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.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {

    static Main.MyScanner sc = new Main.MyScanner();
    // static Main.Parser sc = new Main.Parser(System.in);
    static PrintWriter out = new PrintWriter(System.out, true);

    public static void main(String[] args) throws Exception {

        int n = sc.nextInt(),col[] = new int[n],par[] = new int[n],ans[] = new int[n];

        HashSet<Integer> adj[] = new HashSet[n];

        for(int i = 0 ; i < n ; i++) {
            col[i] = sc.nextInt();
            adj[i] = new HashSet<>();
            if(col[i] == 0)
                ans[i] = -1;
            else
                ans[i] = 1;
            par[i] = -1;
        }

        for(int i = 0 ; i < n-1 ; i++) {
            int x = sc.nextInt()-1,y = sc.nextInt()-1;
            adj[x].add(y);
            adj[y].add(x);
        }
        
        foo(0,col,par,ans,adj);

        int ans2[] = new int[n];

        ans2[0] = ans[0];
        for(Integer child : adj[0]) {
            bar(child, col, par, ans, adj, ans2);
        }

        for(int i = 0 ; i < n ; i++) {
            out.print(ans2[i] + " ");
        }

        out.close();
    }

    private static void bar(int now, int[] col, int[] par, int[] ans, HashSet<Integer>[] adj, int[] ans2) {
        int stSum = ans[now],pSum = ans2[par[now]];
        if(stSum > 0)
            pSum -= stSum;
        if(pSum > 0)
            stSum += pSum;
        ans2[now] = stSum;
        for(Integer child : adj[now]) if(par[now] != child) {
            bar(child, col, par, ans, adj, ans2);
        }
    }

    private static void foo(int now, int[] col, int[] par, int[] ans, HashSet<Integer>[] adj) {
        for(Integer child : adj[now]) if(par[now] != child) {
            par[child] = now;
            foo(child, col, par, ans, adj);
            if(ans[child] > 0)
                ans[now] += ans[child] ;
        }
    }

    static private class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public int mod(long x) {
            return (int) x % 1000000007;
        }

        public int mod(int x) {
            return x % 1000000007;
        }

        boolean hasNext() {
            if (st.hasMoreElements())
                return true;
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return st.hasMoreTokens();
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

    static class Parser {
        final private int BUFFER_SIZE = 65536; // 2^16, a good compromise for
        // some problems
        private InputStream din; // Underlying input stream
        private byte[] buffer; // Self-maintained buffer
        private int bufferPointer; // Current read position in the buffer
        private int bytesRead; // Effective bytes in the buffer read from the
        // input stream

        public Parser(InputStream in) {
            din = in;
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        /**
         * Read the next integer from the input stream.
         *
         * @return The next integer.
         * @throws IOException
         */
        public int nextInt() throws IOException {
            int result = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            while (c >= '0' && c <= '9') {
                result = result * 10 + c - '0';
                c = read();
            }
            if (neg)
                return -result;
            return result;
        }

        /**
         * Read the next byte of data from the input stream.
         *
         * @return the next byte of data, or -1 if the end of the stream is
         *         reached.
         * @throws IOException
         *             if an I/O error occurs.
         */
        public byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        /**
         * Read data from the input stream into the buffer
         *
         * @throws IOException
         *             if an I/O error occurs.
         */
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
    }
}