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 org.omg.CORBA.MARSHAL;

import java.awt.event.InputEvent;
import java.awt.image.AreaAveragingScaleFilter;
import java.io.*;
import java.net.CookieHandler;
import java.util.*;
import java.math.*;
import java.lang.*;


public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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

        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }

    static long gcd(long a,long b){ if(b==0)return a;return gcd(b,a%b); }
    static long modPow(long a,long p,long m){ if(a==1)return 1;long ans=1;while (p>0){ if(p%2==1)ans=(ans*a)%m;a=(a*a)%m;p>>=1; }return ans; }
    static long modInv(long a,long m){return modPow(a,m-2,m);}


    void dfs2(int u,int par,ArrayList<Integer> l[],long ans[],long  child[]){
        for(int v:l[u]){
            if(par!=-1) {
                ans[u] = (ans[par] + (total - child[u])) - (ans[u] + child[u]) + ans[u];
            }
            if(v==par)continue;
            dfs2(v,u,l,ans,child);
        }
    }

    void dfs(int u,int par,int d,ArrayList<Integer> l[],long  ans[],long  val[],long  child[]){
        for(int v:l[u]){
            if(v==par)continue;
            dfs(v,u,d+1,l,ans,val,child);
            ans[u]+=ans[v];
            ans[u]+=child[v];
        }
    }

    long total=0;

    void f(int u,int par,long []child,ArrayList<Integer> l[],long  val[]){
        child[u]=val[u];
        total+=val[u];
        for(int v:l[u]){
            if(v==par)continue;
            f(v,u,child,l,val);
            child[u]+=child[v];
        }
    }

    public void run() {
        Scanner  sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        long val[]=new long[n];
        for (int i = 0; i <n ; i++) {
            val[i]=sc.nextInt();
        }
        ArrayList<Integer> l[]=new ArrayList[n];
        for (int i = 0; i <n ; i++) {
            l[i]=new ArrayList<>();
        }
        for (int i = 0; i <n-1 ; i++) {
            int u=sc.nextInt()-1;
            int v=sc.nextInt()-1;
            l[u].add(v);
            l[v].add(u);
        }
        long ans[]=new long[n];
        long child[]=new long[n];
        f(0,-1,child,l,val);
        dfs(0,-1,0,l,ans,val,child);
        dfs2(0,-1,l,ans,child);

        long max=-1;
        for (int i = 0; i <n ; i++) {
            max=Math.max(max,ans[i]);
        }

        out.println(max);


        out.close();
    }

}