每天早上，FJ醒来，从他家走到谷仓穿过农场。 该场是 N 个田地 （1 <= N <= 250） 的集合，通过 M 双向路径 （1 <= M <= 25，000） 连接，每个田地都有关联的长度。
FJ的房子在1号田地，谷仓在N场。 没有一对田地由多个冗余路径连接，并且可以通过沿着适当的路径顺序在农场中的任何一对田地之间移动。 当从一个油田到另一个油田时，FJ总是选择一条由具有最小总长度的路径序列组成的路线。
农夫约翰的奶牛，一如既往地没有好处，决定干扰他的早晨例行公事。 他们计划在农场的M路径之一上建造一堆干草包，使其长度增加一倍。 奶牛希望选择一条路径来阻挡，以便它们最大限度地增加FJ从房子到谷仓的距离。 请帮助奶牛确定它们可以延长多少FJ的路线。
Every morning, FJ wakes up and walks across the farm from his house to the
barn. The farm is a collection of N fields (1 <= N <= 250) connected by M
bidirectional pathways (1 <= M <= 25,000), each with an associated length.
FJ's house is in field 1, and the barn is in field N. No pair of fields is
joined by multiple redundant pathways, and it is possible to travel between
any pair of fields in the farm by walking along an appropriate sequence of
pathways. When traveling from one field to another, FJ always selects a
route consisting of a sequence of pathways having minimum total length.
Farmer John's cows, up to no good as always, have decided to interfere with
his morning routine. They plan to build a pile of hay bales on exactly one
of the M pathways on the farm, doubling its length. The cows wish to
select a pathway to block so that they maximize the increase in FJ's
distance from the house to the barn. Please help the cows determine
by how much they can lengthen FJ's route.
PROBLEM NAME: rblock
INPUT FORMAT:
* Line 1: Two space-separated integers, N and M.
* Lines 2..1+M: Line j+1 describes the jth bidirectional pathway in
terms of three space-separated integers: A_j B_j L_j, where
A_j and B_j are indices in the range 1..N indicating the
fields joined by the pathway, and L_j is the length of the
pathway (in the range 1...1,000,000).
SAMPLE INPUT (file rblock.in):
5 7
2 1 5
1 3 1
3 2 8
3 5 7
3 4 3
2 4 7
4 5 2
INPUT DETAILS:
There are 5 fields and 7 pathways. Currently, the shortest path from the
house (field 1) to the barn (field 5) is 1-3-4-5 of total length 1+3+2=6.
OUTPUT FORMAT:
* Line 1: The maximum possible increase in the total length of FJ's
shortest route made possible by doubling the length of a
single pathway.
SAMPLE OUTPUT (file rblock.out):
2
OUTPUT DETAILS:
If the cows double the length of the pathway from field 3 to field 4
(increasing its length from 3 to 6), then FJ's shortest route is now 1-3-5,
of total length 1+7=8, larger by two than the previous shortest route length.
* 第 1 行：两个空格分隔的整数，N 和 M。
* 第 2..1+M 行：第 j+1 行用三个空格分隔的整数描述第 j 个双向路径：Aj Bj Lj，其中 Aj 和 Bj 是 1..N 范围内的索引，表示路径连接的字段，Lj 是路径的长度（在 1...1，000，000 范围内）。
*第1行：通过将单条路径的长度增加一倍，使FJ最短路线的总长度可能增加的最大可能。
5 7
2 1 5
1 3 1
3 2 8
3 5 7
3 4 3
2 4 7
4 5 22