#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=int(a);i<int(b);i++)
#define all(p) p.begin(),p.end()
void chmin(int &a,int b){a=min(a,b);}
void chmax(int &a,int b){a=max(a,b);}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	int N;
	cin>>N;
	vector<int> A(N);
	rep(i,0,N) cin>>A[i];
	vector<vector<int>> G(N);
	rep(i,0,N-1){
		int a,b;
		cin>>a>>b;
		a--,b--;
		G[a].push_back(b);
		G[b].push_back(a);
	}
	vector<int> ans(N);
	vector<int> depth(N,-1);
	vector<int> E(N*2);
	stack<int> st;
	st.push(0);
	depth[0]=0;
	rep(i,0,2*N){
		int a=st.top();
		st.pop();
		E[a]=i;
		if(a<N){
			st.push(a+N);
			for(auto x:G[a]){
				if(depth[x]==-1){
					depth[x]=depth[a]+1;
					st.push(x);
				}
			}
		}
	}

	int B=0;
	while((1<<B)<N) B++;
	B++;
	vector table(B,vector<int>(N*2));
	rep(i,0,N){
		table[0][E[i]]=depth[i];
		table[0][E[i+N]]=depth[i]-1;
	}
	rep(i,0,B-1) rep(j,0,N*2){
		table[i+1][j]=table[i][j];
		if(j+(1<<i)<N*2) chmin(table[i+1][j],table[i][j+(1<<i)]);
	}
	auto dist=[&](int a,int b) -> int {
		if(E[a]>E[b]) swap(a,b);
		int l=E[a];
		int r=E[b]+1;
		int z=31-__builtin_clz(r-l);
		return depth[a]+depth[b]-2*min(table[z][l],table[z][r-(1<<z)]);
	};

	vector<int> order(N);
	rep(i,0,N) order[i]=i;
	sort(all(order),[&](int l,int r){
		return A[l]>A[r];
	});
	int L=0,R=0;
	int X=order[0],Y=order[0],D=0;
	while(L<N){
		while(R<N&&A[order[L]]==A[order[R]]){
			int tmpX=dist(X,order[R]);
			int tmpY=dist(Y,order[R]);
			if(tmpX<tmpY) swap(X,Y),swap(tmpX,tmpY);
			if(D<tmpX) D=tmpX,Y=order[R];
			R++;
		}
		rep(i,L,R){
			ans[order[i]]=max(dist(order[i],X),dist(order[i],Y));
		}
		L=R;
	}

	rep(i,0,N){
		if(i) cout<<" ";
		cout<<ans[i];
	}
	cout<<"\n";
}