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.*;

import static java.lang.Math.*;

public class Maximum_White_Subtree implements Runnable {
	boolean multiple = false; // for multiple test cases
	long MOD = 998244353;

	@SuppressWarnings("Duplicates")
	void solve() throws Exception {
		int n = sc.nextInt();
		Graph g = new Graph();
		for (int i = 1; i <= n; i++) {
			g.addVertex(i);
		}
		g.dp = new int[n + 1];
		g.ans = new int[n + 1];

		g.w = new int[n + 1];
		for (int i = 1; i <= n; i++)
			g.w[i] = sc.nextInt();
		for (int i = 1; i < n; i++) {
			int x = sc.nextInt();
			int y = sc.nextInt();
			g.addEdge(x, y);
		}

		g.dfs(1, -1);
		g.dfs2(1, -1);
		for (int i = 1; i <= n; i++) {
			System.out.print(g.ans[i] + " ");
		}
	}

	public class Graph {
		int[] w;

		private class vertex {
			HashMap<Integer, Integer> nbrs = new HashMap<>();
		}

		private HashMap<Integer, vertex> vtces;

		public Graph() {
			vtces = new HashMap<>();
		}

		public void addVertex(int vname) {
			vertex vtx = new vertex();
			this.vtces.put(vname, vtx);
		}

		public void addEdge(int vname1, int vname2) {
			int cost = 0;
			vertex vtx1 = vtces.get(vname1);
			vertex vtx2 = vtces.get(vname2);
			vtx1.nbrs.put(vname2, cost);
			vtx2.nbrs.put(vname1, cost);

		}

		public void display() {
			System.out.println("-------------------------------");
			ArrayList<Integer> keys = new ArrayList<>(vtces.keySet());
			for (Integer key : keys) {
				vertex vtx = vtces.get(key);
				System.out.println(key + "-> " + vtx.nbrs);
			}
			System.out.println("-------------------------------------");
		}

		int[] dp;
		int[] ans;

		public int dfs(int cur, int par) {
			int sum = -1;
			if (w[cur] == 1)
				sum = 1;
			vertex node = vtces.get(cur);

			for (int nbr : node.nbrs.keySet()) {
				if (nbr == par) {
					continue;
				}
				sum += (int) Math.max(0, dfs(nbr, cur));
			}
			dp[cur] = sum;
			return dp[cur];
		}

		public void dfs2(int cur, int par) {

			if (par != -1) {
				int temp = ans[par] - Math.max(0, dp[cur]);
				ans[cur] = dp[cur] + Math.max(0, temp);

			} else {
				ans[cur] = dp[cur];
			}

			vertex node = vtces.get(cur);

			for (int nbr : node.nbrs.keySet()) {
				if (nbr == par) {
					continue;
				}
				dfs2(nbr, cur);
			}

		}

	}

	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			sc = new FastScanner(in);
			if (multiple) {
				int q = sc.nextInt();
				for (int i = 0; i < q; i++)
					solve();
			} else
				solve();
		} catch (Throwable uncaught) {
			Maximum_White_Subtree.uncaught = uncaught;
		} finally {
			out.close();
		}
	}

	public static void main(String[] args) throws Throwable {
		Thread thread = new Thread(null, new Maximum_White_Subtree(), "", (1 << 26));
		thread.start();
		thread.join();
		if (Maximum_White_Subtree.uncaught != null) {
			throw Maximum_White_Subtree.uncaught;
		}
	}

	static Throwable uncaught;
	BufferedReader in;
	FastScanner sc;
	PrintWriter out;
}

class FastScanner {
	BufferedReader in;
	StringTokenizer st;

	public FastScanner(BufferedReader in) {
		this.in = in;
	}

	public String nextToken() throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

	public int nextInt() throws Exception {
		return Integer.parseInt(nextToken());
	}

	public long nextLong() throws Exception {
		return Long.parseLong(nextToken());
	}

	public double nextDouble() throws Exception {
		return Double.parseDouble(nextToken());
	}
}