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: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;

/**
 * Counting of Trees
 */
public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();
            int M = sc.nextInt();

            PriorityQueue<LRC> queue = new PriorityQueue<>((o1, o2) -> {
                int comp = Long.compare(o1.C, o2.C);
                if (comp == 0) {
                    comp = Integer.compare(o1.L, o2.L);
                    if (comp == 0) {
                        comp = Integer.compare(o1.R, o2.R);
                    }
                }
                return comp;
            });

            for (int i = 0; i < M; i++) {
                LRC lrc = new LRC();
                lrc.L = sc.nextInt() - 1;
                lrc.R = sc.nextInt() - 1;
                lrc.C = sc.nextLong();
                queue.add(lrc);
            }

            long[] dp = new long[N];
            for (int i = 1; i < N; i++) {
                dp[i] = Long.MAX_VALUE;
            }

            int r = 0;
            List<LRC> tmp = new ArrayList<>();
            while (queue.size() > 0) {
                LRC lrc = queue.poll();
                if (r < lrc.L) {
                    tmp.add(lrc);
                    continue;
                }

                if (lrc.R <= r) {
                    continue;
                }

                for (int i = lrc.L + 1; i <= lrc.R; i++) {
                    dp[i] = Math.min(dp[i], dp[lrc.L] + lrc.C);
                }

                r = lrc.R;

                queue.addAll(tmp);
            }

            long ans = dp[N - 1];
            if (ans == Long.MAX_VALUE) {
                ans = -1;
            }

            System.out.println(ans);
        }
    }

    static class LRC {

        int L;

        int R;

        long C;

    }

}