Local Area Network

Problem Background

Special for beginners, ^_^

Problem Description

There are $n$ ($n \le 100$) computers in a local area network. Due to carelessness when the network was built, the connections inside the LAN now form cycles. We know that if the LAN forms a cycle, data will keep circulating inside the cycle, causing the network to lag. Because the network cables connecting the computers are different, some connections are not very smooth. We use $f(i, j)$ to denote the smoothness of the connection between $i$ and $j$ ($f(i, j) \le 1000$); the smaller the value of $f(i, j)$, the smoother the connection between $i$ and $j$, and $f(i, j) = 0$ means there is no cable connecting $i$ and $j$.

Now we need to solve the cycle problem: we will remove some cables so that there is no cycle in the network, and the sum $\sum f(i, j)$ of the removed cables is maximized. Find this maximum value.

Input Format

The first line contains two positive integers $n$ and $k$.

The following $k$ lines each contain three positive integers $i\ j\ m$, meaning computers $i$ and $j$ are connected by a cable with smoothness $m$.

Output Format

One positive integer: the maximum value of $\sum f(i, j)$.

Sample Input

5 5
1 2 8
1 3 1
1 5 3
2 4 5
3 4 2

Sample Output

8

Constraints

Time limit: 1s; memory limit: 1024 KiB for each test case.