When FJ's friends visit him on the farm, he likes to show them around. His farm comprises N (1 <= N <= 1000) fields numbered 1..N, the first of which contains his house and the Nth of which contains the big barn. A total M (1 <= M <= 10000) paths that connect the fields in various ways. Each path connects two different fields and has a nonzero length smaller than 35,000.

To show off his farm in the best way, he walks a tour that starts at his house, potentially travels through some fields, and ends at the barn. Later, he returns (potentially through some fields) back to his house again.

He wants his tour to be as short as possible, however he doesn't want to walk on any given path more than once. Calculate the shortest tour possible. FJ is sure that some tour exists for any given farm.

* Line 1: Two space-separated integers: N and M.

* Lines 2..M+1: Three space-separated integers that define a path: The starting field, the end field, and the path's length.

A single line containing the length of the shortest tour.

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

6

USACO 2003 February Green
本題題意大概是最小費用流！
在處理的時候要處理重邊。。。。。其實我們可以證明的，就是如果存在重邊我們最多只需要記錄兩個邊就可以解題！
以最大流最小費用流原理我們知道，消負權最后達到的效果就是最大流的情況下不存在流經兩次的邊。。。。。即每條邊最多只能流經一次，由此可知我們可以最多儲存兩條重邊！
AC 了 79ms很慢