Problem:
Score : 100 points

Problem Statement

Consider a string of length N consisting of 0 and 1.
The score for the string is calculated as follows:

For each i (1 \leq i \leq M), a_i is added to the score if the string contains 1 at least once between the l_i-th and r_i-th characters (inclusive).

Find the maximum possible score of a string.

Constraints

All values in input are integers.

1 \leq N \leq 2 × 10^5

1 \leq M \leq 2 × 10^5

1 \leq l_i \leq r_i \leq N

|a_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
l_1 r_1 a_1
l_2 r_2 a_2
:
l_M r_M a_M

Output

Print the maximum possible score of a string.

Sample Input 1

5 3
1 3 10
2 4 -10
3 5 10

Sample Output 1

20

The score for 10001 is a_1 + a_3 = 10 + 10 = 20.

Sample Input 2

3 4
1 3 100
1 1 -10
2 2 -20
3 3 -30

Sample Output 2

90

The score for 100 is a_1 + a_2 = 100 + (-10) = 90.

Sample Input 3

1 1
1 1 -10

Sample Output 3

0

The score for 0 is 0.

Sample Input 4

1 5
1 1 1000000000
1 1 1000000000
1 1 1000000000
1 1 1000000000
1 1 1000000000

Sample Output 4

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 5

6 8
5 5 3
1 1 10
1 6 -8
3 6 5
3 4 9
5 5 -2
1 3 -6
4 6 -7

Sample Output 5

10

For example, the score for 101000 is a_2 + a_3 + a_4 + a_5 + a_7 = 10 + (-8) + 5 + 9 + (-6) = 10.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[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 ! 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,
        lra:[(usize,usize,i64);M]
    }
    let mut prev = vec![vec![]; N+1];
    for (l,r,a) in lra { 
        prev[r].push((l,a));
    }
    let mut seg: SEG<MAX_RAQ> = SEG::new(0, N+1);
    for r in 1..N+1 {
        // rより前のマックス
        let curmax = seg.query(0, r);
        // キャリーオーバー
        seg.update(r, r+1, curmax);
        for &(l,a) in &prev[r] {
            seg.update(l,r+1,a);
        }
    }
    let res = seg.query(1,N+1);
    let ans = if res < 0 { 0 } else { res };
    println!("{}", ans);
}
#[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>,
}
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],
        }
    }
    fn propagate(&mut self, k: usize, len: usize) {
        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)
    }
}
struct MAX_RAQ;
impl SEGImpl for MAX_RAQ {
    type Monoid = i64;
    type OperatorMonoid = i64;
    fn m0() -> Self::Monoid {
        std::i64::MIN
    }
    fn om0() -> Self::OperatorMonoid {
        0
    }
    fn f(x: Self::Monoid, y: Self::Monoid) -> Self::Monoid {
        std::cmp::max(x, y)
    }
    fn g(x: Self::Monoid, y: Self::OperatorMonoid, len: usize) -> Self::Monoid {
        x + y
    }
    fn h(x: Self::OperatorMonoid, y: Self::OperatorMonoid) -> Self::OperatorMonoid {
        x + y
    }
}