Problem7295--AtCoder Educational DP Contest —— W - Intervals

7295: AtCoder Educational DP Contest —— W - Intervals

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

Consider a string of length N consisting of 0 and 1. The score for the string is calculated as follows:
  • For each i (1≤i≤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.

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.

Constraints

All values in input are integers.
$1 \leq N \leq 2 × 10^5$
$1 \leq M \leq 2 × 10^5$
$1 \leq l_i \leq r_i \leq N$
$|a_i| \leq 10^9$

Sample 1 Input

5 3
1 3 10
2 4 -10
3 5 10

Sample 1 Output

20
The score for 10001 is $a_1 + a_3 = 10 + 10 = 20$.

Sample 2 Input

3 4
1 3 100
1 1 -10
2 2 -20
3 3 -30

Sample 2 Output

90
The score for 100 is $a_1 + a_2 = 100 + (-10) = 90$.

Sample 3 Input

1 1
1 1 -10

Sample 3 Output

0
The score for 0 is $0$.

1 5
1 1 1000000000
1 1 1000000000
1 1 1000000000
1 1 1000000000
1 1 1000000000

5000000000

Sample 4 Input

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 4 Output

10
For example, the score for 101000 is $a_2 + a_3 + a_4 + a_5 + a_7 = 10 + (-8) + 5 + 9 + (-6) = 10$.

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