You are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.

Let's call colour c dominating in the subtree of vertex v if there are no other colours that appear in the subtree of vertex v more times than colour c. So it's possible that two or more colours will be dominating in the subtree of some vertex.

The subtree of vertex v is the vertex v and all other vertices that contains vertex v in each path to the root.

For each vertex v find the sum of all dominating colours in the subtree of vertex v.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of vertices in the tree.

The second line contains n integers ci (1 ≤ ci ≤ n), ci — the colour of the i-th vertex.

Each of the next n - 1 lines contains two integers xj, yj (1 ≤ xj, yj ≤ n) — the edge of the tree. The first vertex is the root of the tree.

Output

Print n integers — the sums of dominating colours for each vertex.

Examples

Input

4
1 2 3 4
1 2
2 3
2 4


Output

10 9 3 4


Input

15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13


Output

6 5 4 3 2 3 3 1 1 3 2 2 1 2 3
import java.io.IOException;
 import java.io.InputStream;
 import java.io.PrintWriter;
 import java.io.*;
 import java.util.*;
 import java.util.LinkedList;
 import java.math.*;
 import java.lang.*;
 import java.util.PriorityQueue;
 import static java.lang.Math.*;
 @SuppressWarnings("unchecked")
 public class Solution implements Runnable {
     static class InputReader {
         private InputStream stream;
         private byte[] buf = new byte[1024];
         private int curChar;
         private int numChars;
         private SpaceCharFilter filter;
         private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

         public InputReader(InputStream stream) {
             this.stream = stream;
         }

         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 String nextLine() {
             String str = "";
             try {
                 str = br.readLine();
             }
             catch (IOException e) {
                 e.printStackTrace();
             }
             return str;
         }
         public int nextInt() {
             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 long nextLong() {
             int c = read();
             while (isSpaceChar(c))
                 c = read();
             int sgn = 1;
             if (c == '-') {
                 sgn = -1;
                 c = read();
             }
             long 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 double nextDouble() {
             int c = read();
             while (isSpaceChar(c))
                 c = read();
             int sgn = 1;
             if (c == '-') {
                 sgn = -1;
                 c = read();
             }
             double res = 0;
             while (!isSpaceChar(c) && c != '.') {
                 if (c == 'e' || c == 'E')
                     return res * Math.pow(10, nextInt());
                 if (c < '0' || c > '9')
                     throw new InputMismatchException();
                 res *= 10;
                 res += c - '0';
                 c = read();
             }
             if (c == '.') {
                 c = read();
                 double m = 1;
                 while (!isSpaceChar(c)) {
                     if (c == 'e' || c == 'E')
                         return res * Math.pow(10, nextInt());
                     if (c < '0' || c > '9')
                         throw new InputMismatchException();
                     m /= 10;
                     res += (c - '0') * m;
                     c = read();
                 }
             }
             return res * sgn;
         }

         public String readString() {
             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 boolean isSpaceChar(int c) {
             if (filter != null)
                 return filter.isSpaceChar(c);
             return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
         }

         public String next() {
             return readString();
         }

         public interface SpaceCharFilter {
             public boolean isSpaceChar(int ch);
         }
     }
     public static long min(long a,long b)
     {
         if(a>b)
         {
             return b;
         }
         return a;
     }
     public static int min(int a,int b)
     {
         if(a>b)
         {
             return b;
         }
         return a;
     }
     public static long max(long a,long b)
     {
         if(a>b)
         {
             return a;
         }
         return b;
     }
     public static int max(int a,int b)
     {
         if(a>b)
         {
             return a;
         }
         return b;
     }
     static class pair implements Comparable<pair>
     {
       int x;
       int y;
       pair(int x,int y)
       {
         this.x = x;
         this.y = y;
       }
       public int compareTo(pair p)
       {
         return this.x-p.x;
       }
     }
     public static int gcd(int a,int b)
     {
         if(a==0)
         return b;
         if(b==0)
         return a;
         while((a%=b)!=0&&(b%=a)!=0);
         return a^b;
     }
     public static int mod(int a)
     {
       if(a>0)
         return a;
       return -a;
     }
     static int mod = (int)1e9+7;
     public static long expo(long exp,long pow)
     {
       long ans = 1;
       while(pow!=0)
       {
         if((pow&1)==1)
         {
           ans = (ans*exp)%mod;
         }
         exp = (exp*exp)%mod;
         pow = pow>>1;
       }
       return ans;
     }
     static int max = (int)1e5;
     public static long fact(int num)
     {
         if(num==0)
         {
           return 1;
         }
         return (fact(num-1)*num)%mod;
     }
     static int[] sieve;
     public static void sieve()
     {
       sieve = new int[max];
       for(int i=1;i<max;i++)
       {
         sieve[i] = i;
       }
       for(int i=2;i<max;i++)
       {
         if(sieve[i]==i)
         {
           for(int j=i*2;j<max;j+=i)
           {
             if(sieve[j]==j)
             {
               sieve[j] = i;
             }
           }
         }
       }
     }
     public static int lcm(int a,int b)
     {
       return a*b/gcd(a,b);
     }
     public static int bsearch(pair[] p,int x)
     {
       int l = 0;
       int r = p.length-1;
       while(r>l)
       {
         int mid = (l+r)/2;
         if(p[mid].y<=x)
         {
           l = mid+1;
         }
         else if(p[mid].x>x)
         {
           r = mid;
         }
         else
         {
           return 0;
         }
       }
       if(x>=p[r].x&&x<p[r].y)
       {
         return 0;
       }
       return p[r].x-x;
     }
     static int n;
     static int maxim = 0;
     static long as = 0;
     static ArrayList<Integer>[] list;
     static int[] size;
     static int[] color;
     static int[] count;
     static long[] ans;
     static boolean[] big;
     public static void dfs1(int v,int p)
     {
       size[v] = 1;
       for(Integer x:list[v])
       {
         if(x!=p)
         {
           dfs1(x,v);
           size[v]+=size[x];
         }
       }
     }
     public static void check(int v)
     {
       count[color[v]]++;
       if(count[color[v]]>maxim)
       {
         maxim = count[color[v]];
         as = color[v];
       }
       else if(count[color[v]]==maxim)
       {
         as+=color[v];
       }
     }
     public static void add(int v,int p)
     {
       check(v);
       for(Integer x:list[v])
       {
         if(x!=p&&!big[x])
         {
           add(x,v);
         }
       }
     }
     public static void rem(int v,int p)
     {
       count[color[v]]--;
       for(Integer x:list[v])
       {
         if(x!=p)
         {
           rem(x,v);
         }
       }
     }
     public static void dfs2(int v,int p,boolean keep)
     {
       int max = 0;
       int bigone = -1;
       for(Integer x:list[v])
       {
         if(x!=p)
         {
           if(size[x]>max)
           {
             max = size[x];
             bigone = x;
           }
         }
       }
       for(Integer x:list[v])
       {
         if(x!=p&&x!=bigone)
         {
           dfs2(x,v,false);
         }
       }
       if(bigone!=-1)
       {
         dfs2(bigone,v,true);
         big[bigone] = true;
       }
       add(v,p);
       ans[v] = as;
       if(bigone!=-1)
       {
         big[bigone] = false;
       }
       if(!keep)
       {
         rem(v,p);
         maxim = 0;
         as = 0;
       }
     }
     public static void main(String args[]) throws Exception {
         new Thread(null, new Solution(),"Main",1<<26).start();
     }
     public void run() {
       InputReader sc  = new InputReader(System.in);
       PrintWriter out = new PrintWriter(System.out);
       int t1 = 1;
       while(t1-->0)
       {
         n = sc.nextInt();
         color = new int[n+1];
         for(int i=1;i<=n;i++)
         {
           color[i] = sc.nextInt();
         }
         list = new ArrayList[n+1];
         size = new int[n+1];
         ans = new long[n+1];
         count = new int[n+1];
         big = new boolean[n+1];
         for(int i=1;i<=n;i++)
         {
           list[i] = new ArrayList<>();
         }
         for(int i=1;i<n;i++)
         {
           int x = sc.nextInt();
           int y = sc.nextInt();
           list[x].add(y);
           list[y].add(x);
         }
         dfs1(1,-1);
         dfs2(1,-1,true);
         for(int i=1;i<=n;i++)
         {
           out.print(ans[i]+" ");
         }
       }
      out.close();
   }
 }
