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: Wrong Answer)

#include <bits/stdc++.h>  // clang-format off
using Int = long long;
#define REP_(i, a_, b_, a, b, ...) for (Int i = (a), lim##i = (b); i < lim##i; i++)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
struct SetupIO { SetupIO() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(13); } } setup_io;
#ifndef _MY_DEBUG
#define dump(...)
#endif  // clang-format on

/**
 *    author:  knshnb
 *    created: Mon Apr 20 00:37:53 JST 2020
 **/

signed main() {
    int n;
    std::cin >> n;
    std::vector<Int> c(n);
    REP(i, n) std::cin >> c[i], c[i]--;
    std::vector<std::vector<int>> g(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v;
        std::cin >> u >> v;
        u--, v--;
        g[u].push_back(v);
        g[v].push_back(u);
    }

    std::vector<Int> ans(n, n * (n + 1) / 2), sz(n, 1);
    std::vector<std::map<Int, Int>> mps(n);
    auto dfs = [&](auto f, int v, int prv) -> void {
        for (int s : g[v]) {
            if (s == prv) continue;
            f(f, s, v);
            sz[v] += sz[s];
            Int connected = sz[s] - mps[s][c[v]];
            ans[c[v]] -= connected * (connected + 1) / 2;
            if (mps[s].size() > mps[v].size()) std::swap(mps[s], mps[v]);
            for (auto& p : mps[s]) {
                mps[v][p.first] += p.second;
            }
        }
        mps[v][c[v]] = sz[v];
    };
    dfs(dfs, 0, -1);
    REP(i, n) {
        Int connected = n - mps[0][i];
        ans[i] -= connected * (connected + 1) / 2;
    }
    for (Int x : ans) std::cout << x << "\n";
}