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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.lang.reflect.Array;
import java.util.Arrays;


public class water {
    public static int dfs1(int last,int poi,int a[][],int b[]){
        int x=b[poi-1];
        for(int i=1;i<a[poi].length;i++){
            if(a[poi][i]!=last)
               x+=dfs1(poi,a[poi][i],a,b);
        }
        if(x>=0) b[poi-1]=x;
        if(b[poi-1]>0)
         return b[poi-1];
        else
            return 0;
    }
    public static void dfs2(int last,int poi,int a[][],int b[],int faz){
        b[poi-1]+=faz;
        for(int i=1;i<a[poi].length;i++){
            if(a[poi][i]!=last){
                int x=b[poi-1];
                if(b[a[poi][i]-1]>0)
                    x-=b[a[poi][i]-1];
                if(x>=0)
                dfs2(poi,a[poi][i],a,b,x);
                else
                    dfs2(poi,a[poi][i],a,b,0);
            }
        }
    }
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastInput input = new FastInput(inputStream);
        FastOutput out = new FastOutput(outputStream);
        int n = input.scanInt();
        int a[]=new int [n];
        int len[]= new int [n+1];
        int b[][]=new int [n-1][2];
        for(int i=0;i<n;i++ ){
            int x= input.scanInt();
            if(x==1){
                a[i]=1;
            }
            else
                a[i]=-1;
        }
        for(int i=0;i<n-1;i++){
            b[i][0]= input.scanInt();
            b[i][1]= input.scanInt();
            len[b[i][0]]++;
            len[b[i][1]]++;
        }
        int c[][]=new int[n+1][];
        for(int i=1;i<n+1;i++){
            c[i]=new int [len[i]+1];
        }
        for(int i=0;i<n-1;i++){
            c[b[i][0]][len[b[i][0]]--]=b[i][1];
            c[b[i][1]][len[b[i][1]]--]=b[i][0];
        }
        dfs1(0,1,c,a);

        dfs2(0,1,c,a,0);
        for(int i=0;i<n;i++){
            System.out.println(" "+a[i]);
        }


    }

    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;
        public FastInput(InputStream is) {
            this.is = is;
        }
        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }
        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }
        public String next() {
            return readString();
        }
        public int scanInt() {
            int sign = 1;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }
            int val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            return (sign*val);
        }

        public String readString(StringBuilder builder) {
            skipBlank();
            while (next > 32) {
                builder.append((char) next);
                next = read();
            }
            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

    }
    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(1 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            return this;
        }
        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }
        public FastOutput println(int c) {
            return append(c).println();
        }
        public FastOutput println(String c) {
            return append(c).println();
        }

        public FastOutput println() {
            //cache.append(System.lineSeparator());
            flush();
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }


}