Galaksija
A long time ago in a galaxy far, far away, there were $N$ planets. There were also $N  1$ interplanetary paths that connected all the planets (directly or indirectly). In other words, the network of planets and paths formed a tree. Additionally, each path was enumerated with an integer that denoted the curiosity of the path.
A pair of planets $A$, $B$ is boring if the following holds:

$A$ and $B$ are different planets;

travelling between planet $A$ and $B$ is possible using one or more interplanetary paths; and

the binary XOR of the curiosity of all the paths in that travel is equal to 0
Alas, the times have changed and an evil emperor is ruling the galaxy. He decided to use the Force to destroy all the interplanetary paths in a certain order. Determine the number of boring pairs of planets before the emperor started the destruction and after each destruction.
Input
The first line of input contains the integer $N$ ($1 \leq N \leq 100\, 000$). Each of the following $N  1$ lines contains three integers $A_ i$, $B_ i$, $Z_ i$ ($1 \leq A_ i, B_ i \leq N$, $0 \leq Z_ i \leq 1\, 000\, 000\, 000$) that denote that planets $A_ i$ and $B_ i$ are directly connected with a path of curiosity $Z_ i$. The following line of input contains the permutation of the first $N  1$ integers that denote the order in which the emperor is destroying the paths. If the $i$th element of the permutation is $j$, then the emperor destroyed the path between planets $A_ j$ and $B_ j$ in the $i$th step.
Output
The output must contain $N$ lines, the $k$th line containing the number of boring pairs A, $B$ from the task after the emperor destroyed exactly $k  1$ paths.
Sample Input 1  Sample Output 1 

2 1 2 0 1 
1 0 
Sample Input 2  Sample Output 2 

3 1 2 4 2 3 4 1 2 
1 0 0 
Sample Input 3  Sample Output 3 

4 1 2 0 2 3 0 2 4 0 3 1 2 
6 3 1 0 