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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class W { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		long M = GetLong();
		var list = new List<(long, long, long)>();
		for(long i = 0; i < M; i++)
			list.Add((GetLong(), GetLong(), GetLong()));

		var dp = new LazySegmentTree((int)N + 1);
		var groups = list.GroupBy(x => x.Item2).OrderBy(x => x.Key);
		foreach(var group in groups)
		{
			long r = group.Key;
			long max = dp.Query(0, r);
			dp.RangeUpdate(r, r + 1, max);
			foreach(var t in group)
				dp.RangeUpdate(t.Item1, t.Item2 + 1, t.Item3);
		}
		WriteLine(dp.Query(0, N + 1));
	}
}

public class LazySegmentTree
{
	private int N;
	private long[] dat;
	private long[] lazy;

	public LazySegmentTree(long n)
	{
		N = 1;		
		while(N < n)
			N <<= 1;
			
		dat = new long[2 * N - 1];
		for(long i = 0; i < 2 * N - 1; i++)
			dat[i] = 0;

		lazy = new long[2 * N - 1];
	}

	private void eval(long k, long l, long r)
	{
		if(lazy[k] == 0)
			return;

		dat[k] += lazy[k];

		// propagate to children
		if(r - l > 1)
		{
			lazy[2 * k + 1] += lazy[k];
			lazy[2 * k + 2] += lazy[k];
		}
		lazy[k] = 0;
	}

	public void RangeUpdate(long a, long b, long x, long k = 0, long l = 0, long r = -1)
	{
		if(r == -1)
			r = N;

		// evaluate propagation from parent
		eval(k, l, r);

		if(b <= l || r <= a)
			return;

		if(a <= l && r <= b)
		{
			// update
			lazy[k] += x;
			eval(k, l, r);
		}
		else
		{
			RangeUpdate(a, b, x, 2 * k + 1, l, (l + r) / 2);
			RangeUpdate(a, b, x, 2 * k + 2, (l + r) / 2, r);
			dat[k] = Max(dat[k * 2 + 1], dat[k * 2 + 2]);
		}
	}

	public long Query(long a, long b, long k = 0, long l = 0, long r = -1)
	{
		if(r == -1)
			r = N;

		if(r <= a || b <= l)
			return long.MinValue / 2;

		eval(k, l, r);

		if(a <= l && r <= b)
			return dat[k];
		else
		{
			long vl = Query(a, b, k * 2 + 1, l, (l + r) / 2);
			long vr = Query(a, b, k * 2 + 2, (l + r) / 2, r);
			return Max(vl, vr);
		}
	}
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}