Problem: You are given a tree consisting of n vertices. A tree is a connected undirected graph with n-1 edges. Each vertex v of this tree has a color assigned to it (a_v = 1 if the vertex v is white and 0 if the vertex v is black).

You have to solve the following problem for each vertex v: what is the maximum difference between the number of white and the number of black vertices you can obtain if you choose some subtree of the given tree that contains the vertex v? The subtree of the tree is the connected subgraph of the given tree. More formally, if you choose the subtree that contains cnt_w white vertices and cnt_b black vertices, you have to maximize cnt_w - cnt_b.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1), where a_i is the color of the i-th vertex.

Each of the next n-1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i).

It is guaranteed that the given edges form a tree.

Output

Print n integers res_1, res_2, ..., res_n, where res_i is the maximum possible difference between the number of white and black vertices in some subtree that contains the vertex i.

Examples

Input


9
0 1 1 1 0 0 0 0 1
1 2
1 3
3 4
3 5
2 6
4 7
6 8
5 9


Output


2 2 2 2 2 1 1 0 2 


Input


4
0 0 1 0
1 2
1 3
1 4


Output


0 -1 1 -1 

Note

The first example is shown below:

<image>

The black vertices have bold borders.

In the second example, the best subtree for vertices 2, 3 and 4 are vertices 2, 3 and 4 correspondingly. And the best subtree for the vertex 1 is the subtree consisting of vertices 1 and 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class MainClass
{
    static long ans = 0L;
    static long[] subtreeSum;
    static long[] A;
    static long ansForRoot = 0L;
    static long S = 0L;
    public static void main(String[] args)throws IOException
    {
        Reader in = new Reader();
        int n = in.nextInt();
        A = new long[n];
        for (int i=0;i<n;i++)   S += (A[i] = in.nextLong());
        ArrayList<Integer>[] adj = (ArrayList<Integer>[])new ArrayList[n];
        for (int i=0;i<n;i++)   adj[i] = new ArrayList<>();
        for (int i=0;i<n-1;i++)
        {
            int x = in.nextInt() - 1;
            int y = in.nextInt() - 1;
            adj[x].add(y);
            adj[y].add(x);
        }
        subtreeSum = new long[n];
        explore(adj, 0, new boolean[n]);
        find(adj, 0, new boolean[n], 0);
        boolean[] visited = new boolean[n];
        visited[0] = true;
        for (int u: adj[0]) recur(adj, u, visited, ansForRoot);
        System.out.println(Math.max(ans, ansForRoot));
    }
    public static void explore(ArrayList<Integer>[] adj, int v, boolean[] visited)
    {
        visited[v] = true;
        subtreeSum[v] += A[v];
        for (int u: adj[v])
        {
            if (!visited[u])
            {
                explore(adj, u, visited);
                subtreeSum[v] += subtreeSum[u];
            }
        }
    }
    public static void find(ArrayList<Integer>[] adj, int v, boolean[] visited, int dist)
    {
        visited[v] = true;
        ansForRoot += A[v] * dist;
        for (int u: adj[v])
        {
            if (!visited[u])
            {
                find(adj, u, visited, dist + 1);
            }
        }
    }
    public static void recur(ArrayList<Integer>[] adj, int v, boolean[] visited, long ansForParent)
    {
        visited[v] = true;
        long ansHere = ansForParent + S - 2 * subtreeSum[v];
        ans = Math.max(ans, ansHere);
        for (int u: adj[v])
        {
            if (!visited[u])
            {
                recur(adj, u, visited, ansHere);
            }
        }
    }
}
class Reader
{
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader()
    {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException
    {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException
    {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1)
        {
            if (c == '\n')
                break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException
    {
        int ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do
        {
            ret = ret * 10 + c - '0';
        }  while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException
    {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException
    {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException
    {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException
    {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException
    {
        if (din == null)
            return;
        din.close();
    }
}