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 Main implements Runnable{
    FastScanner sc;
    PrintWriter pw;
    final class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
 
        public long nlo() {
            return Long.parseLong(next());
        }
 
        public String next() {
            if (st.hasMoreTokens()) return st.nextToken();
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return st.nextToken();
        }
 
        public int ni() {
            return Integer.parseInt(next());
        }
 
        public String nli() {
            String line = "";
            if (st.hasMoreTokens()) line = st.nextToken();
            else try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            while (st.hasMoreTokens()) line += " " + st.nextToken();
            return line;
        }
 
        public double nd() {
            return Double.parseDouble(next());
        }
    }
    public static void main(String[] args)
    {
        new Thread(null,new Main(),"codeforces",1<<25).start();
    }
    public void run()
    {
        sc=new FastScanner();
        pw=new PrintWriter(System.out);
       int t=1;
       while(t-->0)
       solve();
        pw.flush();
        pw.close();
    }
    public long gcd(long a,long b)
    {
        return b==0L?a:gcd(b,a%b);
    }
    public int[] col;
    public int[] wrr,brr,visit;
    public ArrayList<Integer>[] adj;
    public void solve()
    {
        int n=sc.ni();
        brr=new int[n];
        wrr=new int[n];
        visit=new int[n];
        col=new int[n];
        adj=new ArrayList[n];
        for(int i=0;i<n;i++)
        adj[i]=new ArrayList();
        for(int i=0;i<n;i++)
        col[i]=sc.ni();
        for(int i=0;i<n-1;i++)
        {
            int x=sc.ni()-1;
            int y=sc.ni()-1;
            adj[x].add(y);
            adj[y].add(x);
        }
        dfs(0);
        Arrays.fill(visit,0);
        dfs1(0,0,0);
        for(int i=0;i<n;i++)
        pw.print(Math.max(brr[i],-1)+" ");
    }
    public void dfs(int x)
    {
        visit[x]=1;
        int t1=0,t2=0;
        for(int y:adj[x])
        {
            if(visit[y]==0)
            {
            dfs(y);
            t1+=Math.max(0,wrr[y]);
            t2+=Math.max(0,brr[y]);
            }
        }
            if(col[x]==1)
            {
                t1--;
                t2++;
            }
            else
            {
                t2--;
                t1++;
            }
            wrr[x]=t1;
            brr[x]=t2;
    }
    public void dfs1(int x,int w,int b)
    {
        //System.out.println(x+" "+w+" "+b);
        wrr[x]+=Math.max(0,w);
        brr[x]+=Math.max(0,b);
        visit[x]=1;
        w=Math.max(w,0);
        b=Math.max(b,0);
        for(int y:adj[x])
        {
            if(visit[y]==0)
            {w+=Math.max(0,wrr[y]);
            b+=Math.max(0,brr[y]);}
        }
        if(col[x]==1)
        {
            w--;
            b++;
        }
        else
        {
            b--;
            w++;
        }
        for(int y:adj[x])
            if(visit[y]==0)
            dfs1(y,w-Math.max(0,wrr[y]),b-Math.max(0,brr[y]));
    }
}