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.lang.reflect.Array;
import java.util.*;
import java.util.function.DoubleUnaryOperator;
import java.util.stream.Collectors;
import java.util.stream.IntStream;


public class Main {

  public static void main(String[] args) {
    solve();
  }

  final static int MAXN = 200005;
  final static int MAXK = 505;
  static int N = 0;;
  static int M = 0;
  static int K = 0;
  static int W = 0;
  static int H = 0;
  static int T = 0;
  static int[] A;
  static int[] dp;
  static int[][] pre;
  static HashMap<Integer, List<Integer>> g = new HashMap<>();
  static int curAns = Integer.MAX_VALUE;
  static long[] HASH = new long[MAXN];
  static long MOD = (1L << 50) + 7;
  static int[][] memo;
  static boolean[][] seen;

  static int[] colors;
  static List<Pair<Integer, Integer>>[] edges;
  static int[] ans;
  static long[] cal;

  static void dfs(int curr, int parent) {
    dp[curr] = A[curr];
    for (int to: g.get(curr)) {
      if (to != parent) {
        dfs(to, curr);
        dp[curr] += Math.max(0, dp[to]);
      }
    }
  }

  static void dfs2(int curr, int parent) {
    ans[curr] = dp[curr];
    for (int to : g.get(curr)) {
      if (to != parent) {
        dp[curr] -= Math.max(0, dp[to]);
        dp[to] += Math.max(0, dp[curr]);
        dfs2(to, curr);
        dp[to] -= Math.max(0, dp[curr]);
        dp[curr] += Math.max(0, dp[to]);
      }
    }
  }


  static void solve() {
    FastReader scanner = new FastReader();
    PrintWriter out = new PrintWriter(System.out);
    N = scanner.nextInt();
    A = new int[N+1];
    dp = new int[N+1];
    ans = new int[N+1];
    for (int i = 1; i <= N; i++) {
      int v = scanner.nextInt();
      A[i] = v == 1 ? 1 : -1;
      g.put(i, new ArrayList<>());
    }
    for (int i = 0; i < N-1; i++) {
      int u = scanner.nextInt();
      int v = scanner.nextInt();
      g.get(u).add(v);
      g.get(v).add(u);
    }

    dfs(1, -1);
    dfs2(1, -1);
    String s = IntStream.rangeClosed(1, N)
      .mapToObj(i -> String.valueOf(ans[i]))
      .collect(Collectors.joining(" "));

    out.println(s);
    out.close();
  }


  public static class FastReader {
    BufferedReader br;
    StringTokenizer st;


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

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

    int nextInt() {
      return Integer.parseInt(next());//converts string to integer
    }

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

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

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

class CPair {
  public int max_count = 0;
  public long sum = 0;
  public TreeMap<Integer, Integer> a = new TreeMap<>();
}

class UnioinSet {
  private Map<Long, Long> parents = new HashMap<>();

  public Long find(Long u) {
    if (parents.getOrDefault(u, u).equals(u)) {
      return u;
    }

    return find(parents.get(u));
  }

  public void union(Long u, Long v) {
    Long pu = find(u);
    Long pv = find(v);

    parents.put(pu, pv);
  }
}


class Pair<A, B> implements Comparable<Pair<A, B>>{
  private A first;
  private B second;

  public Pair(A first, B second) {
    super();
    this.first = first;
    this.second = second;
  }

  public String toString()
  {
    return "(" + first + ", " + second + ")";
  }

  public A getFirst() {
    return first;
  }

  public void setFirst(A first) {
    this.first = first;
  }

  public B getSecond() {
    return second;
  }

  public void setSecond(B second) {
    this.second = second;
  }

  @Override
  public int compareTo(Pair<A, B> o) {
    int cmp = compare(first, o.first);
    return cmp == 0 ? compare(second, o.second) : cmp;
  }

  private static int compare(Object o1, Object o2) {
    return o1 == null ? o2 == null ? 0 : -1 : o2 == null ? +1
      : ((Comparable) o1).compareTo(o2);
  }

  @Override
  public int hashCode() {
    return 31 * hashcode(first) + hashcode(second);
  }

  private static int hashcode(Object o) {
    return o == null ? 0 : o.hashCode();
  }

  public boolean equals(Object other) {
    if (other instanceof Pair) {
      Pair<A, B> otherPair = (Pair<A, B>) other;
      return
        ((  this.first == otherPair.first ||
          ( this.first != null && otherPair.first != null &&
            this.first.equals(otherPair.first))) &&
          (  this.second == otherPair.second ||
            ( this.second != null && otherPair.second != null &&
              this.second.equals(otherPair.second))) );
    }

    return false;
  }
}