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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.Deque;
import java.util.Stack;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.ArrayList;
import java.io.FileNotFoundException;
import java.util.ArrayDeque;
import java.util.Queue;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.FileInputStream;
import java.util.List;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/main/java/F5";

    FastScanner in;
    PrintWriter out;

    int[] c;
    Graph<SimpleEdge> g;

    int[] ch, mch;
    long[] dp1, dp2;
    int[] pars;

    public void solve() {
        int n = in.nextInt();
        c = new int[n];
        for (int i = 0; i < n; i++) {
            c[i] = in.nextInt() - 1;
        }
        g = Graph.create(n);

        for (int i = 0; i < n - 1; i++) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            g.addDirectionalEdge(a, new SimpleEdge(b));
            g.addDirectionalEdge(b, new SimpleEdge(a));
        }
        ch = new int[n];
        mch = new int[n];
        dp1 = new long[n];
        dp2 = new long[n];
        pars = new int[n];
        Arrays.fill(pars, -1);

        dfs1(0, -1);
        dfs2(0, -1);

        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[c[i]] += n + dp1[i] - dp2[i];
        }
        for (int i = 0; i < n; i++) {
            out.println(res[i]);
        }
        out.close();
    }

    private int dfs1(int u, int pre) {
        int childCnt = 1;
        for (Edge e : g.edges(u)) {
            if (pre == e.to()) {
                continue;
            }
            childCnt += dfs1(e.to(), u);
        }
        return ch[u] = childCnt;
    }

    private void dfs2(int u, int pre) {
        int es = g.edgeNum(u);
        long[] a = new long[es];
        List<SimpleEdge> edges = g.edges(u);

        int par = pars[c[u]];
        pars[c[u]] = u;
        for (int i = 0; i < es; i++) {
            int v = edges.get(i).to();
            if (v == pre) {
                a[i] = g.size() - ch[u];
            } else {
                a[i] = ch[v];
                int orig = ch[u];
                ch[u] = g.size() - ch[v];
                dfs2(v, u);
                ch[u] = orig;
            }
        }
        pars[c[u]] = par;

        long sum = 0;
        for (int i = 0; i < es; i++) {
            sum += a[i];
        }
        // System.out.println(u + " " + Arrays.toString(a) + " " + sum);
        for (int i = 0; i < es; i++) {
            sum -= a[i];
            dp1[u] += a[i] * sum;
        }
        if (par != -1) {
            dp2[u] = (ch[u] - mch[u]) * (ch[par] - mch[par]);
            mch[par] += ch[u];
        }
    }

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }
}


class FastScanner {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream) {
        this.stream = stream;
        // stream = new FileInputStream(new File("dec.in"));
    }

    int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public boolean isEndline(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = nextInt();

        return array;
    }

    public int[][] nextIntMap(int n, int m) {
        int[][] map = new int[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextIntArray(m);
        }
        return map;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int n) {
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nextLong();

        return array;
    }

    public long[][] nextLongMap(int n, int m) {
        long[][] map = new long[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextLongArray(m);
        }
        return map;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) {
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nextDouble();

        return array;
    }

    public double[][] nextDoubleMap(int n, int m) {
        double[][] map = new double[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextDoubleArray(m);
        }
        return map;
    }

    public String next() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String[] nextStringArray(int n) {
        String[] array = new String[n];
        for (int i = 0; i < n; i++)
            array[i] = next();

        return array;
    }

    public String nextLine() {
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndline(c));
        return res.toString();
    }

    public int[][] nextPackedIntArrays(int packN, int size) {
        int[][] res = new int[packN][size];
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < packN; j++) {
                res[j][i] = nextInt();
            }
        }
        return res;
    }
}

class SimpleEdge implements Edge {
    private final int to;

    public SimpleEdge(int to) {
        this.to = to;
    }

    @Override
    public int to() {
        return to;
    }

    @Override
    public long cost() {
        return 1;
    }
}


class Graph<E extends Edge> {
    private final int n;
    private final List<E>[] g;

    public static <E extends Edge> Graph<E> create(int n) {
        @SuppressWarnings("unchecked")
        ArrayList<E>[] l = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            l[i] = new ArrayList<>();
        }
        return new Graph<>(n, l);
    }

    public Graph(int n, List<E>[] g) {
        this.n = n;
        this.g = g;
    }

    public static Graph<SimpleEdge> createDirectionalTree(int[] a, int[] b) {
        if (a.length != b.length) {
            throw new IllegalArgumentException("len(a) != len(b)");
        }
        int n = a.length + 1;
        Graph<SimpleEdge> g = create(n);
        for (int i = 0; i < n - 1; i++) {
            g.addDirectionalEdge(a[i], new SimpleEdge(b[i]));
        }
        return g;
    }

    public static Graph<SimpleEdge> createUndirectionalTree(int[] a, int[] b, boolean oneOrigin) {
        if (a.length != b.length) {
            throw new IllegalArgumentException("len(a) != len(b)");
        }
        int n = a.length + 1;
        Graph<SimpleEdge> g = create(n);

        int adjust = oneOrigin ? 1 : 0;
        for (int i = 0; i < n - 1; i++) {
            g.addDirectionalEdge(a[i] - adjust, new SimpleEdge(b[i] - adjust));
            g.addDirectionalEdge(b[i] - adjust, new SimpleEdge(a[i] - adjust));
        }
        return g;
    }

    public void addDirectionalEdge(int u, E e) {
        g[u].add(e);
    }

    public List<E> edges(int u) {
        return g[u];
    }

    public int edgeNum(int u) {
        return g[u].size();
    }

    public int totalEndgeNum() {
        return Arrays.stream(g)
                .map(List::size)
                .reduce(0, Integer::sum) / 2;
    }

    public int size() {
        return n;
    }

    /**
     *
     * @param start
     * @return The cost of node v is:
     * <ul>
     *     <li>-(1L << 62) if a node is under negative loop</li>
     *     <li>(1L << 62) if there is no edge to v</li>
     *     <li>otherwise minimum cost from node u to a node</li>
     * </ul>
     */
    public long[] bellmanford(int start) {
        final long INF = 1L << 62;
        long[] dist = new long[n];
        Arrays.fill(dist, INF);
        dist[start] = 0;
        for (int i = 0; i < n - 1; i++) {
            for (int u = 0; u < n; u++) {
                for (Edge e : edges(u)) {
                    dist[e.to()] = Math.min(dist[e.to()], dist[u] + e.cost());
                }
            }
        }

        long[] res = Arrays.copyOf(dist, dist.length);
        for (int u = 0; u < n; u++) {
            for (Edge e : edges(u)) {
                int v = e.to();
                if (dist[u] + e.cost() < dist[v]) {
                    res[v] = -INF;
                }
            }
        }
        return res;
    }

    /**
     *
     * @param start
     * @return For each v, true if a node v can be arrived from start node, otherwise false.
     */
    public boolean[] canArrive(int start) {
        boolean[] res = new boolean[size()];
        canArriveInternal(start, res);
        return res;
    }

    private void canArriveInternal(int u, boolean[] visited) {
        visited[u] = true;
        for (Edge e : edges(u)) {
            if (visited[e.to()]) {
                continue;
            }
            canArriveInternal(e.to(), visited);
        }
    }

    public DiameterResult diameter() {
        if (totalEndgeNum() != n - 1) {
            throw new IllegalArgumentException("Graph should be tree");
        }
        int[] parents = new int[size()];
        int[] dist = new int[size()];
        Arrays.fill(dist, -1);
        dfs(0, dist, parents, 0);

        int x = 0;
        for (int i = 1; i < size(); i++) {
            if (dist[x] < dist[i]) {
                x = i;
            }
        }

        int[] dist2 = new int[size()];
        Arrays.fill(dist2, -1);
        parents[x] = x;
        dfs(x, dist2, parents, 0);

        int best = 0;
        for (int i = 0; i < n; i++) {
            if (dist2[best] < dist2[i]) {
                best = i;
            }
        }
        return new DiameterResult(restore(x, best, parents), dist2[best] + 1);
    }

    private int[] restore(int from, int to, int[] parents) {
        List<Integer> pathL = new ArrayList<>();
        int cur = to;
        while (cur != from) {
            pathL.add(cur);
            cur = parents[cur];
        }
        pathL.add(from);

        int[] res = new int[pathL.size()];
        for (int i = 0; i < pathL.size(); i++) {
            res[i] = pathL.get(pathL.size() - i - 1);
        }
        return res;
    }

    private void dfs(int u, int[] dist, int[] parent, int depth) {
        dist[u] = depth;
        for (Edge e : g[u]) {
            if (dist[e.to()] != -1) {
                continue;
            }
            parent[e.to()] = u;
            dfs(e.to(), dist, parent, depth + 1);
        }
    }

    public static class DiameterResult {
        public final int[] path;
        public final int dist;

        public DiameterResult(int[] path, int dist) {
            this.path = path;
            this.dist = dist;
        }

        @Override
        public String toString() {
            return "DiameterResult{" +
                    "path=" + Arrays.toString(path) +
                    ", dist=" + dist +
                    '}';
        }
    }

    /**
     * Assuming edge is SimpleEdge
     * @param start
     * @return
     */
    public int[] bfs(int start) {
        int n = g.length;
        int[] dist = new int[n];
        Arrays.fill(dist, 1 << 30);
        dist[start] = 0;

        Queue<Integer> q = new ArrayDeque<>();
        q.add(start);
        while (!q.isEmpty()) {
            int u = q.poll();
            for (Edge e : g[u]) {
                if (dist[e.to()] == 1 << 30) {
                    dist[e.to()] = dist[u] + 1;
                    q.add(e.to());
                }
            }
        }
        return dist;
    }
}

class EdgeImpl implements Edge {
    private final int to;
    private final long cost;

    public EdgeImpl(int to, long cost) {
        this.to = to;
        this.cost = cost;
    }

    @Override
    public int to() {
        return to;
    }

    @Override
    public long cost() {
        return cost;
    }
}

interface EdgeGenerator<E extends Edge> {
    E generate(int to, E originalEdge);
}

interface Edge {
    int to();

    long cost();
}