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.*;
import java.util.*;

public class codeDSUTree {
	static class Sack{
		int[] cnt,ver,size,st,ft,color;
		long[] ans;
		boolean[] big;
		int N,max;
		long sum;
		int dfsTime=0;
		HashMap<Integer,ArrayList<Integer>> grafo;
		public Sack(int Np){
			N=Np;
			color=new int[N];
			ver=new int[N];
			size=new int[N];
			cnt=new int[N];
			big=new boolean[N];
			ans=new long[N];
			grafo=new HashMap<Integer,ArrayList<Integer>>();
		}
		
		void add(int u, int fa, int x)  
		{  
		    cnt[color[u]]+=x;  
		    if(cnt[color[u]]>max){ 
		    	sum=color[u];
		    	max=cnt[color[u]];
		    }  
		    else{
		    	if(cnt[color[u]]==max){ 
		    		sum+=color[u];
		    	}
		    } 
		    ArrayList<Integer> neig=grafo.get(u);
		    for(int i=0;neig!=null && i<neig.size();i++){
		    	int next=neig.get(i);
		        if(next!=fa && !big[next])  
		            add(next, u, x);  
		    }
		}  
		private void addEdge(int a,int b){
			if(!grafo.containsKey(a)){
				grafo.put(a, new ArrayList<>());
			}
			grafo.get(a).add(b);
		}
		
		public void setColor(int v,int col){
			color[v]=col;
		}
		
		public void add(int a,int b){
			addEdge(a,b);
			addEdge(b,a);
		}
		
		public void solve(int ver){
			dfs(ver,0);
			dfs(ver,0,true);
		}
		
		public void dfs(int v,int p){
			size[v]=1;
			ArrayList<Integer> neig=grafo.get(v);
		    for(int i=0;neig!=null && i<neig.size();i++){
		    	int next=neig.get(i);
		    	if(next != p){
		    		dfs(next,v);
		    		size[v]+=size[next];
		    	}
		    }
		}
		
		public void dfs(int v, int p, boolean keep){
		    int mx = -1; 
		    int bigChild = -1;
		    ArrayList<Integer> neig=grafo.get(v);
		    for(int i=0;neig!=null && i<neig.size();i++){
		    	int next=neig.get(i);
		    	if(next != p && size[next] > mx){
		    		mx = size[next];
		    		bigChild = next;
		    	}
		    }
		    for(int i=0;neig!=null && i<neig.size();i++){
		    	int next=neig.get(i);
		        if(next != p && next != bigChild){
		            dfs(next, v, false);  // run a dfs on small childs and clear them from cnt
		        }
		    }
		    if(bigChild != -1){
		        dfs(bigChild, v, true);  // bigChild marked as big and not cleared from cnt
		        big[bigChild]=true;
		    }
		    add(v,p,1);
		    if(bigChild!=-1){
		    	big[bigChild]=false;
		    }
		    ans[v]=sum;
		    if(!keep){
		        add(v,p,-1);
		        max=0;
		        sum=0;
		    }
		}
		
	}
	public static void main(String[] args) throws Exception {
		BufferedReader bff=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter wff=new PrintWriter(System.out);
		int N=Integer.parseInt(bff.readLine());
		Sack sack=new Sack(N+1);
		String[] st=bff.readLine().split(" ");
		for(int i=1;i<=N;i++){
			sack.setColor(i,Integer.parseInt(st[i-1]));
		}
		for(int i=0;i<N-1;i++){
			st=bff.readLine().split(" ");
			int a=Integer.parseInt(st[0]);
			int b=Integer.parseInt(st[1]);
			sack.add(a,b);
		}
		sack.solve(1);
		for(int i=1;i<=N;i++){
			wff.print(sack.ans[i]);
			if(i+1!=N+1){
				wff.print(" ");
			}
		}
		wff.println();
		wff.flush();
	}
}
