#include<bits/stdc++.h>
using namespace std;
long long n,c[202020],ans[202020],sz[202020],d[202020];
vector<int>v[202020];
int dfs(int x,int y)
{
	sz[x]=1;
	int cc=c[x],lw=0,xx;
	for(int i=0;i<v[x].size();i++)
	{
		int z=v[x][i];
		if(z==y)
		{
			continue;
		}
		xx=d[cc];
		int nw=dfs(z,x);
		sz[x]+=nw;
		xx=d[cc]-xx;
		lw+=xx;
		long long hs=nw-xx;
		ans[cc]+=hs*(hs+1)/2;
	}
	d[cc]+=sz[x];
	d[cc]-=lw;
	return sz[x];
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>c[i];
	}
	for(int i=0;i<n-1;i++)
	{
		int a,b;
		cin>>a>>b;
		v[a].push_back(b);
		v[b].push_back(a);
	}
	dfs(1,-1);
	for(int i=1;i<=n;i++)
	{
		long long nd=n-d[i];
		cout<<n*(n+1)/2-ans[i]-nd*(nd+1)/2<<endl;
	}
	return 0;
}
### Prompt

Your challenge is to write a Cpp solution to the following problem:

We have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i. Additionally, each vertex is painted in a color, and the color of Vertex i is c_i. Here, the color of each vertex is represented by an integer between 1 and N (inclusive). The same integer corresponds to the same color; different integers correspond to different colors.

For each k=1, 2, ..., N, solve the following problem:

* Find the number of simple paths that visit a vertex painted in the color k one or more times.



Note: The simple paths from Vertex u to v and from v to u are not distinguished.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq c_i \leq N
* 1 \leq a_i,b_i \leq N
* The given graph is a tree.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
c_1 c_2 ... c_N
a_1 b_1
:
a_{N-1} b_{N-1}


Output

Print the answers for k = 1, 2, ..., N in order, each in its own line.

Examples

Input

3
1 2 1
1 2
2 3


Output

5
4
0


Input

1
1


Output

1


Input

2
1 2
1 2


Output

2
2


Input

5
1 2 3 4 5
1 2
2 3
3 4
3 5


Output

5
8
10
5
5


Input

8
2 7 2 5 4 1 7 5
3 1
1 2
2 7
4 5
5 6
6 8
7 8


Output

18
15
0
14
23
0
23
0

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
long long n,c[202020],ans[202020],sz[202020],d[202020];
vector<int>v[202020];
int dfs(int x,int y)
{
	sz[x]=1;
	int cc=c[x],lw=0,xx;
	for(int i=0;i<v[x].size();i++)
	{
		int z=v[x][i];
		if(z==y)
		{
			continue;
		}
		xx=d[cc];
		int nw=dfs(z,x);
		sz[x]+=nw;
		xx=d[cc]-xx;
		lw+=xx;
		long long hs=nw-xx;
		ans[cc]+=hs*(hs+1)/2;
	}
	d[cc]+=sz[x];
	d[cc]-=lw;
	return sz[x];
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>c[i];
	}
	for(int i=0;i<n-1;i++)
	{
		int a,b;
		cin>>a>>b;
		v[a].push_back(b);
		v[b].push_back(a);
	}
	dfs(1,-1);
	for(int i=1;i<=n;i++)
	{
		long long nd=n-d[i];
		cout<<n*(n+1)/2-ans[i]-nd*(nd+1)/2<<endl;
	}
	return 0;
}
```