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 (GCC 5.4.1) (judge verdict: Accepted)

n=1<<18;L[1<<18],p;F[1<<18],X[1<<18];i;long D[1<<20],Z[1<<20],A[1<<18],x,z;
//long f(a,k,l,r,b){return a<=l&r<i+2?D[k]+(Z[k]+=x):l<=i&a<r?(D[k]=fmax(f(a,2*k,l,b),f(a,2*k+1,b=l+r>>1,r)))+Z[k]:D[k]+Z[k];}
//long f(a,k,l,r,b,q){q=a<=l&r<i+2;return(D[k]=l<=i&a<r&!q?fmax(f(a,2*k,l,b),f(a,2*k+1,b=l+r>>1,r)):D[k])+(Z[k]+=q?x:0);}
long f(a,k,l,r,b){return(Z[k]+=(b=a<=l&r<i+2)?x:0)+(D[k]=l<=i&a<r&!b?fmax(f(a,2*k,l,b),f(a,2*k+1,b=l+r>>1,r)):D[k]);}

main(j){for(gets(L);~scanf("%d%d%ld",L+j,&p,A+j);F[p]=j++)X[j]=F[p];for(;p?:(p=F[++i],f(i,1,0,n),n/i);p=X[p])x=A[p],x=f(L[p],1,0,n);printf("%ld",x);}