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)
    };

    struct SegmentTree<T: Clone + Copy>{
        n: usize,
        f: fn(T, T) -> T,
        e: T,
        x: Vec<T>
    }

    impl<T: Clone + Copy> SegmentTree<T> {
        fn new(n: usize, f: fn(T, T) -> T, e: T) -> SegmentTree<T> {
            let m = 1 << format!("{:b}", n).len();
            SegmentTree { n: m, f: f, e: e, x: vec![e; 2 * m - 1] }
        }
        fn update(&mut self, i: usize, y: T) {
            let mut j = i + self.n - 1;
            self.x[j] = y;
            while j > 0 {
                j = (j - 1) / 2;
                self.x[j] = (self.f)(self.x[2 * j + 1], self.x[2 * j + 2]);
            }
        }
        fn find(&self, s: usize, t: usize) -> T { self.q(0, 0, self.n, s, t) }
        fn q(&self, i: usize, l: usize, r: usize, s: usize, t: usize) -> T {
            if l >= t || r <= s { self.e }
            else if s <= l && r <= t { self.x[i] }
            else {
                (self.f)(
                    self.q(2 * i + 1, l, (l + r) / 2, s, t),
                    self.q(2 * i + 2, (l + r) / 2, r, s, t)
                )
            }
        }
    }

    const INF: i64 = 1_000_000_000_000_000;
    let mut dp = SegmentTree::new(N + 1, std::cmp::min, INF);
    dp.update(1, 0);
    let mut E = (0..M).map(|i| (L[i], C[i], R[i])).collect::<Vec<_>>();
    E.sort();
    for &(l, c, r) in &E {
        let x = dp.find(l, N + 1);
        if x + c < dp.find(r, N + 1) {
            dp.update(r, x + c);
        }
    }
    let res = dp.find(N, N + 1);
    let ans = if res < INF { res } else { -1 };
    // for i in 1..(N + 1) {
    //     println!("{}: {}", i, dp.find(i, N + 1));
    // }

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