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_byline {
    ($($r:tt)* ) => {
        let stdin = std::io::stdin();
        let mut q = std::collections::VecDeque::new();
        let mut next = || {
            if q.is_empty() {
                let mut s = String::new();
                stdin.read_line(&mut s);
                for v in s.split_whitespace() {
                    q.push_back(v.to_string());
                }
            }
            q.pop_front().unwrap()
        };
        input_inner!{next, $($r)*}
    };

}

#[allow(unused_macros)]
macro_rules! input {
    ($($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>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

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

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

trait Printable {
    fn p(&self);
}

impl<T: std::fmt::Display> Printable for T {
    fn p(&self) {
        println!("{}", self);
    }
}

impl<T: std::fmt::Display> Printable for [T] {
    fn p(&self) {
        for i in 0..self.len() {
            if i != 0 {
                print!(" ");
            }
            print!("{}", self[i]);
        }
        println!("");
    }
}

struct SegmentTree {
    n: usize,
    data: Vec<i64>,
}

fn gcd(a: usize, b: usize) -> usize {
    if b != 0 {
        gcd(b, a % b)
    } else {
        a
    }
}

impl SegmentTree {
    fn f(&self, a: i64, b: i64) -> i64 {
        min(a, b)
    }

    pub fn initial() -> i64 {
        1 << 60
    }

    fn new(size: usize) -> Self {
        let n = {
            let mut res = 1;
            while res < size {
                res <<= 1
            }
            res
        };
        let data = vec![Self::initial(); n * 2 - 1];
        SegmentTree { n: n, data: data }
    }

    fn update(&mut self, k: usize, a: i64) {
        let mut index = k + self.n - 1;
        self.data[index] = a;
        while index > 0 {
            index = (index - 1) / 2;
            self.data[index] = self.f(self.data[index * 2 + 1], self.data[index * 2 + 2]);
        }
    }

    // [a, b)
    fn query(&mut self, a: usize, b: usize) -> i64 {
        let (l, r) = (0, self.n);
        self.query_iter(a, b, 0, l, r)
    }

    fn query_iter(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> i64 {
        if r <= a || b <= l {
            Self::initial()
        } else if a <= l && r <= b {
            self.data[k]
        } else {
            let vl = self.query_iter(a, b, k * 2 + 1, l, (l + r) / 2);
            let vr = self.query_iter(a, b, k * 2 + 2, (l + r) / 2, r);
            self.f(vl, vr)
        }
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

fn main() {
    input! {
        n: usize,
        m: usize,
        mut edges: [(usize1, usize1, usize); m],
    }

    let mut st = SegmentTree::new(n + 1);
    st.update(0, 0);
    edges.sort();
    for &(l, r, c) in &edges {
        let next = st.query(l, r) as usize + c;
        let old = st.query(r, r + 1) as usize;
        st.update(r, min(next, old) as i64);
    }

    let a = st.query(n - 1, n);
    if a >= 1 << 60 {
        println!("-1");
    } else {
        println!("{}", a);
    }
}