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.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		var a=sc.Arr(s[1],()=>sc.Ia);
		a=a.OrderBy(x=>x[1]).ThenBy(x=>x[2]).ThenBy(x=>x[0]).ToArray();
		long inf=long.MaxValue/2;
		St st=new St(s[0]+1,false,false,inf);
		st.Ud(1,0);
		for(int i = 0;i<s[1];i++) {
			long p=st.Get(a[i][0],a[i][1]-1).d+a[i][2];
			if(st.Get(a[i][1],a[i][1]).d>p){
				st.Ud(a[i][1],p);
			}
		}
		long ans=st.Get(s[0],s[0]).d;
		Console.WriteLine("{0}",ans>=inf?-1:ans);
	}
}
public class St{
	public class Dt{
		public int n;
		public long d;
		public Dt(long d,int n){this.d=d;this.n=n;}
	}
	public Dt[] dat;
	private int m=1;
	private bool mm,ku;
	private Dt du;
	private Func<Dt,Dt,bool> compare;
	public St(int n,bool mm,bool ku,long df){
		this.mm=mm;this.ku=ku;
		if(mm){du=new Dt(long.MinValue,-1);compare=CoMax;}
		else{du=new Dt(long.MaxValue,-1);compare=CoMin;}
		while(m<n){m<<=1;}
		m--;
		dat=new Dt[m+n+1];
		dat[m+n]=du;
		for(int i=m+n-1;i>=m;i--){dat[i]=new Dt(df,i-m);}
		for(int i=m-1;i>=0;i--){dat[i]=(i<<1)+1<m+n?dat[(i<<1)+1]:du;}
	}
	private bool CoMax(Dt x,Dt y){return x.d>y.d;}
	private bool CoMin(Dt x,Dt y){return x.d<y.d;}
	public void Ud(int q,long b){
		q+=m;
		if(ku){b+=dat[q].d;}
		dat[q].d=du.d;
		dat[q]=new Dt(b,q-m);
		q=(q-1)>>1;
		while(q>=0){
			Dt o=compare(dat[2*q+1],dat[2*q+2])?dat[2*q+1]:dat[2*q+2];
			if(dat[q]==o){break;}
			dat[q]=o;
			q=(q-1)>>1;
		}
	}
	private Dt Fdg(int a,int b,int k,int l,int r){
		if(r<a||b<l){return du;}
		if(a<=l&&r<=b){return dat[k];}
		Dt p=Fdg(a,b,k*2+1,l,(l+r)>>1);
		Dt q=Fdg(a,b,k*2+2,(l+r+1)>>1,r);
		return compare(p,q)?p:q;
	}
	public Dt Get(int a,int b){return Fdg(a,b,0,0,m);}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}