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::cmp;
// use std::collections::HashMap;
// use std::collections::HashSet;
// use std::collections::VecDeque;
use std::collections::BTreeSet;


// const INF: i64 = 1_000_000_000;
// const MOD: i64 = 998244353;

fn main() {
    let cin = stdin();
    let mut sc = Scanner::new(cin.lock());
    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut lrcs = vec![];
    for _ in 0..m {
        let l: usize = sc.read();
        let r: usize = sc.read();
        let c: i64 = sc.read();
        lrcs.push((l, r, c));
    }

    lrcs.sort_by_key(|&(l, r, c)| l);
    let mut setc = BTreeSet::new();
    let mut setx = BTreeSet::new();
    setc.insert((0, 1, 0));
    setx.insert((1, 0, 0));

    // let inf = 1_000_000_000_000_000_000i64;
    // let mut ans = vec![inf; n+1];
    // ans[0] = 0;
    let mut i = 0;
    for (l, r, c) in lrcs {
        // println!("{:?}", (l, r, c));
        let setx_ok = setx.split_off(&(l, 0, 0));
        for (x, cost, nonce) in setx.into_iter() {
            setc.remove(&(cost, x, nonce));
        }
        setx = setx_ok;
        if let Some(&(cost, _, _)) = setc.iter().next() {
            let new_cost = cost + c;
            i += 1;
            setc.insert((new_cost, r, i));
            setx.insert((r, new_cost, i));
        }
    }

    {
        let setx_ok = setx.split_off(&(n, 0, 0));
        for (x, cost, nonce) in setx.into_iter() {
            setc.remove(&(cost, x, nonce));
        }
        setx = setx_ok;
    }
    let tmp = setc.iter().next();
    let ans = if let Some(&(cost, _, _)) = tmp {
        cost
    } else {
        -1
    };
    println!("{}", ans);
}

// thanks, ir5
use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }
}