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.io.IOException;

import java.util.*;
//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;

//import sun.net.www.content.audio.wav;



    
   public  class Codeforces {
        
        public static long mod = (long)Math.pow(10, 9)+7 ;
        public static double epsilon=0.00000000008854;//value of epsilon
        public static InputReader sc = new InputReader(System.in);
        public static PrintWriter pw = new PrintWriter(System.out);
        
        public static long gcd(long a,long b){
            while(b>0){
                long t=b;
                b=a%b;
                a=t;
            }
            return a;
        }
        public static int fun(int n,int h,int th,int dp[][],int a[],int l,int r){
            if(n==a.length){
                if(l<=h&&r>=h)
                return 1;
                else return 0;
            }
            if(dp[n][h]>-1){
                return dp[n][h];
            }
            if(n>0&&l<=h&&r>=h){
                //pw.println(h);
                dp[n][h]=1;
            }
            else dp[n][h]=0;
            //pw.println(n+" "+(h+a[n]+th)%th+" "+(h+a[n]-1+th)%th);
            return dp[n][h]+=Math.max(fun(n+1, (h+a[n]+th)%th, th, dp, a,l,r),fun(n+1, (h+a[n]-1+th)%th, th, dp, a,l,r));
        }
        public static ArrayList<ArrayList <Integer>> GetGraph(int n,int m){
            ArrayList<ArrayList <Integer>> a=new ArrayList<>();
            for(int i=0;i<n;i++){
                a.add(new ArrayList<>());
            }
            for(int i=0;i<m;i++){
                int u=sc.nextInt()-1;
                int v=sc.nextInt()-1;
                a.get(u).add(v);
                a.get(v).add(u);
            } 
            return a;
        }
        static int dfs(int src, ArrayList<ArrayList<Integer>> list, int vis[],int dp[],int p[])
            {
                //Here 0-white,1-gray & 2-black;
            // Time complexity O(n+m)
            
            vis[src]=1;
            for(int i=0;i<list.get(src).size();i++){
                int v=list.get(src).get(i);
                if(vis[v]==0){
                    p[v]=src;
                  dp[src] += Math.max(dfs(v, list, vis, dp, p), 0);
                }
            }
            vis[src]=2;
            return dp[src];

            }

            static void dfs1(int src, ArrayList<ArrayList<Integer>> list, int vis[],int dp[],int p[])
            {
                //Here 0-white,1-gray & 2-black;
            // Time complexity O(n+m)
            
            vis[src]=1;
            
            for(int i=0;i<list.get(src).size();i++){
                int v=list.get(src).get(i);
                if(vis[v]==0){
                    //p[v]=src;
                    if(dp[v]>=0){
                        int pv=dp[src]-dp[v];
                        dp[v]+=Math.max(pv, 0);
                    }
                    else{
                        dp[v]+=Math.max(dp[src], 0);
                    }
                    dfs1(v, list, vis, dp, p);
                }
            }
            vis[src]=2;
            //return dp[src];

            }
        public static void main(String[] args) {
            // code starts..
            int n=sc.nextInt();
            int a[]=scanArray(n);
            ArrayList<ArrayList<Integer>> g=GetGraph(n, n-1);
            int p[]=new int[n];
            int dp[]=new int[n];
            for(int i=0;i<n;i++){
                if(a[i]==0){
                    dp[i]=-1;
                }
                else dp[i]=1;
            }
            dfs(0, g, new int[n], dp, p);
            dfs1(0, g, new int[n], dp, p);
            for(int i=0;i<n;i++){
                pw.print(dp[i]+" ");
            }
            // Code ends...
            pw.flush();
            pw.close();
        }
       
        public static Comparator<Integer[]> column(int i){
            return 
            new Comparator<Integer[]>() {
                @Override
                public int compare(Integer[] o1, Integer[] o2) {
                    return o1[i].compareTo(o2[i]);//for ascending
                    //return o2[i].compareTo(o1[i]);//for descending
                }
            };
        }
        public static String reverseString(String s){
            StringBuilder input1 = new StringBuilder(); 
            input1.append(s);  
            input1 = input1.reverse();
            return input1.toString();
        }
        public static int[] scanArray(int n){
            int a[]=new int [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
    
            return a;
        }
        public static long[] scanLongArray(int n){
            long a[]=new long [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLong();
    
            return a;
        }
        public static String [] scanStrings(int n){
            String a[]=new String [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLine();
    
            return a;
        }
        
    }
    
    class InputReader {
    
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;
    
            public InputReader(InputStream stream) {
                this.stream = stream;
            }
    
            public int snext() {
                if (snumChars == -1)
                    throw new InputMismatchException();
                if (curChar >= snumChars) {
                    curChar = 0;
                    try {
                        snumChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snumChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }
    
            public int nextInt() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public long nextLong() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nextInt();
                }
                return a;
            }
    
            public String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
            }
    
            public String nextLine() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isEndOfLine(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;
            }
    
            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            }
    
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }