#include <string>
#include <vector>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <map>
#include <list>
#include <set>
#include <numeric>
#include <queue>
#include <stack>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <climits>
#include <cfloat>
#include <ctime>
#include <complex>
#include <cassert>
#include <array>
#include <bitset> 
#include <unordered_map>
#include <random>
using namespace std;
typedef long long LL;
typedef pair<LL,LL> P;


const int L=2e5+9;
LL c[L];
vector<int> es[L];
LL ps[L];
LL w[L];
LL cnt[L];
LL ret[L];
LL N;
LL dfs(int r, int p)
{
	int pcnt=cnt[c[r]];
	int pps=ps[c[r]];
	ps[c[r]]=r;
	LL s=1;
	ret[c[r]]+=s;
	LL sum=1;
	for(auto i:es[r]){
		if(i==p){
			continue;
		}
		w[r]=0;
		auto v=dfs(i,r);
		auto t=w[r]+v;
		ret[c[r]]+=t*s;
		s+=t;
		sum+=v;
	}
	{
		auto t=N-sum-pcnt;
		ret[c[r]]+=t*s;
	}
	cnt[c[r]]+=s;
	w[pps]-=sum;
	ps[c[r]]=pps;
	return sum;
}

int main(){
    scanf("%lld",&N);
    for(int i = 1 ; i <= N ; i++){
        scanf("%lld",&c[i]);
    }
    for(int i = 0 ; i < N-1 ; i++){
		LL a,b;
        scanf("%lld",&a);
        scanf("%lld",&b);
		es[a].push_back(b);
		es[b].push_back(a);
    }
	dfs(1,0);
	for(int i=1;i<=N;i++){
		cout << ret[i] << endl;
	}
    return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 <string>
#include <vector>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <map>
#include <list>
#include <set>
#include <numeric>
#include <queue>
#include <stack>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <climits>
#include <cfloat>
#include <ctime>
#include <complex>
#include <cassert>
#include <array>
#include <bitset> 
#include <unordered_map>
#include <random>
using namespace std;
typedef long long LL;
typedef pair<LL,LL> P;


const int L=2e5+9;
LL c[L];
vector<int> es[L];
LL ps[L];
LL w[L];
LL cnt[L];
LL ret[L];
LL N;
LL dfs(int r, int p)
{
	int pcnt=cnt[c[r]];
	int pps=ps[c[r]];
	ps[c[r]]=r;
	LL s=1;
	ret[c[r]]+=s;
	LL sum=1;
	for(auto i:es[r]){
		if(i==p){
			continue;
		}
		w[r]=0;
		auto v=dfs(i,r);
		auto t=w[r]+v;
		ret[c[r]]+=t*s;
		s+=t;
		sum+=v;
	}
	{
		auto t=N-sum-pcnt;
		ret[c[r]]+=t*s;
	}
	cnt[c[r]]+=s;
	w[pps]-=sum;
	ps[c[r]]=pps;
	return sum;
}

int main(){
    scanf("%lld",&N);
    for(int i = 1 ; i <= N ; i++){
        scanf("%lld",&c[i]);
    }
    for(int i = 0 ; i < N-1 ; i++){
		LL a,b;
        scanf("%lld",&a);
        scanf("%lld",&b);
		es[a].push_back(b);
		es[b].push_back(a);
    }
	dfs(1,0);
	for(int i=1;i<=N;i++){
		cout << ret[i] << endl;
	}
    return 0;
}

```