The war

In the war, the intelligence about the enemy is very important. Now, our troop has mastered the situation of the enemy's war zones, and known that these war zones can communicate to each other directly or indirectly through the network. We also know the enemy is going to build a new communication line to strengthen their communication network. Our task is to destroy their communication network, so that some of their war zones can't communicate. Each line has its "cost of destroy". If we want to destroy a line, we must spend the "cost of destroy" of this line. We want to finish this task using the least cost, but our enemy is very clever. Now, we know the network they have already built, but we know nothing about the new line which our enemy is going to build. In this condition, your task is to find the minimum cost that no matter where our enemy builds the new line, you can destroy it using the fixed money. Please give the minimum cost. For efficiency, we can only destroy one communication line.

The input contains several cases. For each cases, the first line contains two positive integers n, m (1<=n<=10000, 0<=m<=100000) standing for the number of the enemy's war zones (numbered from 1 to n), and the number of lines that our enemy has already build. Then m lines follow. For each line there are three positive integer a, b, c (1<=a, b<=n, 1<=c<=100000), meaning between war zone A and war zone B there is a communication line with the "cost of destroy " c.

For each case, if the task can be finished output the minimum cost, or output ‐1.

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

-1
3

For the second sample input: our enemy may build line 2 to 3, 2 to 4,

3 to 4. If they build line 2 to 3, we will destroy line 1 to 4, cost 3. If they

build line 2 to 4, we will destroy line 1 to 3, cost 2. If they build line 3 to 4,

we will destroy line 1 to 2, cost 1. So, if we want to make sure that we can

destroy successfully, the minimum cost is 3.

The 36th ACM/ICPC Asia Regional Dalian Site —— Online Contest