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.lang.*;
import java.io.*;
import java.math.*;
import java.text.*;
public class Prac{     
    static class InputReader { 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        public InputReader(InputStream st) {
            this.stream = st;
        } 
        public int read() {
            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 ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public String rs() {
            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 String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        } 
    }
    public static class Key {

        private final int x;
        private final int y;

        public Key(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Key)) return false;
            Key key = (Key) o;
            return x == key.x && y == key.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }

    }
    
    static PrintWriter w = new PrintWriter(System.out);
    static long mod=998244353L,mod1=1000000007;
    static int co[][];
    static void dsort(){
        Arrays.parallelSort(co,(o1,o2)->o1[0]!=o2[0]?o1[0]-o2[0]:o1[1]-o2[1]);
    }
    static class Pair{
        int w,b;
        public Pair(int w,int b){
            this.b=b;
            this.w=w;
        }
    }
    static int c[],dp[],n,ans[];
    static ArrayList<Integer> arr[];
    static int dfs(int i,int p){
        int di=-1;
        if(c[i]==1)di=1;
        for(int j:arr[i]){
            if(j!=p){
                di+=(Math.max(0,dfs(j,i)));
            }
        }
        
        return dp[i] =di;
    }
    static void dfs1(int i,int p){
        for(int j:arr[i]){
            if(j!=p){
                if(dp[j]<0){
                    dp[j]+=Math.max(0,dp[i]);
                }
                else{
                    dp[j]+=Math.max(0,dp[i]-dp[j]);
                }
                dfs1(j,i);
            }
        }
    }
    public static void main (String[] args)throws IOException{
        InputReader sc=new InputReader(System.in);
        n=sc.ni();
        c=new int[n+1];
        dp=new int[n+1];
        ans=new int[n+1];
        arr=new ArrayList[n+1];
        for(int i=1;i<=n;i++){
            c[i]=sc.ni();
            arr[i]=new ArrayList<>();
        }
        for(int i=0;i<n-1;i++){
            int u=sc.ni(),v=sc.ni();
            arr[u].add(v);
            arr[v].add(u);
        }
        dfs(1,1);
//        for(int i=1;i<=n;i++){
//            w.print(dp[i]+" ");
//        }
        dfs1(1,1);
        //ans[1]=dp[1];
        for(int i=1;i<=n;i++){
            w.print(dp[i]+" ");
        }
        w.println();
        w.close();
    }
}