[Usaco2013 Open]Yin and Yang

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Farns (1 <= N <= 100,000) which are connected by N-1 edges such that he can reach any barn from any 
other. Farmer John wants to choose a path which starts and ends at two different barns, such that he
does not traverse any edge twice. He worries that his path might be a little long, so he also wantst
o choose another "rest stop" barn located on this path (which is distinct from the start or the end)
. Along each edge is a herd of cows, either of the Charcolais (white hair) or the Angus (black hair)
 variety. Being the wise man that he is, Farmer John wants to balance the forces of yin and yang tha
t weigh upon his walk. To do so, he wishes to choose a path such that he will pass by an equal numbe
r of Charcolais herds and Angus herds-- both on the way from the start to his rest stop, and on thew
ay from the rest stop to the end. Farmer John is curious how many different paths he can choose that
 are "balanced" as described above. Two paths are different only if they consist of different setsof
 edges; a path should be counted only once even if there are multiple valid "rest stop" locationsalo
ng the path that make it balanced. Please help determine the number of paths Farmer John can cho


* Line 1: The integer N.
* Lines 2..N: Three integers a_i, b_i and t_i, representing the two barns that edge i connects. t_i 
is 0 if the herd along that edge is Charcolais, and 1 if the herd is Angus.


Line 1: One integer, representing the number of possible paths Farmer John can choose from.


1 2 0
3 1 1
2 4 0
5 2 0
6 3 1
5 7 1
There are 7 barns and 6 edges. The edges from 1 to 2, 2 to 4 and 2 to 5 have Charcolais herds along 


No path of length 2 can have a suitable rest stop on it, so we can only consider paths of length 4. 
The only path that has a suitable rest stop is 3-1-2-5-7, with a rest stop at 2.