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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# coding: utf-8
# Your code here!
from itertools import accumulate, groupby

n,m = [int(i) for i in input().split()]
lra = [[int(i) for i in input().split()] for _ in range(m)] + [[n+1,n+1,0]]
compare_r = lambda x: x[1]
lra.sort(key = compare_r)

imos = [0]*(n+2)

left = [0]*(n+2) # l[i] = [0,i)に含まれる区間でdp
rprev = 0
c=0
for rr,gp in groupby(lra, compare_r):
    for l,r,a in gp:
        l-=1
        imos[l] += a
        imos[r] -= a
        c+=a

    cc = left[rprev] + max(0,c)
    for i in range(rprev+1,rr+1):
        left[i] = cc
    rprev = rr

    c=0

imos = list(accumulate(imos))

dp = [0]*(n+1)
for i in range(n):
    dp[i] = imos[i] + left[i]


#print(sorted(lra, key=compare_r))
#print(imos)
#print(left)
#print(dp)
print(max(dp))