### Til the Cows Come Home

Time Limit: 1000 ms Memory Limit: 65536 KiB

#### Problem Description

Bessie is out in the field and wants to get back to the barn to get as much sleep as possible before Farmer John wakes her for the morning milking. Bessie needs her beauty sleep, so she wants to get back as quickly as possible.

Farmer John's field has N (2 <= N <= 1000) landmarks in it, uniquely numbered 1..N. Landmark 1 is the barn; the apple tree grove in which Bessie stands all day is landmark N. Cows travel in the field using T (1 <= T <= 2000) bidirectional cow-trails of various lengths between the landmarks. Bessie is not confident of her navigation ability, so she always stays on a trail from its start to its end once she starts it.

Given the trails between the landmarks, determine the minimum distance Bessie must walk to get back to the barn. It is guaranteed that some such route exists.

#### Input

* Line 1: Two integers: T and N
*Lines 2..T+1: Each line describes a trail as three space-separated integers. The first two integers are the landmarks between which the trail travels. The third integer is the length of the trail, range 1..100.

#### Output

* Line 1: A single integer, the minimum distance that Bessie must travel to get from landmark N to landmark 1.

#### Sample Input

5 5
1 2 20
2 3 30
3 4 20
4 5 20
1 5 100

#### Sample Output

90

#### Hint

poj2387 有链接提示的题目请先去链接处提交程序，AC后提交到SDUTOJ中，以便查询存档。 INPUT DETAILS: There are five landmarks. OUTPUT DETAILS: Bessie can get home by following trails 4, 3, 2, and 1.

#### Source

USACO 2004 November