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.

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.

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.

Sample Input 1

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

Sample Output 1

4

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

Sample Input 2

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

Sample Output 2

1

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

Sample Input 3

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

Sample Output 3

5

There may be multi-edges and self-loops.

见题面 Input 部分

见题面 Output 部分