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 static readonly long INF = long.MaxValue / 2;
        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;
            }
        }
        
        struct Pair<T, U> : IComparable<Pair<T, U>>
            where T : IComparable<T>
            where U : IComparable<U>
        {
            public T first;
            public U second;
            private bool CompWithFirst;
 
            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
 
            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
        
     public class PriorityQueue<T> where T : IComparable<T>
    {
 
        private List<T> Q;
        private readonly int r;
 
        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }
 
 
        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);
 
            while (n != 0)
            {
                int pIndex = (n - 1) / 2;
 
                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }
 
                n = pIndex;
            }
        }
 
        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);
 
            int cur = 0;
            int comp;
 
            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {
 
                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }
 
                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }
 
                cur = comp;
            }
        }
 
        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }
 
 
 
        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }
 
        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }
 
        public T Peek()
        {
            return Q[0];
        }
 
        public int CountItem()
        {
            return Q.Count();
        }
    }
        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(long.Parse).ToArray();
                    int l = (int)longInput[0] - 1;
                    int r = (int)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<Pair<int, long>>(false);
                var p = new Pair<int, long>();
                p.first = 0;
                p.second = 0;
                pq.Enqueue(p);
                var d = new long[n];
                for (int i=0; i < n; i++) d[i] = INF;
                d[0] = 0;
                while (pq.CountItem() > 0)
                {
                    var v = pq.Dequeue();
//                    WriteLine($"To:{v.To}Cost:{v.Cost}");
                    if (d[v.first] < v.second) continue;
                    foreach (var e in G[v.first])
                    {
                        if (d[e.To] > d[v.first] + e.Cost)
                        {
                            d[e.To] = d[v.first] + e.Cost;
                            var pp = new Pair<int, long>();
                            pp.first = e.To;
                            pp.second = d[e.To];
                            pq.Enqueue(pp);
                        }
                    }
                
                }

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