#pragma GCC optimize("Ofast")
#include<stdio.h>
#include<algorithm>
#include<vector>
using namespace std;
long long ans[200005]={0},num[200005],sz[200005]={0},color[200005]={0};
vector<long long> g[200005];
long long f(long long v){
	return v*(v+1)>>1;
}
void DFS(long long v,long long p){
	sz[v]=1;
	int temp=color[num[v]];
	for(auto x:g[v]){
		if(x==p)
			continue;
		color[num[v]]=0;
		DFS(x,v);
		sz[v]+=sz[x];
		ans[num[v]]-=f(sz[x]-color[num[v]]);
	}
	color[num[v]]=temp+sz[v];
}
int main(){
	long long i,n,from,to;
	scanf("%lld",&n);
	for(i=1;i<=n;i++)
		scanf("%lld",&num[i]);
	for(i=0;i<n-1;i++){
		scanf("%lld%lld",&from,&to);
		g[from].emplace_back(to);
		g[to].emplace_back(from);
	}
	DFS(1,-1);
	for(i=1;i<=n;i++)
		printf("%lld\n",ans[i]+f(n)-f(n-color[i]));
}

### Prompt

Generate 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
#pragma GCC optimize("Ofast")
#include<stdio.h>
#include<algorithm>
#include<vector>
using namespace std;
long long ans[200005]={0},num[200005],sz[200005]={0},color[200005]={0};
vector<long long> g[200005];
long long f(long long v){
	return v*(v+1)>>1;
}
void DFS(long long v,long long p){
	sz[v]=1;
	int temp=color[num[v]];
	for(auto x:g[v]){
		if(x==p)
			continue;
		color[num[v]]=0;
		DFS(x,v);
		sz[v]+=sz[x];
		ans[num[v]]-=f(sz[x]-color[num[v]]);
	}
	color[num[v]]=temp+sz[v];
}
int main(){
	long long i,n,from,to;
	scanf("%lld",&n);
	for(i=1;i<=n;i++)
		scanf("%lld",&num[i]);
	for(i=0;i<n-1;i++){
		scanf("%lld%lld",&from,&to);
		g[from].emplace_back(to);
		g[to].emplace_back(from);
	}
	DFS(1,-1);
	for(i=1;i<=n;i++)
		printf("%lld\n",ans[i]+f(n)-f(n-color[i]));
}

```