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.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map.Entry;
import java.util.TreeMap;

public class Main {
	static ContestScanner in;static Writer out;public static void main(String[]args)
	{try{in=new ContestScanner();out=new Writer();Main solve=new Main();solve.solve(in,out);
	in.close();out.close();}catch(IOException e){e.printStackTrace();}}
	void dump(int[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
	void dump(int[]a,int n){for(int i=0;i<a.length;i++)out.printf("%"+n+"d",a[i]);out.println();}
	void dump(long[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
	void dump(char[]a){for(int i=0;i<a.length;i++)out.print(a[i]);out.println();}
	long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
	String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
	void sort(int[]a){m_sort(a,0,a.length,new int[a.length]);}
	void m_sort(int[]a,int s,int sz,int[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a,j,j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];
	} /* qsort(3.5s)<<msort(9.5s)<<<shuffle+qsort(17s)<Arrays.sort(Integer)(20s) */
	void swap(int[]a,int i,int j){final int t=a[i];a[i]=a[j];a[j]=t;}
	int binarySearchSmallerMax(int[]a,int v)// get maximum index which a[idx]<=v
	{int l=0,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return a[s]>v?-1:s;}
	void solve(ContestScanner in,Writer out)throws NumberFormatException,IOException{
		int n = in.nextInt();
		node = new List[n];
		int[] col = new int[n];
		set = new MultiSet[n];
		ans = new long[n];
		max = new int[n];
		for(int i=0; i<n; i++){
			col[i] = in.nextInt();
			node[i] = new ArrayList<>();
			set[i] = new MultiSet<>();
			set[i].add(col[i]);
			ans[i] = col[i];
		}
		for(int i=0; i<n-1; i++){
			int x = in.nextInt()-1;
			int y = in.nextInt()-1;
			node[x].add(y);
			node[y].add(x);
		}
		merge(0, -1);
		StringBuilder sb = new StringBuilder();
		for(int i=0; i<n; i++){
			sb.append(ans[i]).append(" ");
		}
		out.println(sb.toString().trim());
	}
	MultiSet<Integer>[] set;
	List<Integer>[] node;
	long[] ans;
	int[] max;
	MultiSet<Integer> merge(int now, int p){
		max[now] = 1;
		for(int i: node[now]){
			if(i==p) continue;
			MultiSet<Integer> s = merge(i, now);
			MultiSet<Integer> par, chl;
			if(s.size()>set[now].size()){
				par = s; chl = set[now];
				max[now] = max[i]; ans[now] = ans[i];
			}else{
				par = set[now]; chl = s;
			}
			for(Entry<Integer, Integer> e: chl.entrySet()){
				par.add(e.getKey(), e.getValue());
				final int value = par.get(e.getKey());
				if(value > max[now]){
					max[now] = value;
					ans[now] = e.getKey();
				}else if(value == max[now]){
					ans[now] += e.getKey();
				}
			}
			set[now] = par;
		}
		return set[now];
	}
}

class MultiSet<T> extends HashMap<T, Integer>{
	@Override
	public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key)
	{final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
}
class OrderedMultiSet<T> extends TreeMap<T, Integer>{
	@Override
	public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key)
	{final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
}
class Pair implements Comparable<Pair>{
	int a,b;int hash;Pair(int a,int b){this.a=a;this.b=b;hash=(a<<16|a>>16)^b;}
	public boolean equals(Object obj){Pair o=(Pair)(obj);return a==o.a&&b==o.b;}
	public int hashCode(){return hash;}
	public int compareTo(Pair o){if(a!=o.a)return a<o.a?-1:1;else if(b!=o.b)return b<o.b?-1:1;return 0;}
}
class Timer{
	long time;
	public void set(){time=System.currentTimeMillis();}
	public long stop(){return time=System.currentTimeMillis()-time;}
	public void print()
	{System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
	@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}