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: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
struct Edge{
    public Vertex v;
    public long cost;
    public Edge(Vertex v0,long c){
        v = v0;
        cost = c;
    }
}
class Vertex{
    public bool finished;
    public List<Vertex> edges;
    public List<long> costs;
    public long cost;
    public void AddEdge(Vertex v,long c){
        edges.Add(v);
        costs.Add(c);
    }
    public Vertex(){
        edges = new List<Vertex>();
        costs = new List<long>();
        cost = -1;
        finished = false;
    }
}
class Dijkstra{
	int E;
	Vertex[] point;
    Vertex S;
    public long GetCost(int i){
        return point[i].cost;
    }
    public Dijkstra(int[] f,int[] t,long[] cost,int n,int s){
        point = new Vertex[n];
        for(int i=0;i<n;i++){
            point[i] = new Vertex();
        }
        E = f.Length;
        for(int i=0;i<E;i++){
            point[f[i]].AddEdge(point[t[i]],cost[i]);
        }
        S = point[s];
        calc();
    }
    void calc(){
        Heap H = new Heap(2*E+1);
        S.cost = 0;
        H.push(new Edge(S,0));
        while(!H.Empty()){
            Vertex v = H.pop().v;
            if(v.finished){
                continue;
            }
            v.finished = true;
            for(int i=0;i<v.edges.Count;i++){
                Vertex vi = v.edges[i];
                if(vi.cost == -1 || vi.cost > v.costs[i]+v.cost){
                    vi.cost = v.costs[i]+v.cost;
                    H.push(new Edge(vi,vi.cost));
                }
            }
        }
    }
}
class Heap{
    public int size;
    Edge[] obj;
    public Heap(int maxsize){
        size = 0;
        obj = new Edge[maxsize];
    }
    public void push(Edge a){
        int i = size;
        size++;
        while(i > 0){
            int p = (i - 1)/2;
            if(obj[p].cost <= a.cost){
                obj[i] = a;
                break;
            }
            obj[i] = obj[p];
            i = p;
        }
        if(i == 0){
            obj[0] = a;
        }
    }
    public bool Empty(){
        return size == 0;
    }
    public Edge pop(){
        Edge t = obj[0];
        int i = 0;
        size--;
        while(2*i+1 < size){
            int p = 2*i+1;
            if(p+1 < size && obj[p+1].cost < obj[p].cost){
                p++;
            }
            if(obj[p].cost < obj[size].cost){
                obj[i] = obj[p];
                i = p;
            }
            else{
                obj[i] = obj[size];
                break;
            }
        }
        if(2*i+1 >= size){
            obj[i] = obj[size];
        }
        return t;
    }
}
class Solve{
    public Solve(){}
    StringBuilder sb;
    ReadData re;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        re = new ReadData();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        int N = re.i();
        int M = re.i();
        int[] F = new int[M+N-1];
        int[] T = new int[M+N-1];
        long[] Cost = new long[M+N-1];
        for(int i=0;i<M;i++){
            int L = re.i()-1;
            int R = re.i()-1;
            long C = re.l();
            F[i] = L;
            T[i] = R;
            Cost[i] = C;
        }
        for(int i=0;i<N-1;i++){
            F[i+M] = i+1;
            T[i+M] = i;
            Cost[i+M] = 0;
        }
        Dijkstra dijkstra = new Dijkstra(F,T,Cost,N,0);
        sb.Append(dijkstra.GetCost(N-1)+"\n");
    }
}
class ReadData{
    string[] str;
    int counter;
    public ReadData(){
        counter = 0;
    }
    public string s(){
        if(counter == 0){
            str = Console.ReadLine().Split(' ');
            counter = str.Length;
        }
        counter--;
        return str[str.Length-counter-1];
    }
    public int i(){
        return int.Parse(s());
    }
    public long l(){
        return long.Parse(s());
    }
    public double d(){
        return double.Parse(s());
    }
    public int[] ia(int N){
        int[] ans = new int[N];
        for(int j=0;j<N;j++){
            ans[j] = i();
        }
        return ans;
    }
    public int[] ia(){
        str = Console.ReadLine().Split(' ');
        counter = 0;
        int[] ans = new int[str.Length];
        for(int j=0;j<str.Length;j++){
            ans[j] = int.Parse(str[j]);
        }
        return ans;
    }
    public long[] la(int N){
        long[] ans = new long[N];
        for(int j=0;j<N;j++){
            ans[j] = l();
        }
        return ans;
    }
    public long[] la(){
        str = Console.ReadLine().Split(' ');
        counter = 0;
        long[] ans = new long[str.Length];
        for(int j=0;j<str.Length;j++){
            ans[j] = long.Parse(str[j]);
        }
        return ans;
    }
    public double[] da(int N){
        double[] ans = new double[N];
        for(int j=0;j<N;j++){
            ans[j] = d();
        }
        return ans;
    }
    public double[] da(){
        str = Console.ReadLine().Split(' ');
        counter = 0;
        double[] ans = new double[str.Length];
        for(int j=0;j<str.Length;j++){
            ans[j] = double.Parse(str[j]);
        }
        return ans;
    }
    public List<int>[] g(int N,int[] f,int[] t){
        List<int>[] ans = new List<int>[N];
        for(int j=0;j<N;j++){
            ans[j] = new List<int>();
        }
        for(int j=0;j<f.Length;j++){
            ans[f[j]].Add(t[j]);
            ans[t[j]].Add(f[j]);
        }
        return ans;
    }
    public List<int>[] g(int N,int M){
        List<int>[] ans = new List<int>[N];
        for(int j=0;j<N;j++){
            ans[j] = new List<int>();
        }
        for(int j=0;j<M;j++){
            int f = i()-1;
            int t = i()-1;
            ans[f].Add(t);
            ans[t].Add(f);
        }
        return ans;
    }
    public List<int>[] g(){
        int N = i();
        int M = i();
        List<int>[] ans = new List<int>[N];
        for(int j=0;j<N;j++){
            ans[j] = new List<int>();
        }
        for(int j=0;j<M;j++){
            int f = i()-1;
            int t = i()-1;
            ans[f].Add(t);
            ans[t].Add(f);
        }
        return ans;
    }
}
public static class Define{
    public const long mod = 1000000007;
}
public static class Debug{
    public static void Print(double[,,] k){
        for(int i=0;i<k.GetLength(0);i++){
            for(int j=0;j<k.GetLength(1);j++){
                for(int l=0;l<k.GetLength(2);l++){
                    Console.Write(k[i,j,l]+" ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
        }
    }
    public static void Print(double[,] k){
        for(int i=0;i<k.GetLength(0);i++){
            for(int j=0;j<k.GetLength(1);j++){
                Console.Write(k[i,j]+" ");
            }
            Console.WriteLine();
        }
    }
    public static void Print(double[] k){
        for(int i=0;i<k.Length;i++){
            Console.WriteLine(k[i]);
        }
    }
    public static void Print(long[,,] k){
        for(int i=0;i<k.GetLength(0);i++){
            for(int j=0;j<k.GetLength(1);j++){
                for(int l=0;l<k.GetLength(2);l++){
                    Console.Write(k[i,j,l]+" ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
        }
    }
    public static void Print(long[,] k){
        for(int i=0;i<k.GetLength(0);i++){
            for(int j=0;j<k.GetLength(1);j++){
                Console.Write(k[i,j]+" ");
            }
            Console.WriteLine();
        }
    }
    public static void Print(long[] k){
        for(int i=0;i<k.Length;i++){
            Console.WriteLine(k[i]);
        }
    }
    public static void Print(int[,,] k){
        for(int i=0;i<k.GetLength(0);i++){
            for(int j=0;j<k.GetLength(1);j++){
                for(int l=0;l<k.GetLength(2);l++){
                    Console.Write(k[i,j,l]+" ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
        }
    }
    public static void Print(int[,] k){
        for(int i=0;i<k.GetLength(0);i++){
            for(int j=0;j<k.GetLength(1);j++){
                Console.Write(k[i,j]+" ");
            }
            Console.WriteLine();
        }
    }
    public static void Print(int[] k){
        for(int i=0;i<k.Length;i++){
            Console.WriteLine(k[i]);
        }
    }
}