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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const int M2 = 998244353;
    const long LM = (long)1e18;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    const string dstring = "RDLU";
    static void Main()
    {
        int n, m;
        sc.Multi(out n, out m);
        var sg = new LazySegtree<long, long>(n, Math.Max, (x, y, len) => x + y, (x, y) => x + y, 0);
        var q = new List<P>[n];
        for (int i = 0; i < n; i++)
            q[i] = new List<P>();

        for (int i = 0; i < m; i++)
        {
            int l, r, a;
            sc.Multi(out l, out r, out a);
            q[r - 1].Add(new P(l - 1, a));
        }
        for (int i = 0; i < n; i++)
        {
            sg.update(i, i + 1, Math.Max(sg.run(0, i), 0));
            foreach (var item in q[i])
                sg.update(item.v1, i + 1, item.v2);
        }
        Prt(Math.Max(sg.run(0, n), 0));
        sw.Flush();
    }

    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));
}
class pair<T, U> : IComparable<pair<T, U>>
{
    public T v1;
    public U v2;
    public pair(T v1, U v2) {
        this.v1 = v1;
        this.v2 = v2;
    }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) {
        a = v1; b = v2;
    }
}
static class util
{
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static T sq<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan
{
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => Console.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P {
        get {
            int a, b;
            Multi(out a, out b);
            return new P(a, b);
        }
    }
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
}

class LazySegtree<T, U> {
    int n;
    T[] data;
    U[] lazy;
    bool[] is_lazy;
    Func<T, T, T> calc;
    Func<T, U, int, T> apply;
    Func<U, U, U> merge;
    T ex_data;

    public LazySegtree(int m, Func<T, T, T> calc, Func<T, U, int, T> apply, Func<U, U, U> merge, T ex_data) {
        this.calc = calc;
        this.apply = apply;
        this.merge = merge;
        this.ex_data = ex_data;
        n = 1;
        while (n < m) n <<= 1;
        data = new T[n * 2 - 1];
        lazy = new U[n * 2 - 1];
        is_lazy = new bool[n * 2 - 1];
        for (int i = 0; i < data.Length; i++) data[i] = ex_data;
    }
    public LazySegtree(int m, Func<T, T, T> calc, Func<T, U, int, T> apply, Func<U, U, U> merge, T ex_data, T ini) : this(m, calc, apply, merge, ex_data) {
        for (int i = 0; i < m; i++) data[i + n - 1] = ini;
        for (int i = n - 2; i >= 0; i--) data[i] = calc(data[i * 2 + 1], data[i * 2 + 2]);
    }
    public LazySegtree(int m, Func<T, T, T> calc, Func<T, U, int, T> apply, Func<U, U, U> merge, T ex_data, IList<T> ini) : this(m, calc, apply, merge, ex_data) {
        for (int i = 0; i < m; i++) data[i + n - 1] = ini[i];
        for (int i = n - 2; i >= 0; i--) data[i] = calc(data[i * 2 + 1], data[i * 2 + 2]);
    }
    void assign_lazy(int k, U x) {
        if (k >= lazy.Length) return;
        if (is_lazy[k]) lazy[k] = merge(lazy[k], x);
        else {
            is_lazy[k] = true;
            lazy[k] = x;
        }
    }
    void eval(int k, int len){
        if (!is_lazy[k]) return;
        assign_lazy(k * 2 + 1, lazy[k]);
        assign_lazy(k * 2 + 2, lazy[k]);
        data[k] = apply(data[k], lazy[k], len);
        is_lazy[k] = false;
    }
    T update(int s, int t, U x, int k, int l, int r) {
        eval(k, r - l);
        if (r <= s || t <= l) return data[k];
        if (s <= l && r <= t) {
            assign_lazy(k, x);
            return apply(data[k], lazy[k], r - l);
        }
        return data[k] = calc(update(s, t, x, k * 2 + 1, l, (l + r) / 2),
                              update(s, t, x, k * 2 + 2, (l + r) / 2, r));
    }
    T run(int s, int t, int k, int l, int r) {
        eval(k, r - l);
        if (r <= s || t <= l) return ex_data;
        if (s <= l && r <= t) return data[k];
        return calc(run(s, t, k * 2 + 1, l, (l + r) / 2),
                    run(s, t, k * 2 + 2, (l + r) / 2, r));
    }

    // [s, t)
    public void update(int s, int t, U x) => update(s, t, x, 0, 0, n);
    // [s, t)
    public T run(int s, int t) => run(s, t, 0, 0, n);
}