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 ProblemF {

    public static InputStream inputStream = System.in;

    public static OutputStream outputStream = System.out;

    public static void main(String[] args) {
        MyScanner scanner = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        int n = scanner.nextInt();
        boolean[] colors = new boolean[n + 1];
        for (int i = 0; i < n; i++) {
            int x = scanner.nextInt();
            if (x == 1) {
                colors[i + 1] = true;
            }
        }

        Tree tree = new Tree(n, colors);
        for (int i = 0; i < n - 1; i++) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            tree.addEde(x, y);
        }
        tree.makeTree(1);

        tree.specifyNodesInitialValues();

        Map<Integer, Integer> ans = new HashMap<>();
        ans.put(1, tree.nodes.get(1).value);

        tree.solve(tree.root, ans);

        for (int i = 1; i <= n; i++) {
            out.print(ans.get(i) + " ");
        }


        out.flush();
    }

    private static class Tree {

        private Node root;

        private Map<Integer, Node> nodes;

        private Tree(int n, boolean[] colors) {
            this.nodes = new HashMap<>();
            for (int i = 1; i <= n; i++) {
                nodes.put(i, new Node(i, colors[i]));
            }
        }

        private void addEde(int x, int y) {
            nodes.get(x).addChild(nodes.get(y));
            nodes.get(y).addChild(nodes.get(x));
        }

        private void makeTree(int r) {
            root = nodes.get(r);
            root.specifyParent(root);
        }

        private void specifyNodesInitialValues() {
            root.specifyValue();
        }

        private void solve(Node node, Map<Integer, Integer> ans) {
            for (Node child : node.children) {
                int x = node.value;
                int y = child.value;
                if (child.value > 0) {
                    node.value -= child.value;
                }
                if (node.value > 0) {
                    child.value += node.value;
                }
                ans.put(child.label, child.value);
                solve(child, ans);
                node.value = x;
                child.value = y;
            }
        }
    }

    private static class Node {

        private int label;

        private boolean color;

        private int value;

        private Node parent;

        private List<Node> children;

        private Node(int label, boolean color) {
            this.label = label;
            this.color = color;
            this.children = new ArrayList<>();
        }

        private void addChild(Node child) {
            this.children.add(child);
        }

        private void specifyParent(Node parent) {
            this.parent = parent;
            for (Node child : new ArrayList<>(children)) {
                if (child.label != parent.label) {
                    child.specifyParent(this);
                } else {
                    children.remove(child);
                }
            }
        }

        private void specifyValue() {
            for (Node child : children) {
                child.specifyValue();
                if (child.value > 0) {
                    value += child.value;
                }
            }
            if (color) {
                value++;
            } else {
                value--;
            }
        }
    }

    private static class MyScanner {
        private BufferedReader bufferedReader;
        private StringTokenizer stringTokenizer;

        private MyScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private String next() {
            while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

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

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

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

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

    private static class Pair<F, S> {

        private F first;

        private S second;

        public Pair() {
        }

        public Pair(F first, S second) {
            this.first = first;
            this.second = second;
        }
    }
}