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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.math.*;
public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		ArrayList<State>[] map=new ArrayList[n];
		map[0]=new ArrayList<>();
		for(int i=n-1; i>=1; i--){
			map[i]=new ArrayList<>();
			map[i].add(new State(i-1,0));
		}
		for(int i=0; i<m; i++){
			int l=sc.nextInt()-1;
			int r=sc.nextInt()-1;
			int c=sc.nextInt();
			map[l].add(new State(r,c));
		}
		PriorityQueue<State> q=new PriorityQueue<>();
		int[] dist=new int[n];
		Arrays.fill(dist,-1);
		q.add(new State(0,0));
		while(!q.isEmpty() && dist[n-1]==-1){
			State s=q.poll();
			if(dist[s.l]!=-1){
				continue;
			}
			dist[s.l]=s.c;
			for(State ss:map[s.l]){
				if(dist[ss.l]==-1){
					q.add(new State(ss.l,ss.c+s.c));
				}
			}
		}
		System.out.println(dist[n-1]);
	}
	static class State implements Comparable<State>{
		int l,c;
		State(int l,int c){
			this.l=l;
			this.c=c;
		}
		@Override
		public int compareTo(State o){
			return this.c-o.c;
		}
	}
}