E - Destruction

Score : $500$ points

Problem Statement

We have a connected undirected graph with $N$ vertices and $M$ edges.
The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $A_i$ and $B_i$.

Takahashi is going to remove zero or more edges from this graph.

When removing Edge $i$, a reward of $C_i$ is given if $C_i \geq 0$, and a fine of $|C_i|$ is incurred if $C_i<0$.

Find the maximum total reward that Takahashi can get when the graph must be connected after removing edges.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $N-1 \leq M \leq 2\times 10^5$
• $1 \leq A_i,B_i \leq N$
• $-10^9 \leq C_i \leq 10^9$
• The given graph is connected.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $B_1$ $C_1$

$A_2$ $B_2$ $C_2$

$\vdots$

$A_M$ $B_M$ $C_M$

Output

Print the answer.

4 5
1 2 1
1 3 1
1 4 1
3 2 2
4 2 2

4

Removing Edges $4$ and $5$ yields a total reward of $4$. You cannot get any more, so the answer is $4$.

3 3
1 2 1
2 3 0
3 1 -1

1

There may be edges that give a negative reward when removed.

2 3
1 2 -1
1 2 2
1 1 3

5

There may be multi-edges and self-loops.