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)

const INF: i64=std::i64::MAX/2;
fn main() {
    let (n,m) = {
        let t = rv::<usize>();
        (t[0], t[1])
    };
    let mut g = vec![vec![];n];
    for _ in 0..m {
        let t = rv::<usize>();
        let (l,r,c) = (t[0]-1,t[1]-1,t[2]as i64);
        g[l].push((r,c));
    }
    for i in 1..n {
        g[i].push((i-1,0));
    }
    let mut q = std::collections::BinaryHeap::new();
    q.push((INF-0,n-0));
    let mut d = vec![INF;n];
    while let Some((s,v)) = q.pop() {
        let s=INF-s;
        let v=n-v;
        if d[v]<=s {continue;}
        d[v]=s;
        if v==n-1 {break;}
        for &(u,c) in &g[v] {
            q.push((INF-(s+c),n-u));
        }
    }
    let t = d[n-1];
    println!("{}",if t<INF {t} else {-1});
}
fn rl() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}
fn rv<T>() -> Vec<T>
  where T: std::str::FromStr, T::Err: std::fmt::Debug, {
    rl().split_whitespace().map(|x|x.parse::<T>().unwrap()).collect()
}