#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
#define ll long long
//increase stack size
#pragma comment(linker, "/STACK:16777216")

ll mxm() {return LLONG_MIN;}
template<typename... Args>
ll mxm(ll a, Args... args) { return max(a,mxm(args...)); }

ll mnm() {return LLONG_MAX;}
template<typename... Args>
ll mnm(ll a, Args... args) { return min(a,mnm(args...)); }

template<class T> ostream& operator<<(ostream& os,vector<T> V){
	os<<"[ ";for(auto v:V)os<<v<<" ";return os<<"]";
}
template<class L,class R> ostream& operator<<(ostream& os,pair<L,R> P){
	return os<<"("<<P.first<<","<<P.second<<")";
}

#define TRACE
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__,__VA_ARGS__)
template<typename Arg1>
void __f(const char* name,Arg1&& arg1){
	cout<<name<<" : "<<arg1<<endl;
}
template <typename Arg1,typename... Args>
void __f(const char* names,Arg1&& arg1,Args&&... args){
	const char* comma=strchr(names+1,',');cout.write(names,comma-names)<<" : "<<arg1<<" | ";__f(comma+1,args...);
}
#else
#define trace(...) 1
#endif

#define ld long double
#define pll pair<ll,ll>
#define ii pair<int,int>
#define vll vector<ll>
#define vii vector<ii>
#define vi vector<int>
#define vpll vector<pll>
#define vld vector<ld>
#define vvld vector<vld>
#define vvi vector<vi>
#define vvll vector<vll>
#define vvpll vector<vpll>
#define vvii vector<vii>
#define I insert
#define F first
#define S second
#define pb push_back
#define endl "\n"
#define all(x)	x.begin(),x.end()

const int mod=1e9+7;
// 128 bit: __int128
inline int add(int a,int b){a+=b;if(a>=mod)a-=mod;return a;}
inline int sub(int a,int b){a-=b;if(a<0)a+=mod;return a;}
inline int mul(int a,int b){return (a*1ll*b)%mod;}
inline int power(int a,int b){int rt=1;while(b>0){if(b&1)rt=mul(rt,a);a=mul(a,a);b>>=1;}return rt;}
inline int inv(int a){return power(a,mod-2);}

struct compare{
	bool operator() (const int &a,const int &b) const{
		return a>b;
	}
};

const int N = 2e5 + 5;

int st[4 * N], n;

void upd(int x, int val, int l = 0, int r = N - 1, int id = 1){
	if(l > x || r < x)
		return;
	if(l == x && r == x){
		st[id] = val;
		return;
	}
	int mid = l + r >> 1;
	upd(x, val, l, mid, id * 2), upd(x, val, mid + 1, r, id * 2 + 1);
	st[id] = max(st[id * 2], st[id * 2 + 1]);
}

int get(int x, int y, int l = 0, int r = N - 1, int id = 1){
	if(l > y || r < x) return 0;
	if(l >= x && r <= y)
		return st[id];
	int mid = l + r >> 1;
	return max(get(x, y, l, mid , id * 2), get(x, y, mid + 1, r, id * 2 + 1));
}

vvi adj(N);
vi val(N), ans(N), vis(N);

void dfs(int i, int p){
	int prev = get(val[i], val[i]);
	vis[i] = 1;
	int c = get(0, val[i] - 1);
	ans[i] = max(p, c + 1);
	upd(val[i], c + 1);
	for(auto j : adj[i]){
		if(!vis[j])
			dfs(j, ans[i]);
	}
	upd(val[i], prev);
}

int main()
{
	ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);cout<<setprecision(25);
	cin >> n;
	set<int> vals;
	for(int i = 0; i < n; i++)
		cin >> val[i], vals.I(val[i]);
	vi temp;
	for(auto j : vals)
		temp.pb(j);
	map<int, int> iidx;
	for(int j = 0; j < temp.size(); j++)
		iidx[temp[j]] = j + 1;
	for(int i = 0; i < n; i++)
		val[i] = iidx[val[i]];
	for(int i = 0; i < n - 1; i++){
		int u, v;
		cin >> u >> v;
		--u, --v;
		adj[u].pb(v), adj[v].pb(u);
	}
	dfs(0, 0);
	for(int i = 0; i < n; i++)
		cout << ans[i] << endl;
}

Measured memory_bytes: 45528