Problem:
Score : 600 points

Problem Statement

We have N points numbered 1 to N arranged in a line in this order.

Takahashi decides to make an undirected graph, using these points as the vertices.
In the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.
The i-th operation is as follows:

The operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i \leq s < t \leq R_i, add an edge of length C_i between Vertex s and Vertex t.

The integers L_1, ..., L_M, R_1, ..., R_M, C_1, ..., C_M are all given as input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i < R_i \leq N

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 C_1
:
L_M R_M C_M

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.
If there is no shortest path, print -1 instead.

Sample Input 1

4 3
1 3 2
2 4 3
1 4 6

Sample Output 1

5

We have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.

Sample Input 2

4 2
1 2 1
3 4 2

Sample Output 2

-1

Sample Input 3

10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3

Sample Output 3

28

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

public static class Program
{
    private const long INF = 1001001001;
        struct Edge : IComparable<Edge>
        {
            public int To;
            public long Cost;
            
            public int CompareTo(Edge other)
            {
                if (Cost > other.Cost) return 1;
                if (Cost == other.Cost) return 0;
                return -1;
            }
        }
        
        class PriorityQueue<T> where T : IComparable<T>
        {
            public readonly T[] Array;
            public readonly bool Greater;
            public int Count { get; private set; }

            public PriorityQueue(int capacity, bool greater = true)
            {
                Array = new T[capacity];
                Greater = greater;
            }

            public void Enqueue(T item)
            {
                Array[Count] = item;
                Count += 1;
                UpHeap();
            }

            public T Dequeue()
            {
                // 先頭要素を末尾にして再構成
                Swap(0, Count - 1);
                Count -= 1;
                DownHeap();

                return Array[Count];
            }


            private void UpHeap()
            {
                var n = Count - 1;
                while (n != 0)
                {
                    // 親要素の座標
                    var parent = (n - 1) / 2;

                    if (Compare(Array[n], Array[parent]) > 0)
                    {
                        Swap(n, parent);
                        n = parent;
                    }
                    else
                    {
                        break;
                    }
                }
            }

            private void DownHeap()
            {
                var parent = 0;
                while (true)
                {
                    var child = 2 * parent + 1;
                    if (child > Count - 1) break;

                    if (child < Count - 1 && Compare(Array[child], Array[child + 1]) < 0)
                    {
                        // 左より右の子のほうが大きい値の場合、右を入れ替え対象にする
                        child += 1;
                    }

                    if (Compare(Array[parent], Array[child]) < 0)
                    {
                        Swap(parent, child);
                        parent = child;
                    }
                    else
                    {
                        break;
                    }
                }
            }

            private int Compare(T a, T b)
            {
                var c = a.CompareTo(b);
                if (!Greater)
                {
                    c = -c;
                }
                return c;
            }

            private void Swap(int a, int b)
            {
                var tmp = Array[a];
                Array[a] = Array[b];
                Array[b] = tmp;
            }
        }
        
        public static void Main(string[] args)
        {
            try
            {
                var intInput = ReadLine().Split(' ').Select(int.Parse).ToArray();
                int n = intInput[0];
                int m = intInput[1];

                //グラフの生成
                var G = new List<Edge>[n];
                for (int i = 0; i < n-1; i++)
                {
                    var e = new Edge {To = i, Cost = 0};
                    if (G[i+1] == null) G[i+1] = new List<Edge>();
                    G[i+1].Add(e);
                }

                for (int i = 0; i < m; i++)
                {
                    var longInput = ReadLine().Split(' ').Select(int.Parse).ToArray();
                    int l = longInput[0] - 1;
                    int r = longInput[1] - 1;
                    long cost = longInput[2];
                
                    var e = new Edge {To = r, Cost = cost};
                    if (G[l] == null) G[l] = new List<Edge>();
                    G[l].Add(e);
                }

//                for (int i = 0; i < n; i++)
//                {
//                    foreach (var e in G[i])
//                    {
//                        WriteLine($"From:{i}To:{e.To}Cost:{e.Cost}");
//                    }
//                }

                var pq = new PriorityQueue<Edge>(100000);
                pq.Enqueue(new Edge {Cost = 0, To = 0});
                var d = new long[n];
                for (int i=0; i < n; i++) d[i] = INF;
                d[0] = 0;
                while (pq.Count > 0)
                {
                    var v = pq.Dequeue();
//                    WriteLine($"To:{v.To}Cost:{v.Cost}");
                    if (d[v.To] < v.Cost) continue;
                    foreach (var e in G[v.To])
                    {
                        if (d[e.To] > d[v.To] + e.Cost)
                        {
                            d[e.To] = d[v.To] + e.Cost;
                            pq.Enqueue(new Edge{Cost = d[e.To], To = e.To});
                        }
                    }
                
                }

                long ans = d[n - 1];
                if (ans == INF) ans = -1;
                WriteLine(ans);
            }
            catch (Exception e)
            {
                WriteLine(e.StackTrace);
            }
            
        }
    }