#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
#define mod 998244353
#include<string.h>
#define inf 9000000000000000000
#define maxn 200006
typedef pair<ll,ll> pll;
typedef pair<int,int> pint;
#define endl '\n'
#define mapint_iterator map<int,int> :: iterator
#define mapll_iterator map<ll,ll> :: iterator
#define setint_iterator set<int> :: iterator
#define setll_iterator set<ll> :: iterator
#define setpint_iterator set<pint> :: iterator
#define setpll_iterator set<pll> :: iterator
#define trace(x) cout<<#x<<": "<<x<<" "<<endl
#define trace2(x,y) cout<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x,y,z) cout<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a,b,c,d) cout<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define cout1(a) cout<<a<<endl
#define cout2(a,b) cout<<a<<' '<<b<<endl
#define cout3(a,b,c) cout<<a<<" "<<b<<" "<<c<<endl
#define cout4(a,b,c,d) cout<<a<<" "<<b<<" "<<c<<" "<<d<<endl
#define vcout(v,i) cout<<v[i].fi<<" "<<v[i].se<<endl
typedef priority_queue<ll,vector<ll>,greater<ll> > pqset;
typedef priority_queue<pint,vector<pint>,greater<pint> > pqset_ll;
#define pb push_back
#define fi first
#define se second
#include<ext/pb_ds/assoc_container.hpp>
ll dxk[]={0,0,1,-1,1,1,-1,-1};
ll dyk[]={1,-1,0,0,1,-1,1,-1};
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> os;
typedef tree<pll,null_type,less<pll>,rb_tree_tag,tree_order_statistics_node_update> os_pair;
#define acc (ios::sync_with_stdio(false),cin.tie(0))
#define rep(i,n) for(ll i=0;i<n;i++)
#define per(i,n) for(ll i=n-1;i>=0;i--)
#define rep1(i,n) for(ll i=1;i<=n;i++)
#define per1(i,n) for(ll i=n;i>0;i--)
#define repeat(i,start,n) for(ll i=start;i<n;i++)
#define print(a,n) for(ll i=0;i<n;i++){ cout<<a[i]<<" ";}
ll ll_max(ll a,ll b,ll c){return max(a,max(b,c));}
int int_max(int a,int b,int c){return max(a,max(b,c));}
ll ll_min(ll a,ll b,ll c){return min(a,min(b,c));}
int int_min(int a,int b,int c){return min(a,min(b,c));}
ll max(int a,ll b){ return max((ll)a,b);}
ll min(int a,ll b){ return min((ll)a,b);} 
ll min(ll a,int b){ return min(a,(ll)b);}
ll max(ll a,int b){ return max(a,(ll)b);}
ll dx[]={0,0,1,-1};
ll dy[]={1,-1,0,0};
ll power(ll a,ll b){
	if(a==1)
		return 1;
	if(b==0)
		return 1;
	ll c=power(a,b/2);
	ll res=1;
	if(b%2){
		res=(c*c)%mod;
		res*=a;
		res%=mod;
	}
	else
		res=((c*c)%mod);
	return res;
}
//ifstream cin("b_read_on.txt"); ofstream cout("output3.txt");
//Chronology: Binary Search,Greedy,dp,dfs and similar
//Use (<<) for multiplication
//Use (>>) for division
// In dp, first try top-down,then bottom-up
//ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);cout<<fixed;cerr.tie(NULL);
// find_by_order -> value at index
// order_of_key -> index of value
int dp[200001];
int a[200001];
vector<int> v[200001];
ll Tree[4*maxn];
map<pint,int> c;
int n;
void update_max(int node,int start,int end,int i,ll val){
	if(start==end){
		Tree[node]=val;
		return;
	}
	int mid=((start+end)>>1);
	if(i<=mid)
		update_max(2*node+1,start,mid,i,val);
	else
		update_max(2*node+2,mid+1,end,i,val);
	//According to the question,change from here
	Tree[node]=max(Tree[2*node+1],Tree[2*node+2]);
}
ll query_max(int node,int start,int end,int l,int r){ 
	if(start>end||end<l||start>r)
		return 0;//0 in case of sum , high value in case of min , low value in case of max and soooo on 
	if(start>=l&&end<=r)
		return(Tree[node]);
	int mid = (start+end)/2 ; 
	ll p1 = query_max(node*2+1, start, mid, l,r);
	ll p2 = query_max(node*2+2, mid+1, end , l,r);
	return max(p1,p2);
}
void dfs(int i,int p){
	map<pint,int> :: iterator j1=c.lower_bound({a[i],0});
	int u=0;
	if(j1->se>=1)
		u=query_max(0,0,n-1,0,max(0,(j1->se)-1));
	update_max(0,0,n-1,c[{a[i],i}],u+1);
	dp[i]=query_max(0,0,n-1,0,n-1);
	rep(j,v[i].size()){
		if(v[i][j]==p)
			continue;
		dfs(v[i][j],i);
	}
	update_max(0,0,n-1,c[{a[i],i}],0);
}
void solve(int countu){
	cin>>n;
	vector<pint> v1;
	rep(i,n){
		cin>>a[i+1];
		v1.pb({a[i+1],i+1});
	}
	sort(v1.begin(),v1.end());
	rep(i,v1.size())
		c[v1[i]]=i;
	rep(i,n-1){
		int a1,b1;
		scanf("%d%d",&a1,&b1);
		v[a1].pb(b1);
		v[b1].pb(a1);
	}
	dfs(1,-1);
	repeat(i,1,n+1)
		cout1(dp[i]);
}
int main(){
	//ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);cout<<fixed;cerr.tie(NULL);cout.precision(10);
    int t=1;
	//scanf("%d",&t);
	int countu=1;
    while(t--){
    	solve(countu);
    	countu++;
    }
}




Measured memory_bytes: 51272