/*
Things to notice:
1. do not calculate useless values
2. do not use similar names
 
Things to check:
1. submit the correct file
2. time (it is log^2 or log)
3. memory
4. prove your naive thoughts 
5. long long
6. corner case like n=0,1,inf or n=m
7. check if there is a mistake in the ds or other tools you use
8. fileio in some oi-contest

9. module on time 
10. the number of a same divisor in a math problem
11. multi-information and queries for dp and ds problems
*/
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pii pair<long long,long long>
#define mp make_pair
#define pb push_back
const int mod=998244353;
const int inf=0x3f3f3f3f;
const int INF=1e18;
vector <pii > g[200005]; 
struct LCA
{
	int dep[200005],dfn[200005],times;
	int dist[200005];
	int st[20][400005],Lg[400005];
	void dfs(int u,int fa)
	{
		dfn[u]=++times,st[0][times]=u;
		for(int i=0;i<g[u].size();i++)
		{
			int v=g[u][i].fi;
			if(v==fa) continue;
			dep[v]=dep[u]+1,dist[v]=dist[u]+1LL*g[u][i].se,dfs(v,u);
			st[0][++times]=u;
		}
	}
	int mindep(int x,int y)
	{
		if(dep[x]<dep[y]) return x;
		return y;
	}
	void build()
	{
		times=0,dep[1]=dist[1]=0;
		dfs(1,-1);
		Lg[1]=0,Lg[2]=1;
		for(int i=3;i<=times;i++) Lg[i]=Lg[i/2]+1;
		for(int k=1;k<20;k++) for(int i=1;i+(1<<k)-1<=times;i++) 
			st[k][i]=mindep(st[k-1][i],st[k-1][i+(1<<(k-1))]);
	}
	int getlca(int u,int v)
	{
		u=dfn[u],v=dfn[v];
		if(u>v) swap(u,v);
		int s=Lg[v-u+1];
		return mindep(st[s][u],st[s][v-(1<<s)+1]);
	}
	int getdis(int u,int v)
	{
		int l=getlca(u,v);
		return dist[u]+dist[v]-2LL*dist[l];	
	}
}Lca;
int n;
int a[200005],ans[200005];
pii b[200005];
void solve()
{
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i],b[i]=mp(a[i],i);
	sort(b+1,b+1+n),reverse(b+1,b+1+n);
	for(int i=1;i<n;i++)
	{
		int u,v;
		cin>>u>>v;
		g[u].pb(mp(v,1)),g[v].pb(mp(u,1));
	}
	Lca.build();
	pii diam=mp(-1,-1);
	for(int i=1;i<=n;i++)
	{
		int j=i;
		while(j+1<=n&&b[j+1].fi==b[j].fi) j++;
		for(int l=i;l<=j;l++)
		{
			int u=b[l].se;
			if(diam==mp(-1LL,-1LL)) diam=mp(u,u);
			else
			{
				int x=diam.fi,y=diam.se;
				if(Lca.getdis(u,x)>=Lca.getdis(x,y)&&Lca.getdis(u,x)>=Lca.getdis(u,y)) diam=mp(u,x);
				else if(Lca.getdis(u,y)>=Lca.getdis(x,y)&&Lca.getdis(u,y)>=Lca.getdis(u,x)) diam=mp(u,y);
				else diam=mp(x,y);
			}
		}
		for(int l=i;l<=j;l++)
		{
			int u=b[l].se;
			ans[u]=max(Lca.getdis(u,diam.fi),Lca.getdis(u,diam.se));
		}
		i=j; 
	}
	for(int i=1;i<=n;i++) cout<<ans[i]<<" ";
}
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	int _=1;
//	cin>>_;
	while(_--) solve();
	return 0;
}