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;

class D
{
    static void Main()
    {
#if DEBUG
        string exampleInput =
        @"10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3
";
        Console.SetIn(new System.IO.StringReader(exampleInput));
#endif

        var NM = Console.ReadLine().Split(' ').Select(int.Parse).ToList();

        var result = new long[NM[0]];
        var L = Enumerable.Range(0, NM[0]).Select(_ => new List<List<int>>()).ToList();
        for (int m = 0; m < NM[1]; m++)
        {
            var LRC = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
            LRC[0]--;
            LRC[1]--;
            L[LRC[0]].Add(LRC);
        }
        var list = new SortedDictionary<int, int>();
        long shortestR = 0;
        for (int i = 0; i < NM[0]; i++)
        {
            foreach (var lrc in L[i])
            {
                int v;
                int r = -lrc[1];
                if (list.TryGetValue(r, out v))
                {
                    if (v > lrc[2]) list[r] = lrc[2];
                }
                else
                {
                    list.Add(r, lrc[2]);
                }
            }
            if (i > 0 && result[i] == 0) continue;
            if (i != shortestR) continue;
            long minC = (long)1e18;
            foreach (var rc in list)
            {
                var r = -rc.Key;
                var c = result[i] + rc.Value;
                if (result[r] == 0) result[r] = c;
                else result[r] = Math.Min(result[r], c);
                if (c < minC)
                {
                    minC = c;
                    shortestR = r;
                }
            }
            list.Clear();
        }
        Console.WriteLine(result.Last() == 0 ? -1 : result.Last());
        Console.Out.Flush();
    }
}