#ifdef LOCAL
//#define _GLIBCXX_DEBUG
#endif
//#pragma GCC target("avx512f,avx512dq,avx512cd,avx512bw,avx512vl")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<int, int> Pi;
typedef vector<ll> Vec;
typedef vector<int> Vi;
typedef vector<string> Vs;
typedef vector<P> VP;
typedef vector<vector<ll>> VV;
typedef vector<vector<int>> VVi;
typedef vector<vector<vector<ll>>> VVV;
typedef vector<vector<vector<vector<ll>>>> VVVV;

#define REP(i, a, b) for(ll i=(a); i<(b); i++)
#define PER(i, a, b) for(ll i=(a); i>=(b); i--)
#define rep(i, n) REP(i, 0, n)
#define per(i, n) PER(i, n, 0)
const ll INF = 1e18+18;
const ll MAX = 100005;
const ll MOD = 1000000007;
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl;
#define YES(n) cout << ((n) ? "YES" : "NO") << endl;
#define ALL(v) v.begin(), v.end()
#define rALL(v) v.rbegin(), v.rend()
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a,b)
#define Each(a, b) for(auto &a :b)
#define REPM(i, mp) for (auto i = mp.begin(); i != mp.end(); ++i)
#ifdef LOCAL
#define dbg(x_) cerr << #x_ << ":" << x_ << endl;
#define dbgmap(mp) cerr << #mp << ":"<<endl; for (auto i = mp.begin(); i != mp.end(); ++i) { cerr << i->first <<":"<<i->second << endl;}
#define dbgarr(n, m, arr) rep(i,n){rep(j,m){cerr<<arr[i][j]<<" ";}cerr<<endl;}
#define dbgdp(n, arr) rep(i,n){cerr<<arr[i]<<" ";}cerr<<endl;
#define dbgmint(n, arr) rep(i,n){cerr<<arr[i].x<<" ";}cerr<<endl;
#define dbgarrmint(n, m, arr) rep(i,n){rep(j,m){cerr<<arr[i][j].x<<" ";}cerr<<endl;}
#else
#define dbg(...)
#define dbgmap(...)
#define dbgarr(...)
#define dbgdp(...)
#define dbgmint(...)
#define dbgarrmint(...)
#endif
#define out(a) cout<<a<<endl
#define out2(a, b) cout<<a<<" "<<b<<endl
#define vout(v) rep(i,v.size()){cout<<v[i]<<" ";}cout<<endl
#define Uniq(v) v.erase(unique(v.begin(), v.end()), v.end())
#define fi first
#define se second

template<class T>
bool chmax(T &a, const T &b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmin(T &a, const T &b) {
    if(b < a) {
        a = b;
        return true;
    }
    return false;
}

template<typename T1, typename T2>
ostream &operator<<(ostream &s, const pair<T1, T2> &p) { return s<<"("<<p.first<<", "<<p.second<<")"; }

template<typename T>
istream &operator>>(istream &i, vector<T> &v) {
    rep(j, v.size())i>>v[j];
    return i;
}

// vector
template<typename T>
ostream &operator<<(ostream &s, const vector<T> &v) {
    int len = v.size();
    for(int i = 0; i < len; ++i) {
        s<<v[i];
        if(i < len-1) s<<"	";
    }
    return s;
}

// 2 dimentional vector
template<typename T>
ostream &operator<<(ostream &s, const vector<vector<T> > &vv) {
    int len = vv.size();
    for(int i = 0; i < len; ++i) {
        s<<vv[i]<<endl;
    }
    return s;
}


//mint
struct mint {
    ll x; // typedef long long ll;
    mint(ll x = 0) : x((x%MOD+MOD)%MOD) {}

    mint &operator+=(const mint a) {
        if((x += a.x) >= MOD) x -= MOD;
        return *this;
    }

    mint &operator-=(const mint a) {
        if((x += MOD-a.x) >= MOD) x -= MOD;
        return *this;
    }

    mint &operator*=(const mint a) {
        (x *= a.x) %= MOD;
        return *this;
    }

    mint operator+(const mint a) const {
        mint res(*this);
        return res += a;
    }

    mint operator-(const mint a) const {
        mint res(*this);
        return res -= a;
    }

    mint operator*(const mint a) const {
        mint res(*this);
        return res *= a;
    }

    mint pow(ll t) const {
        if(!t) return 1;
        mint a = pow(t>>1);
        a *= a;
        if(t & 1) a *= *this;
        return a;
    }

    // for prime MOD
    mint inv() const {
        return pow(MOD-2);
    }

    mint &operator/=(const mint a) {
        return (*this) *= a.inv();
    }

    mint operator/(const mint a) const {
        mint res(*this);
        return res /= a;
    }
};

struct combination {
    vector<mint> fact, ifact;

    combination(int n) : fact(n+1), ifact(n+1) {
        assert(n < MOD);
        fact[0] = 1;
        for(int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
        ifact[n] = fact[n].inv();
        for(int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
    }

    mint operator()(int n, int k) {
        if(k < 0 || k > n) return 0;
        return fact[n]*ifact[k]*ifact[n-k];
    }
};

template<typename Monoid>
struct SegmentTree {
    using F = function<Monoid(Monoid, Monoid)>;

    int sz;
    vector<Monoid> seg;

    const F f;
    const Monoid M1;

    SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
        sz = 1;
        while (sz < n) sz <<= 1;
        seg.assign(2*sz, M1);
    }

    void set(int k, const Monoid &x) {
        seg[k+sz] = x;
    }

    void build() {
        for(int k = sz-1; k > 0; k--) {
            seg[k] = f(seg[2*k+0], seg[2*k+1]);
        }
    }

    void update(int k, const Monoid &x) {
        k += sz;
        seg[k] = x;
        while (k >>= 1) {
            seg[k] = f(seg[2*k+0], seg[2*k+1]);
        }
    }

    Monoid query(int a, int b) {
        Monoid L = M1, R = M1;
        for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if(a & 1) L = f(L, seg[a++]);
            if(b & 1) R = f(seg[--b], R);
        }
        return f(L, R);
    }

    Monoid operator[](const int &k) const {
        return seg[k+sz];
    }

    template<typename C>
    int find_subtree(int a, const C &check, Monoid &M, bool type) {
        while (a < sz) {
            Monoid nxt = type ? f(seg[2*a+type], M) : f(M, seg[2*a+type]);
            if(check(nxt)) a = 2*a+type;
            else M = nxt, a = 2*a+1-type;
        }
        return a-sz;
    }


    template<typename C>
    int find_first(int a, const C &check) {
        Monoid L = M1;
        if(a <= 0) {
            if(check(f(L, seg[1]))) return find_subtree(1, check, L, false);
            return -1;
        }
        int b = sz;
        for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if(a & 1) {
                Monoid nxt = f(L, seg[a]);
                if(check(nxt)) return find_subtree(a, check, L, false);
                L = nxt;
                ++a;
            }
        }
        return -1;
    }

    template<typename C>
    int find_last(int b, const C &check) {
        Monoid R = M1;
        if(b >= sz) {
            if(check(f(seg[1], R))) return find_subtree(1, check, R, true);
            return -1;
        }
        int a = sz;
        for(b += sz; a < b; a >>= 1, b >>= 1) {
            if(b & 1) {
                Monoid nxt = f(seg[--b], R);
                if(check(nxt)) return find_subtree(b, check, R, true);
                R = nxt;
            }
        }
        return -1;
    }
};


int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout<<std::setprecision(10);

    ll n;
    cin>>n;
    Vec a(n);
    cin>>a;
    dbg(a);
    VV g(n);
    rep(i, n-1) {
        ll u, v;
        cin>>u>>v;
        u--;
        v--;
        g[u].pb(v);
        g[v].pb(u);
    }

    Vec comp = a;
    sort(ALL(comp));
    Uniq(comp);

    auto ith = [&](ll x){
        return lower_bound(ALL(comp),x) - comp.begin();
    };

    SegmentTree<ll> seg(n, [](ll a, ll b) { return max(a, b); }, 0);
    seg.build();

    Vec dp(n);
    auto dfs = [&](auto dfs, ll v, ll parent)->void {
        ll now = a[v];
        ll old = seg.query(ith(now),ith(now)+1);
        ll mx = seg.query(0, ith(now));
        if(parent>-1){
            chmax(dp[v],dp[parent]);
        }
        chmax(dp[v], mx+1);
        if(old<mx+1) {
            seg.update(ith(now), mx+1);
        }
        Each(x, g[v]) {
            if(x == parent)continue;
            dfs(dfs, x, v);
        }
        seg.update(ith(now), old);
    };
    dfs(dfs, 0, -1);
    rep(i, n) {
        out(dp[i]);
    }
    return 0;
}


Measured memory_bytes: 77572