Til the Cows Come Home     cowhome.X

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 <= 1,000) 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 <=
2,000) 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.

PROBLEM NAME: cowhome

INPUT FORMAT:

* 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.

SAMPLE INPUT:

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

OUTPUT FORMAT:

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

SAMPLE OUTPUT:

90

OUTPUT DETAILS:

Bessie can get home by following trails 4, 3, 2, and 1.