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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
	static final long MOD=1000000007;//998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		int M=sc.nextInt();
		ArrayList<Pair2> arrayList=new ArrayList<>();
		for (int i = 0; i < M; i++) {
			int x=sc.nextInt()-1;
			int y=sc.nextInt()-1;
			int z=sc.nextInt();
			arrayList.add(new Pair2(x, y, z));
		}
		Collections.sort(arrayList);
		LazysegTreemin lazysegTreemin=new LazysegTreemin(N);
		int c=0;
		for (int i = 0; i < N; i++) {
			long sum=0;
			long max=-lazysegTreemin.getmin(0, i, 0, 0, lazysegTreemin.size);
			if (i==0) {
				max=0;
			}
			while (c<M) {
				if (arrayList.get(c).y!=i) {
					break;
				}
				int l=arrayList.get(c).x;
				long w=(long)arrayList.get(c).z;
				sum+=w;
				if (l<i) {
					lazysegTreemin.add(l, i, -w, 0, 0, lazysegTreemin.size);
				}
				
				c++;
			}
			lazysegTreemin.add(i, i+1, -max-sum, 0, 0, lazysegTreemin.size);
		}
		System.out.println(lazysegTreemin.getmin(0, 0, 0, 0, lazysegTreemin.size));
		System.out.println(Math.max(0, -lazysegTreemin.getmin(0, N, 0, 0, lazysegTreemin.size)));
   	}
	static class LazysegTreemin{
		int size;
		long[] dat;
		long[] lazy;
		long INF=Long.MAX_VALUE/2;
		public LazysegTreemin(int n) {
			int n_=1;
			while (n_<n) {
				n_*=2;
			}
			size=n_;
			dat=new long[2*n_-1];
			lazy=new long[2*n_-1];
		}
		void propagate(int k,int l,int r) {
			if (lazy[k]!=0) {
				dat[k] += lazy[k];
				if(r - l > 1) {
		            lazy[2*k+1] += lazy[k];
		            lazy[2*k+2] += lazy[k];
		        }
		        lazy[k] = 0;
			}
		}
		void add(int a,int b,long x,int k,int l,int r) {//a<=x<b加算　add(...,0,0,seg.size)で呼ぶ
			this.propagate(k,l,r);
			if (a<=l&&r<=b) {
				lazy[k]+=x;
				this.propagate(k,l,r);
			}
			else if (l<b&&a<r) {//交わっている場合
				this.add(a, b, x, k*2+1,l,(l+r)/2);
				this.add(a, b, x, k*2+2, (l+r)/2, r);
				dat[k] = Math.min(dat[2*k+1],dat[2*k+2]);
			}
		}
		long getmin(int a,int b,int k,int l,int r) {//kが節点番号,l rがその節点番号の範囲
			if (r<=a||b<=l) {
				return INF;
			}
			this.propagate(k, l, r);
			if (a<=l&&r<=b) {
				return dat[k];
			}
			else {
				long vl=this.getmin(a, b, k*2+1,l,(l+r)/2);
				long vr=this.getmin(a, b, k*2+2, (l+r)/2, r);
				return (Math.min(vl, vr));
			}
		}
	}
	static class Pair2 implements Comparable<Pair2>{
    	public int x;
    	public int y;
    	public int z;
    	public Pair2(int x,int y,int z) {
    		this.x=x;
    		this.y=y;
    		this.z=z;
    	}
    	@Override
    	public boolean equals(Object obj) {
    		if(obj instanceof Pair2) {
    			Pair2 other = (Pair2) obj;
    			return other.x==this.x && other.y==this.y&& other.z==this.z;
    		}
    		return false;
    	}//同値の定義
    	@Override
    	public int hashCode() {
    		return Objects.hash(this.x,this.y,this.z);
    	}//これ書かないと正しく動作しない（要　勉強）
    	@Override
    	public int compareTo( Pair2 p2 ){
    		if (this.y>p2.y) {
    			return 1;
    		}
    		else if (this.y<p2.y) {
    			return -1;
    		}
    		else {
    			return 0;
    		}
    	}
    }
		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
	}