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.util.*;
import java.text.*;
import java.lang.*;
import java.math.*;

public class Main{
	static ArrayList a[] = new ArrayList [200001];
	static int val[] =  new int [200001];
	static int dp[] = new int [200001];
	static int ans[] = new int [200001];
	static void dfs(int n , int p) {
		dp[n] = val[n];
		for(int i = 0 ; i < a[n].size() ; i++) {
			int idx = (int) a[n].get(i);
			if(idx == p) continue;
			dfs(idx , n);
			dp[n] = Math.max(dp[n], dp[n] + dp[idx]);
		}
		
	}
	static void dfs1(int n , int p) {
		for(int i = 0 ; i < a[n].size() ; i++) {
			int idx = (int) a[n].get(i);
			if(idx == p) continue;
			ans[idx] = dp[idx];
			if(ans[idx] >= 0) {
				ans[idx] = Math.max(ans[n], ans[idx]);
			}
			else {
				ans[idx] = Math.max(ans[idx], ans[n] - 1);
			}
			dfs1(idx , n);
		}
		
	}
	public void solve () throws IOException  {
       
    	InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        for(int i = 1 ; i <= n ; i++) {
        	val[i] = in.nextInt();
        	a[i] = new ArrayList<Integer>();
        	if(val[i] == 0) val[i]--;
        }
        for(int i = 0; i < n - 1; i++) {
        	int x = in.nextInt();
        	int y = in.nextInt();
        	a[x].add(y);
        	a[y].add(x);
        }
        dfs(1 , 0);
        ans[1] = dp[1];
        dfs1(1 , 0);
        for(int i = 1 ; i <= n ; i++) {
        	pw.print(ans[i] +" ");
        }
        pw.flush(); 
        pw.close();
    }
	
    public static void main(String[] args) throws Exception {
        
        
        new Thread(null,new Runnable() {
            public void run() {
                    try {
                        new Main().solve();
                    } catch (FileNotFoundException e) {
                        e.printStackTrace();
                    } catch (IOException e) {
						e.printStackTrace();
					}
            }  
        },"1",1<<26).start();
        
        
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static 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);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
       
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        public static long LCM (long a,long b) {
            return ((a*b)/(GCD(a,b)));
        }
        
        static class pair implements Comparable<pair>
        {
            Integer y ;
            Long x ;
            
            pair(long  l, int w )
            {
                this.x=l;
                this.y=w;
            }

           
            public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            public int hashCode()
            {
                return x.hashCode()*3 +  y.hashCode();
                
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
       
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        static class Segment{ 
    		int seg[]; 
    		int a[];
    		int lazy[];
    	    Segment (int n){
    			seg=new int[4*n];
    		}
    	    public void build(int node,int start,int end) {
    	    	if(start==end) {
    	    		seg[node] = 0;
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	build(2*node+1,start,mid);
    	    	build(2*node+2,mid+1,end);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public void update(int node,int start,int end,int id,int val) {
    	    	if(start==end) {
    	    		seg[node] = seg[node] + val;
    	    		return;
    	    	}
    	    	int mid=(start+end)/2;
    	    	if(id>=start && id<=mid) {
    	    		update(2*node+1,start,mid,id,val);
    	    	}
    	    	else
    	    		update(2*node+2,mid+1,end,id,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int query(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    	    }
    	    public void updateRange(int node,int start,int end,int l,int r,int val) {
    	    	if(lazy[node]!=0) {
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(l>end || r<start)
    	    		return ;
    	    	if(start>=l && end<=r) {
    	    		seg[node]=(end-start+1)*val;
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=val;
    	    			lazy[2*node+2]+=val;
    	    		}
    	    		lazy[node]=0;
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	updateRange(2*node+1,start,mid,l,r,val);
    	    	updateRange(2*node+2,mid+1,end,l,r,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int queryRange(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(lazy[node]!=0) {
    	    		seg[node]=(end-start+1)*lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    	    }
    	    
    	}
       
        
                    
         
}