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: Wrong Answer)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[macro_export]
macro_rules ! chmax { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: max ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! chmin { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: min ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! max { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: max ( $ x , max ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! min { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: min ( $ x , min ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! dvec { ( $ t : expr ; $ len : expr ) => { vec ! [ $ t ; $ len ] } ; ( $ t : expr ; $ len : expr , $ ( $ rest : expr ) ,* ) => { vec ! [ dvec ! ( $ t ; $ ( $ rest ) ,* ) ; $ len ] } ; }
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    input!{
        n:usize,m:usize,
        LRC:[(usize,usize,i64);m]
    }

    let mut lrc = vec![];
    for (l,r,c) in LRC {
        lrc.push((l-1,r-1,c));
    }

    lrc.sort_by_key(|&x| x.1);
    lrc.sort_by_key(|&x| x.0);

    let max = 1<<60;
    let mut seg: SEG<MIN_RUQ> = SEG::new(max, n);
    let (l,r,c) = lrc[0];
    seg.update(l,r+1,c);

    for i in 1..m {
        let (l,r,c) = lrc[i];

        let precost = seg.query(l, r+1);

        let newcost = precost+c;

        let oldval = seg.query(r, r+1);
        if oldval > newcost {
            seg.update(r, r+1, newcost);
        }
    }

    let ncost = seg.query(n-1, n);
    if ncost >= max {
        println!("-1"); 
    } else {
        println!("{}", ncost);
    }
}

struct MIN_RUQ;
impl SEGImpl for MIN_RUQ {
    type Monoid = i64;
    type OperatorMonoid = i64;
    fn m0() -> Self::Monoid {
        1<<60
    }
    fn om0() -> Self::OperatorMonoid {
        0
    }
    fn f(x: Self::Monoid, y: Self::Monoid) -> Self::Monoid {
        std::cmp::min(x, y)
    }
    fn g(x: Self::Monoid, y: Self::OperatorMonoid, len: usize) -> Self::Monoid {
        y
    }
    fn h(x: Self::OperatorMonoid, y: Self::OperatorMonoid) -> Self::OperatorMonoid {
        y
    }
}
#[doc = " https://ei1333.github.io/luzhiled/snippets/structure/segment-tree.html"]
trait SEGImpl {
    type Monoid: Copy;
    type OperatorMonoid: Copy + PartialEq;
    fn m0() -> Self::Monoid;
    fn om0() -> Self::OperatorMonoid;
    fn f(x: Self::Monoid, y: Self::Monoid) -> Self::Monoid;
    fn g(x: Self::Monoid, y: Self::OperatorMonoid, len: usize) -> Self::Monoid;
    fn h(x: Self::OperatorMonoid, y: Self::OperatorMonoid) -> Self::OperatorMonoid;
}
struct SEG<T: SEGImpl> {
    n: usize,
    data: Vec<T::Monoid>,
    lazy: Vec<T::OperatorMonoid>,
    weight: Vec<usize>,
}
impl<T: SEGImpl> SEG<T> {
    fn new(init: T::Monoid, n: usize) -> SEG<T> {
        let mut m = 1;
        while m < n {
            m *= 2;
        }
        SEG {
            n: m,
            data: vec![init; m * 2],
            lazy: vec![T::om0(); m * 2],
            weight: Self::mk_weight(&vec![1; n]),
        }
    }
    fn mk_weight(xs: &[usize]) -> Vec<usize> {
        let n = xs.len();
        let mut m = 1;
        while m < n {
            m *= 2;
        }
        let mut res = vec![0; 2 * m];
        for i in 0..n {
            res[m + i] = xs[i];
        }
        for k in (1..m).rev() {
            let l = 2 * k;
            let r = 2 * k + 1;
            res[k] = res[l] + res[r];
        }
        res
    }
    fn set_weight(&mut self, weight: &[usize]) {
        self.weight = Self::mk_weight(weight);
    }
    fn propagate(&mut self, k: usize, len: usize) {
        let len = self.weight[k];
        if self.lazy[k] != T::om0() {
            if k < self.n {
                self.lazy[2 * k + 0] = T::h(self.lazy[2 * k + 0], self.lazy[k]);
                self.lazy[2 * k + 1] = T::h(self.lazy[2 * k + 1], self.lazy[k]);
            }
            self.data[k] = T::g(self.data[k], self.lazy[k], len);
            self.lazy[k] = T::om0();
        }
    }
    fn do_update(
        &mut self,
        a: usize,
        b: usize,
        x: T::OperatorMonoid,
        k: usize,
        l: usize,
        r: usize,
    ) -> T::Monoid {
        self.propagate(k, r - l);
        if r <= a || b <= l {
            self.data[k]
        } else if a <= l && r <= b {
            self.lazy[k] = T::h(self.lazy[k], x);
            self.propagate(k, r - l);
            self.data[k]
        } else {
            self.data[k] = T::f(
                self.do_update(a, b, x, 2 * k + 0, l, (l + r) >> 1),
                self.do_update(a, b, x, 2 * k + 1, (l + r) >> 1, r),
            );
            self.data[k]
        }
    }
    fn update(&mut self, a: usize, b: usize, x: T::OperatorMonoid) -> T::Monoid {
        let n = self.n;
        self.do_update(a, b, x, 1, 0, n)
    }
    fn do_query(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> T::Monoid {
        self.propagate(k, r - l);
        if r <= a || b <= l {
            T::m0()
        } else if a <= l && r <= b {
            self.data[k]
        } else {
            T::f(
                self.do_query(a, b, 2 * k + 0, l, (l + r) >> 1),
                self.do_query(a, b, 2 * k + 1, (l + r) >> 1, r),
            )
        }
    }
    fn query(&mut self, a: usize, b: usize) -> T::Monoid {
        let n = self.n;
        self.do_query(a, b, 1, 0, n)
    }
}