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)

use std::io::*;
fn dijkstra(start: usize, graph: &Vec<Vec<(usize, i64)>>) -> Vec<i64> {
    let mut dist = vec![std::i64::MAX; graph.len()];
    dist[start] = 0;
    let mut bh = std::collections::BinaryHeap::new();
    bh.push((0i64, start));
    while let Some((cost, v)) = bh.pop() {
        if dist[v] < -cost {
            continue;
        }
        for e in graph[v].iter() {
            let nv = e.0;
            let nc = e.1;
            if dist[nv] > -cost + nc {
                dist[nv] = -cost + nc;
                bh.push((-dist[nv], nv));
            }
        }
    }
    dist
}
fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let m: usize = itr.next().unwrap().parse().unwrap();
    let mut g: Vec<Vec<(usize, i64)>> = vec![Vec::new(); n];
    for _ in 0..m {
        let l: usize = itr.next().unwrap().parse().unwrap();
        let r: usize = itr.next().unwrap().parse().unwrap();
        let c: i64 = itr.next().unwrap().parse().unwrap();
        g[l - 1].push((r - 1, c));
    }
    for i in (1..n).rev() {
        g[i].push((i - 1, 0));
    }
    let d = dijkstra(0, &g);
    if d[n - 1] == std::i64::MAX {
        println!("-1");
    } else {
        println!("{}", d[n - 1]);
    }
}