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 System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        static List<Rect> goals;

        public static void Main(string[] args)
        {
            // 整数配列の入力
            var inputIntArray = Console.ReadLine().Split(' ').Select(i => int.Parse(i));
            int n = inputIntArray.ElementAt(0);
            int m = inputIntArray.ElementAt(1);

            List<Rect> rect = new List<Rect>();

            List<Rect> starts = new List<Rect>();
            goals = new List<Rect>();

            for (int i = 0; i < m; i++)
            {
                var next = new Rect(Console.ReadLine());

                foreach(var neigbor in rect)
                {
                    if (next.L <= neigbor.R && next.R >= neigbor.L)
                    {
                        next.Neighbors.Add(neigbor);
                        neigbor.Neighbors.Add(next);
                    }
                }

                if(next.L == 1)
                {
                    starts.Add(next);
                }
                else if(next.R == n)
                {
                    goals.Add(next);
                }
                rect.Add(next);
            }

            foreach(var start in starts)
            {
                start.minDist = start.C;

                Recursive(start);
            }

            long result = long.MaxValue;
            foreach(var goals in goals)
            {
                result = Math.Min(result, goals.minDist);
            }
            if(result == long.MaxValue)
            {
                result = -1;
            }

            Console.WriteLine(result);
        }

        public static void Recursive(Rect target)
        {
            foreach(var next in target.Neighbors)
            {
                long dist = target.minDist + next.C;
                if(next.minDist > dist)
                {
                    next.minDist = dist;

                    Recursive(next);
                }
            }
        }

        public class Rect
        {
            public int L { get; set; }
            public int R { get; set; }
            public long C { get; set; }

            public long minDist { get; set; }

            public List<Rect> Neighbors { get; set; }

            public Rect(string input)
            {
                var inputIntArray = input.Split(' ').Select(i => int.Parse(i));
                L = inputIntArray.ElementAt(0);
                R = inputIntArray.ElementAt(1);
                C = inputIntArray.ElementAt(2);
                minDist = long.MaxValue;
                Neighbors = new List<Rect>();
            }

            public void SetDist(long dist)
            {
                if(this.minDist > dist)
                {
                    this.minDist = dist;
                }
            }
        }
    }
}