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.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author MakeMoroccoGreatAgain
 */
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);
    FMaximumWhiteSubtree solver = new FMaximumWhiteSubtree();
    solver.solve(1, in, out);
    out.close();
  }

  static class FMaximumWhiteSubtree {
    public final void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      int[] a = in.nextIntArrayOneBased(n);
      int[][] e = in.nextIntMatrix(n - 1, 2);
      int[][] t = GraphUtils.packUndirectedUnweighted(e, n);
      int[] dp = new int[n + 1];
      Arrays.fill(dp, -n * 2);
      solveSubtrees(t, dp, a, 1, 0);
      solve(t, dp, 1, 0, 0);
      out.println(StringUtils.joinRange(1, n, dp));
    }

    private final void solveSubtrees(int[][] t, int[] dp, int[] a, int u, int p) {
      dp[u] = a[u] * 2 - 1;
      for (int v : t[u]) {
        if (v == p) {
          continue;
        }
        solveSubtrees(t, dp, a, v, u);
        dp[u] += Math.max(0, dp[v]);
      }
    }

    private final void solve(int[][] t, int[] dp, int u, int p, int parDiff) {
      dp[u] += Math.max(0, parDiff);
      for (int v : t[u]) {
        if (v == p) {
          continue;
        }
        solve(t, dp, v, u, dp[u] - Math.max(0, dp[v]));
      }
    }
  }

  static class StringUtils {
    private StringUtils() {
      throw new RuntimeException("DON'T");
    }

    public static final String joinRange(String delimiter, int from, int to, int[] a) {
      if (from > to) {
        return "";
      }
      StringBuilder sb = new StringBuilder();
      sb.append(a[from]);
      for (int i = from + 1; i <= to; i++) {
        sb.append(delimiter).append(a[i]);
      }
      return sb.toString();
    }

    public static final String joinRange(int from, int to, int[] a) {
      return joinRange(" ", from, to, a);
    }
  }

  static final class InputReader {
    private final InputStream stream;
    private final byte[] buf = new byte[1 << 16];
    private int curChar;
    private int numChars;

    public InputReader() {
      this.stream = System.in;
    }

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

    private final int read() {
      if (this.numChars == -1) {
        throw new UnknownError();
      } else {
        if (this.curChar >= this.numChars) {
          this.curChar = 0;

          try {
            this.numChars = this.stream.read(this.buf);
          } catch (IOException ex) {
            throw new InputMismatchException();
          }

          if (this.numChars <= 0) {
            return -1;
          }
        }

        return this.buf[this.curChar++];
      }
    }

    public final int nextInt() {
      int c;
      for (c = this.read(); isSpaceChar(c); c = this.read()) {}

      byte sgn = 1;
      if (c == 45) { // 45 == '-'
        sgn = -1;
        c = this.read();
      }

      int res = 0;

      while (c >= 48 && c <= 57) { // 48 == '0', 57 == '9'
        res *= 10;
        res += c - 48; // 48 == '0'
        c = this.read();
        if (isSpaceChar(c)) {
          return res * sgn;
        }
      }

      throw new InputMismatchException();
    }

    private static final boolean isSpaceChar(final int c) {
      return c == 32 || c == 10 || c == 13 || c == 9
          || c == -1; // 32 == ' ', 10 == '\n', 13 == '\r', 9 == '\t'
    }

    public final int[][] nextIntMatrix(final int n, final int m) {
      int[][] arr = new int[n][m];
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
          arr[i][j] = nextInt();
        }
      }
      return arr;
    }

    public final int[] nextIntArrayOneBased(final int n) {
      int[] ret = new int[n + 1];
      for (int i = 1; i <= n; i++) {
        ret[i] = nextInt();
      }
      return ret;
    }
  }

  static final class GraphUtils {
    private GraphUtils() {
      throw new RuntimeException("DON'T");
    }

    public static final int[][] packUndirectedUnweighted(int[][] edges, int n) {
      int[][] g = new int[n + 1][];
      int[] size = new int[n + 1];
      for (int[] edge : edges) {
        ++size[edge[0]];
        ++size[edge[1]];
      }
      for (int i = 0; i <= n; i++) {
        g[i] = new int[size[i]];
      }
      for (int[] edge : edges) {
        g[edge[0]][--size[edge[0]]] = edge[1];
        g[edge[1]][--size[edge[1]]] = edge[0];
      }
      return g;
    }
  }
}