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:
//                I know stuff but probably my rating tells otherwise...
//                  Kaafi din baad aaye hai... Swagat nhi kariyega???
//               Kya hua, code samajhne ki koshish kar rhe ho?? Mat karo,
//                      mujhe bhi samajh nhi aata kya likha hai


import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class _1324F {
    static LinkedList<Integer> adj[];
    static int ar[];
    static long white[], black[], ans[];
    static void Mangni_ke_bail_ke_dant_na_dekhal_jye() {
        n = ni();
        adj = new LinkedList[n+5];
        ar = new int[n+5];
        white = new long[n+5];
        black = new long[n+5];
        ans = new long[n+5];

        for(int i=0;i<=n;i++)adj[i] = new LinkedList<>();
        for(int i=1;i<=n;i++)ar[i] = ni();

        for(int i=1;i<n;i++) {
            int x = ni();
            int y = ni();
            adj[x].add(y);
            adj[y].add(x);
        }

        dfs1(1,0);
        dfs2(1,0);
        for(int i = 1;i<=n;i++)p(ans[i]);
        pl();

    }

    static void dfs1(int i, int p){
        for(int x:adj[i]){
            if(x == p)continue;
            dfs1(x,i);

            if(white[x] > black[x]){
                white[i] += white[x];
                black[i] += black[x];
            }
        }

        if(ar[i]==1)white[i]++;
        else black[i]++;
        ans[i] = white[i] - black[i];
    }

    static void dfs2(int i, int p){
        for(int x:adj[i]){
            if(x == p)continue;;
            ans[x] = max(ans[x], ans[i] + (white[x] <= black[x] ? ans[x] : 0));
            dfs2(x,i);
        }
    }


    //----------------------------------------The main code ends here------------------------------------------------------
    /*-------------------------------------------------------------------------------------------------------------------*/
    //-----------------------------------------Rest's all dust-------------------------------------------------------------


    static int mod9 = 1_000_000_007;
    static int n, m, l, k, t;
    static AwesomeInput input;
    static PrintWriter pw;

    static long power(long a, long b) {
        long x = max(a, b);
        if (b == 0) return 1;
        if ((b & 1) == 1) return a * power(a * a, b >> 1);
        return power(a * a, b >> 1);
    }

    // The Awesome Input Code is a fast IO method //
    static class AwesomeInput {
        private InputStream letsDoIT;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        private AwesomeInput(InputStream incoming) {
            this.letsDoIT = incoming;
        }

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

        private long ForLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        private String ForString() {
            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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);
        }
    }

    // functions to take input//
    static int ni() {
        return (int) input.ForLong();
    }

    static String ns() {
        return input.ForString();
    }

    static long nl() {
        return input.ForLong();
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o) {
        pw.print(o + "");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    // Fast Sort is Radix Sort
    public static int[] fastSort(int[] f) {
        int n = f.length;
        int[] to = new int[n];
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }

    public static void main(String[] args) {      //threading has been used to increase the stack size.
        try {
            input = new AwesomeInput(System.in);
            pw = new PrintWriter(System.out, true);
            input = new AwesomeInput(new FileInputStream("/home/saurabh/Desktop/input.txt"));
            pw = new PrintWriter(new BufferedWriter(new FileWriter("/home/saurabh/Desktop/output.txt")), true);

        } catch (Exception e) {
        }

        new Thread(null, null, "AApan_gand_hawai_dusar_ke_kare_dawai", 1 << 25)  //the last parameter is stack size desired.
        {
            public void run() {
                try {
                    double s = System.currentTimeMillis();
                    Mangni_ke_bail_ke_dant_na_dekhal_jye();
                    //System.out.println(("\nExecution Time : " + ((double) System.currentTimeMillis() - s) / 1000) + " s");
                    pw.flush();
                    pw.close();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
}