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(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}


pub mod ds {
    pub struct SegmentTree<T, F> {
        n: usize,
        pub data: Vec<T>,
        init: T,
        f: F,
    }
    impl<T, F> SegmentTree<T, F>
    where
        T: Copy,
        F: Fn(T, T) -> T,
    {
        pub fn new(size: usize, init: T, f: F) -> Self {
            let mut n = 1;
            while n < size {
                n *= 2;
            }
            SegmentTree {
                n: n,
                init: init,
                f: f,
                data: vec![init; n * 2 - 1],
            }
        }
        pub fn update(&mut self, mut k: usize, x: T) {
            k += self.n - 1;
            self.data[k] = (self.f)(self.data[k], x);
            while k > 0 {
                k = (k - 1) / 2;
                self.data[k] = (self.f)(self.data[2 * k + 1], self.data[2 * k + 2]);
            }
        }
        pub fn set(&mut self, mut k: usize, x: T) {
            k += self.n - 1;
            self.data[k] = x;
            while k > 0 {
                k = (k - 1) / 2;
                self.data[k] = (self.f)(self.data[2 * k + 1], self.data[2 * k + 2]);
            }
        }
        #[doc = " [l, r)"]
        pub fn query(&self, l: usize, r: usize) -> T {
            assert!(l < r);
            self.do_query(l, r, 0, 0, self.n)
        }
        fn do_query(&self, l: usize, r: usize, k: usize, a: usize, b: usize) -> T {
            if b <= l || r <= a {
                self.init
            } else if l <= a && b <= r {
                self.data[k]
            } else {
                let q1 = self.do_query(l, r, k * 2 + 1, a, (a + b) / 2);
                let q2 = self.do_query(l, r, k * 2 + 2, (a + b) / 2, b);
                (self.f)(q1, q2)
            }
        }
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};
#[allow(unused_imports)]
use std::io::{stdout, stdin, BufWriter, Write};

use std::cmp::Ordering;
use ds::SegmentTree;

#[derive(Debug, Copy, Clone, Eq, PartialEq)]
struct Rev(usize);

impl Ord for Rev {
    fn cmp(&self, other: &Rev) -> Ordering {
        other.0.cmp(&self.0)
    }
}

impl PartialOrd for Rev {
    fn partial_cmp(&self, other: &Rev) -> Option<Ordering> {
        Some(other.0.cmp(&self.0))
    }
}

fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }

    input!{
      n: usize,
      m: usize,
      mut lrcs: [(usize1, usize, usize); m],
    }
    lrcs.sort();

    const INF: usize = 1 << 60;
    let mut seg = SegmentTree::new(n, INF, |a, b|min(a, b));
    seg.set(0, 0);

    for (l, r, c) in lrcs {
        let a = seg.query(r-1, r);
        let b = seg.query(l, r) + c;
        seg.update(r-1, min(a, b));
    }
    let ans = seg.query(n-1, n);
    if ans >= INF {
        puts!("{}\n", -1);
    } else {
        puts!("{}\n", ans);
    }
}