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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author real
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        ArrayList<ArrayList<Integer>> list;
        long[] val;
        long[] cost;
        long ans = 0;
        long totsum = 0;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            val = new long[n + 1];
            for (int i = 0; i < n; i++) {
                val[i + 1] = in.nextInt();
                totsum += val[i + 1];
            }
            list = in.initlist(n);
            for (int i = 0; i < n - 1; i++) {
                int u = in.nextInt();
                int v = in.nextInt();
                list.get(u).add(v);
                list.get(v).add(u);
            }
            cost = new long[n + 1];
            dfs(1, 0);
            long ans1 = calculate(1, 0, 0);
            calc(1, 0, ans1);
            out.print(ans);
        }

        void dfs(int node, int parent) {
            cost[node] = val[node];
            for (int x : list.get(node)) {
                if (x != parent) {
                    dfs(x, node);
                    cost[node] += cost[x];
                }
            }
        }

        long calculate(int node, int parent, int level) {
            long ans = level * val[node];
            for (int x : list.get(node)) {
                if (x != parent) {
                    ans += calculate(x, node, level + 1);
                }
            }
            return ans;
        }

        void calc(int node, int p, long sum) {
            // System.out.println(sum+" "+node);
            ans = Math.max(ans, sum);
            for (int x : list.get(node)) {
                if (x != p) {
                    calc(x, node, sum + totsum - 2 * cost[x]);
                }
            }
        }

    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar;
        private int snumChars;

        public InputReader(InputStream st) {
            this.stream = st;
        }

        public int read() {
            //*-*------clare------
//remeber while comparing 2 non primitive data type not to use ==
//remember Arrays.sort for primitive data has worst time case complexity of 0(n^2) bcoz it uses quick sort
//again silly mistakes ,yr kb tk krta rhega ye mistakes
//try to write simple codes ,break it into simple things
            // for test cases make sure println(); ;)
//knowledge>rating
        /*
        public class Main
        implements Runnable{
    public static void main(String[] args) {
        new Thread(null,new Main(),"Main",1<<26).start();

    }
    public void run() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();//chenge the name of task
        solver.solve(1, in, out);
        out.close();
    }
         */

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

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public ArrayList<ArrayList<Integer>> initlist(int n) {
            ArrayList<ArrayList<Integer>> list = new ArrayList<>();
            for (int i = 0; i <= n; i++) {
                list.add(new ArrayList<Integer>());
            }
            return list;
        }

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

    }
}