { var inputs = ReadStringArray(5); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5)); return (v1, v2, v3, v4, v5); } public (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>() { var inputs = ReadStringArray(6); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5)); var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6)); return (v1, v2, v3, v4, v5, v6); } public (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>() { var inputs = ReadStringArray(7); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5)); var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6)); var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7)); return (v1, v2, v3, v4, v5, v6, v7); } public T1[] ReadValueArray<T1>(int N) { var v1 = new T1[N]; for (int i = 0; i < N; i++) { v1[i] = ReadValue<T1>(); } return v1; } public (T1[], T2[]) ReadValueArray<T1, T2>(int N) { var (v1, v2) = (new T1[N], new T2[N]); for (int i = 0; i < N; i++) { var (t1, t2) = ReadValue<T1, T2>(); v1[i] = t1; v2[i] = t2; } return (v1, v2); } public (T1[], T2[], T3[]) ReadValueArray<T1, T2, T3>(int N) { var (v1, v2, v3) = (new T1[N], new T2[N], new T3[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3) = ReadValue<T1, T2, T3>(); v1[i] = t1; v2[i] = t2; v3[i] = t3; } return (v1, v2, v3); } public (T1[], T2[], T3[], T4[]) ReadValueArray<T1, T2, T3, T4>(int N) { var (v1, v2, v3, v4) = (new T1[N], new T2[N], new T3[N], new T4[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4) = ReadValue<T1, T2, T3, T4>(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; } return (v1, v2, v3, v4); } public (T1[], T2[], T3[], T4[], T5[]) ReadValueArray<T1, T2, T3, T4, T5>(int N) { var (v1, v2, v3, v4, v5) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4, t5) = ReadValue<T1, T2, T3, T4, T5>(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; v5[i] = t5; } return (v1, v2, v3, v4, v5); } public (T1[], T2[], T3[], T4[], T5[], T6[]) ReadValueArray<T1, T2, T3, T4, T5, T6>(int N) { var (v1, v2, v3, v4, v5, v6) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4, t5, t6) = ReadValue<T1, T2, T3, T4, T5, T6>(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; v5[i] = t5; v6[i] = t6; } return (v1, v2, v3, v4, v5, v6); } public (T1[], T2[], T3[], T4[], T5[], T6[], T7[]) ReadValueArray<T1, T2, T3, T4, T5, T6, T7>(int N) { var (v1, v2, v3, v4, v5, v6, v7) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N], new T7[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4, t5, t6, t7) = ReadValue<T1, T2, T3, T4, T5, T6, T7>(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; v5[i] = t5; v6[i] = t6; v7[i] = t7; } return (v1, v2, v3, v4, v5, v6, v7); } } }