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

public class CFA {
  BufferedReader br;
  PrintWriter out;
  StringTokenizer st;
  boolean eof;
//  private static final long MOD = 1000L * 1000L * 1000L + 7;
  private static final long MOD = 998244353L;
  private static final int[] dx = {0, -1, 0, 1};
  private static final int[] dy = {1, 0, -1, 0};
  private static final String yes = "Yes";
  private static final String no = "No";

  void solve() {
//    int T = nextInt();
    int T = 1;
    for (int i = 0; i < T; i++) {
      helper();
    }
  }

  int n;
  List<List<Integer>> graph;
  long[] subtree;
  long res;
  long[] dist;
  long treeSize;
  int[] arr;
  void helper() {
    n = nextInt();
    arr = nextIntArr(n);
    graph = new ArrayList<>();
    for (int i = 0; i < n; i++) {
      graph.add(new ArrayList<>());
    }
    for (int i = 0; i < n - 1; i++) {
      int from = nextInt() - 1;
      int to = nextInt() - 1;
      graph.get(from).add(to);
      graph.get(to).add(from);
    }
    subtree = new long[n];
    dist = new long[n];
    dfs(-1, 0, 0);

    treeSize = 0;
    for (int v : arr) {
      treeSize += v;
    }

    res = 0;
    long tmp = 0;
    for (int i = 0; i < n; i++) {
      tmp += dist[i] * arr[i];
    }
    dfs2(-1, 0, tmp);

    outln(res);
  }

  void dfs2(int par, int cur, long pref) {
    res = Math.max(res, pref);
    for (int nxt : graph.get(cur)) {
      if (nxt == par) {
        continue;
      }
      dfs2(cur, nxt, pref + treeSize - 2 * subtree[nxt]);
    }
  }

  void dfs(int par, int cur, int d) {
    subtree[cur] += arr[cur];
    dist[cur] = d;
    for (int nxt : graph.get(cur)) {
      if (nxt == par) {
        continue;
      }
      dfs(cur, nxt, d + 1);
      subtree[cur] += subtree[nxt];
    }
  }


  void shuffle(long[] a) {
    int n = a.length;
    for(int i = 0; i < n; i++) {
      int r = i + (int) (Math.random() * (n - i));
      long tmp = a[i];
      a[i] = a[r];
      a[r] = tmp;
    }
  }

  int gcd(int a, int b) {
    while(a != 0 && b != 0) {
      int c = b;
      b = a % b;
      a = c;
    }
    return a + b;
  }
  private void outln(Object o) {
    out.println(o);
  }
  private void out(Object o) {
    out.print(o);
  }
  private void formatPrint(double val) {
    outln(String.format("%.9f%n", val));
  }
  public CFA() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);
    solve();
    out.close();
  }
  public static void main(String[] args) {
    new CFA();
  }

  public long[] nextLongArr(int n) {
    long[] res = new long[n];
    for(int i = 0; i < n; i++)
      res[i] = nextLong();
    return res;
  }
  public int[] nextIntArr(int n) {
    int[] res = new int[n];
    for(int i = 0; i < n; i++)
      res[i] = nextInt();
    return res;
  }
  public String nextToken() {
    while (st == null || !st.hasMoreTokens()) {
      try {
        st = new StringTokenizer(br.readLine());
      } catch (Exception e) {
        eof = true;
        return null;
      }
    }
    return st.nextToken();
  }
  public String nextString() {
    try {
      return br.readLine();
    } catch (IOException e) {
      eof = true;
      return null;
    }
  }
  public int nextInt() {
    return Integer.parseInt(nextToken());
  }
  public long nextLong() {
    return Long.parseLong(nextToken());
  }
  public double nextDouble() {
    return Double.parseDouble(nextToken());
  }
}