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::collections::{BTreeMap, BinaryHeap};

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner(s.lock());
    let n: usize = sc.read();
    let m: usize = sc.read();

    let mut edges = vec![vec![]; n];
    for _ in 0..m {
        let l: usize = sc.read::<usize>() - 1;
        let r: usize = sc.read::<usize>() - 1;
        let c: i64 = sc.read();
        edges[l].push((r, c));
    }

    //    eprintln!("{:?}", edges);
    let mut heap = BinaryHeap::new();
    heap.push((0, 0));
    for cur in 0..n {
        while let Some((c, v)) = heap.pop() {
            let z = (-v) as usize;
            if z >= cur {
                heap.push((c, v));
                break;
            }
        }
        if let Some(&(cost, v)) = heap.peek() {
            let v = (-v) as usize;
            let cur_cost = -cost;
            if v == n - 1 {
                println!("{}", cur_cost);
                return;
            }
            for &(next, cost) in edges[cur].iter() {
                let next_cost = cost + cur_cost;
                heap.push((-next_cost, -(next as i64)));
            }
        } else {
            println!("-1");
            return;
        }

        //        eprintln!("{:?}", heap);
    }
}

pub struct Scanner<R>(R);

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}