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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (N, M): (usize, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap()
        )
    };
    let (L, R, C): (Vec<usize>, Vec<usize>, Vec<i64>) = {
        let (mut L, mut R, mut C) = (vec![], vec![], vec![]);
        for _ in 0..M {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            L.push(iter.next().unwrap().parse().unwrap());
            R.push(iter.next().unwrap().parse().unwrap());
            C.push(iter.next().unwrap().parse().unwrap());
        }
        (L, R, C)
    };

    let G = {
        let mut G = vec![std::collections::HashMap::new(); N + 1];
        let mut E = (0..M).collect::<Vec<_>>();
        E.sort_by_key(|&i| C[i]);
        E.reverse();
        for &i in &E { G[L[i]].insert(R[i], C[i]); }
        for i in 1..N { G[i + 1].insert(i, 0); }
        G
    };

    const INF: i64 = 1_000_000_000_000_000;
    let mut dp = vec![INF; N + 1];
    let mut q = std::collections::BinaryHeap::new();
    q.push((0, 1));
    while let Some((dist, i)) = q.pop() {
        let dist = -dist;
        if dist < dp[i] {
            dp[i] = dist;
            for (&j, &w) in &G[i] { q.push((-(dist + w), j)); }
        }
    }
    let ans = if dp[N] < INF { dp[N] } else { -1 };

    println!("{}", ans);
}