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.InputStream;
import java.io.OutputStream;
import java.util.List;
import java.util.ArrayList;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.IOException;
import java.util.InputMismatchException;
import java.lang.Math;

public class MaxCostTree {
    public static void main (String[] args) {
        InputStream inpStream = System.in;
        OutputStream outStream = System.out;
        
        //Input a weighted undirected tree
        InputReader in = new InputReader(inpStream);
        OutputWriter out = new OutputWriter(outStream);
        MaxCostSolve cost = new MaxCostSolve();
        cost.solve(1, in, out);
        out.close();
    }

    static class MaxCostSolve {
        int n;
        List<Integer>[] graph;
        int[] arr;
        long[] treeSum;
        int[] depth;
        long ans = 0;

        public void solve (int testNumber, InputReader in, OutputWriter out) {
            
            //Input the nodes in the graph             
            n = in.readInt();
            arr = in.readIntArray(n);
            graph = new List[n];
                
            for (int i = 0; i < n; i++) {
                graph[i] = new ArrayList<>();            
            }         
            for (int i = 0; i < n - 1; i++) {
                int u = in.readInt() - 1;
                int v = in.readInt() - 1;
                graph[u].add(v);
                graph[v].add(u);            
            }
            
            /*
            System.out.println("Graph");
            for (int i = 0; i < n; i++) {
                List<Integer> list = graph[i];
                for (Integer elem : list) {
                    System.out.print(elem + " ");                            
                }            
                System.out.println();
            }
            */
            
            treeSum = new long[n];
            depth = new int[n];
            dfs0(0);
            
            //Cost of the tree with vertex 0 as the node     
            for (int i = 0; i < n; i++) {
                ans += depth[i]*(long)arr[i];                   
            }          
             
            dfs(0, 0, ans);
            out.print(ans);
            
        }
            
        //Calculate the depth at which each node is present in the graph and sum of the weights of the tree as an array where index i is the root.      
        void dfs0 (int v) {
            treeSum[v] += arr[v];
            for (int to : graph[v]) {
                graph[to].remove((Integer) v);
                depth[to] = depth[v] + 1;
                dfs0(to); 
                treeSum[v] += treeSum[to];           
            }        
        }
        
        //We are re-rooting here, trying out different vertices as roots and calculating distances
        void dfs (int v, long sumUp, long curAns) {
            ans = Math.max(ans, curAns);
            for (int to : graph[v]) {
                long addSum = (treeSum[v] - treeSum[to]) + sumUp;
                //sumUp is the change occured when the root is changing
                dfs(to, sumUp + treeSum[v] - treeSum[to], curAns + addSum - treeSum[to]);
                //when the roots change, ans also changes by curAns + addSum - treeSum[to] amount            
            }        
        }
    }
    
    static class InputReader{
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader (InputStream stream) {
            this.stream = stream;        
        }        
        
        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();            
            }        
            return array;
        }    
        
        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 int readInt() {
            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 boolean isSpaceChar (int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            } 
            return isWhiteSpace(c);
       }
        
       public static boolean isWhiteSpace (int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
       }          
        
       public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch); 
       }
    }
    
    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter (OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));        
        }    
        
        public OutputWriter (Writer writer) {
            this.writer = new PrintWriter(writer);        
        }

        public void close() {   
            writer.close();        
        }
        
        public void print (long i) {
            writer.print(i);        
        }
    }
}