Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2 1
1 2
2 3

Sample Output 1

5
4
0

Let P_{i,j} denote the simple path connecting Vertex i and j.

There are 5 simple paths that visit a vertex painted in the color 1 one or more times:

P_{1,1}\,,\,
P_{1,2}\,,\,
P_{1,3}\,,\,
P_{2,3}\,,\,
P_{3,3}

There are 4 simple paths that visit a vertex painted in the color 2 one or more times:

P_{1,2}\,,\,
P_{1,3}\,,\,
P_{2,2}\,,\,
P_{2,3}

There are no simple paths that visit a vertex painted in the color 3 one or more times.

Sample Input 2

1
1

Sample Output 2

1

Sample Input 3

2
1 2
1 2

Sample Output 3

2
2

Sample Input 4

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

Sample Output 4

5
8
10
5
5

Sample Input 5

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

Sample Output 5

18
15
0
14
23
0
23
0

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long ul;
typedef unsigned long long ull;
typedef long long ll;
typedef vector<ll> vint;
typedef vector< vector<ll> > vvint;
typedef vector< vector< vector<ll> > > vvvint;
typedef vector<string> vstring;
typedef vector< vector<string> > vvstring;
typedef vector<char> vchar;
typedef vector< vector<char> > vvchar;
typedef vector<long double> vdouble;
typedef vector< vector<long double> > vvdouble;
typedef vector< vector< vector<long double> > > vvvdouble;
typedef pair<ll,ll> pint;
typedef vector<pint> vpint;
typedef vector<bool> vbool;

#define rep(i,n) for(ll i=0;i<n;i++)
#define repf(i,f,n) for(ll i=f;i<n;i++)
#define repr(i,n) for(ll i=n-1;i>=0;i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define ALL(obj) (obj).begin(), (obj).end()
// #define LLONG_MAX 9223372036854775806
#define MOD 1000000007
const double PI=3.14159265358979323846;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> T Ceil(T a, T b){return (a+b-1)/b;}

int dy[]={0, 0, 1, -1, 1, -1, -1, 1};
int dx[]={1, -1, 0, 0, 1, 1, -1, -1};

void printv(vint &v){
    for(auto e:v) cout<<e<<" ";
        cout<<endl;
    }

ll n;
ll c[(int)2e5+100];
vint edges[(int)2e5+100];

ll memo[(int)2e5+100];
ll cnt_i[(int)2e5+100];
ll cnt;
ll ans[(int)2e5+100];

void f(ll par, ll now){

    memo[now] = cnt - cnt_i[c[now]];

    for(auto to:edges[now]){
        if(to == par) continue;
        f(now, to);
        ll tmp = (cnt - cnt_i[c[now]]) - memo[now];
        // cout<<"tmp: "<<tmp<<endl;
        ans[c[now]] -=  tmp*(tmp+1)/2;
        cnt_i[c[now]] += tmp;
    }
    cnt++;
    cnt_i[c[now]]++;
}

int main() {
    cout<<fixed<<setprecision(10);

    cnt = 0;
    cin>>n;
    rep(i,n){ cin>>c[i+1];}
    rep(i,n-1){
        ll a,b; cin>>a>>b;
        edges[a].push_back(b);
        edges[b].push_back(a);
    }
    edges[0].push_back(1);
    f(0, 1);
    repf(i,1,n+1){
        ll tmp = (cnt-cnt_i[i]);
        ans[i] -= tmp*(tmp+1)/2;
    }

    repf(i,1,n+1){
        cout<< ans[i] + n*(n+1)/2<<endl;
    }



    return 0;

}