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.*;import java.math.*;

public class Main
{
    static class Node{
        int mx1,mx2,idx;
        public Node(int idx){
            mx1=0;
            mx2=0;
            this.idx=idx;
        }
    }

    static class Graph{
        ArrayList<Integer> l[];
        int V,in[],out[],col[];
        Node node[];

        public Graph(int v){
            V=v;
            l=new ArrayList[V+1];
            in=new int[V+1];
            out=new int[V+1];
            col=new int[V+1];
            node=new Node[V+1];

            node[0]=new Node(0);

            for(int i=1;i<=V;i++){
                l[i]=new ArrayList<Integer>();
                node[i]=new Node(i);
            }
        }

        void addEdge(int u,int v){
            l[u].add(v);
            l[v].add(u);
        }

        void dfs1(int n,int par){
            Node curr=node[n];
            int take=0;

            in[n]=((col[n]==1)?1:-1);

            ArrayList<Integer> x=l[n];

            for(Integer child :x){
                if(child==par)
                    continue;
                dfs1(child,n);

                if(in[child]>=curr.mx1){
                    int temp=curr.mx1;
                    curr.mx1=in[child];
                    curr.mx2=temp;
                }

                if(in[child]>0)
                    take+=in[child];
            }

            in[n]+=take;
        }

        void dfs2(int n,int par){
            int rem=Math.max(in[n], 0);

            int take=in[par]+out[par]-rem;

            if(take+in[n]>in[n])
                out[n]=take;

            ArrayList<Integer> x=l[n];
            for(Integer child : x){
                if(child==par)
                    continue;
                dfs2(child,n);
            }
        }
    }

    public static void process()throws IOException
    {
        int n=ni();
        Graph g=new Graph(n);
        for(int i=1;i<=n;i++) g.col[i]=ni();

        for(int i=1;i<n;i++) g.addEdge(ni(),ni());
        g.dfs1(1,0);
        g.dfs2(1,0);

       // pn(Arrays.toString(g.in));
        //pn(Arrays.toString(g.out));
        for(int i=1;i<=n;i++) p(((g.in[i])+(g.out[i]))+" ");
        pn("");
    }


   	static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

    	oj = System.getProperty("ONLINE_JUDGE") != null;
    	if(!oj) sc=new AnotherReader(100);

        long s = System.currentTimeMillis();
        int t=1;
        while(t-->0)
            process();
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }

    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;



/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}