#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>

#define for0(i,n) for(ll i = 0;i < (n);i++)
#define for1(i,n) for(ll i = 1;i<=(n);i++)
#define for2(i,n) for(ll i = 2;i<=(n);i++)
std::pair<int,int> DR[] = {{-1,0},{0,1},{1,0},{0,-1},{-1,1},{-1,-1},{1,1},{1,-1}};
#define rep(i,st,en,cnt) for(ll i = st;i <= en;i+=cnt)
#define PB push_back
#define MP make_pair
#define fastio cin.tie(0);cout.tie(0);ios::sync_with_stdio(0)
#define all(x) x.begin(),x.end()
#define F first
#define S second
#define EPS 1e-8
#define INF 0x3f3f3f3f3
#define NEGINF -INF
#define TYPEMAX(type)   std::numeric_limits<type>::max()
#define inp_arr(a,n) for0(i,n) {cin>>a[i];}
#define out_arr(a,n) for0(i,n) {cout<<a[i]<<" ";}

using namespace std;

typedef pair<int,int> ii;
typedef pair<long long,long long> pll;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef long long ll;
typedef vector<long long> vl;
typedef vector<vector<ll> > vvl;
typedef vector<pair<long long, long long> > vll;

const ll mod =  998244353;
/*
ll nop = 100;
vi primes(nop+1,1);

void sieve(){
    primes[1] = primes[0] = 0;
    for(ll i = 2;i * i <= nop;i++){
        if(primes[i]){
            for(ll j = i*i; j <= nop;j+=i){
                primes[j] = 0;
            }
        }
    }
}
*/
ll gcd(ll a,ll b){    //a larger, b smaller
    if(b>a) swap(b,a);
    if(b==0) return a;
    return gcd(b,a%b);
}

void extgcd(ll a,ll b,ll& x,ll& y){  //a smaller b larger
    if(a==0) {
        x = a;y = b;
        return;
    }
    extgcd(b%a,a,x,y);
    ll y1 = y,x1 = x;
    x = y1 - (b/a)*x1;
    y = x1;
}

ll lcm(ll a,ll b){
    return (a*b)/gcd(a,b);
}

ll bexp(ll num,ll e){
    ll ans = 1;
    while(e>0){
        if(e&1){
            ans *= num;
        }
        num *= num;
        e>>= 1;
    }
    return ans;
}

ll mexp(ll num,ll e){
    ll ans = 1;
    while(e>0){
        if(e&1){
            ans = (ans*num)%mod;
        }
        num = (num*num)%mod;
        e>>=1;
    }
    return ans%mod;
}

ll modinv(ll a){
    return mexp(a,mod-2);
}

int n;
vvi gr;
vi a;
vi ans;
multiset<int> ss;

void dfs(int u,int p = -1) {
    int flag = 0,erased = -1;
    auto tmp = ss.lower_bound(a[u]);
    if(tmp != ss.end()) {
        erased = *tmp;
        ss.erase(tmp);
        flag = 1;
    }
    ss.insert(a[u]);
    ans[u] = ss.size();
    for(int v : gr[u]) {
        if(v == p) continue;
        dfs(v,u);
    }
    if(flag) {
        if(p != -1) ss.insert(erased);
    }
    ss.erase(ss.find(a[u]));
}

void solve() {
    cin>>n;
    gr.resize(n);
    a.resize(n);
    inp_arr(a,n);
    for0(i,n-1) {
        int u,v;
        cin>>u>>v;
        u--,v--;
        gr[u].PB(v);
        gr[v].PB(u);
    }
    ans.resize(n,0);
    dfs(0);
    for0(i,n) {
        cout<<ans[i]<<"\n";
    }
}

int main() {
    fastio;
    #ifndef ONLINE_JUDGE
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
    #endif
    int t = 1;
    //cin>>t;
    for1(T,t){
        solve();
        //cout<<"Case #"<<T<<": "<< <<"\n";
    }
    /* #ifndef ONLINE_JUDGE
    cout<<"\nTime Elapsed: " << 1.0*clock() / CLOCKS_PER_SEC << " sec\n";
    #endif */
    return 0;
}


Measured memory_bytes: 32900