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.
• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq l_i \leq r_i \leq N$
• $|a_i| \leq 10^9$

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.

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

20

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

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

90

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

1 1
1 1 -10

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

The answer may not fit into a 32-bit integer type.

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

10

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