+ محدودیت زمان: ۲ ثانیه
+ محدودیت حافظه: ۶۴ مگابایت
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A long time ago in the University of Tehran, there were $N$ buildings. There were also $N-1$ pathways that connected all the buildings (directly or indirectly). In other words, the network of buildings and paths formed a tree. Additionally, each path was enumerated with an integer that denoted the curiosity of the path.
A pair of buildings A, B is boring if the following holds:
* A and B are different buildings
* travelling between building A and B is possible using one or more pathways
* binary **XOR** of the curiosity of all the paths in that travel is equal to 0
Unfortunately, times have changed, and an evil dean named Zein is now ruling the department. He decided to use the Force to destroy all the pathways in a **certain order**. Determine the number of boring pairs of buildings before Zein started the destruction and after each destruction.
# Input
The first line of input contains the integer N.
Each of the following $N-1$ line contains three integers $a_i$, $b_i$, $z_i$, that denote that buildings $a_i$ 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 Zein is destroying the paths. If the $i^{th}$ element of the permutation is j, then Zein destroyed the path between buildings $a_i$ and $b_i$ 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 Zein destroyed exactly $k-1$ paths.
# Constraints
* $1 \leq N \leq 10^5 $
* $1 \leq a_i,b_i \leq N $
* $0 \leq z_i \leq 10^9 $
# Sample Test Data
## input 1
```
3
1 2 5
2 3 5
2 1
```
## output 1
```
1
0
0
```
## input 2
```
4
1 2 0
2 3 0
2 4 0
3 1 2
```
## output 2
```
6
3
1
0
```