#ifdef NACHIA
// #define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#include <atcoder/modint>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<(i64)(n); i++)
#define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = std::priority_queue<A,std::vector<A>,std::greater<A>>;
using Modint = atcoder::static_modint<998244353>;

#include <iterator>
#include <functional>

template<class Elem> struct vec;

template<class Iter>
struct seq_view{
    using Ref = typename std::iterator_traits<Iter>::reference;
    using Elem = typename std::iterator_traits<Iter>::value_type;
    Iter a, b;
    Iter begin() const { return a; }
    Iter end() const { return b; }
    int size() const { return (int)(b-a); }
    seq_view(Iter first, Iter last) : a(first), b(last) {}
    seq_view sort() const { std::sort(a, b); return *this; }
    Ref& operator[](int x){ return *(a+x); }
    template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
        ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
        x().sort([&](int l, int r){ return f(a[l],a[r]); });
        return x;
    }
    template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
    template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
    ret rle(F eq = F()) const {
        auto x = ret();
        for(auto& a : (*this)){
            if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
        } return x;
    }
    template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
    Iter uni() const { return std::unique(a, b); }
    Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
    Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
    int lbi(const Elem& x) const { return lb(x) - a; }
    int ubi(const Elem& x) const { return ub(x) - a; }
    seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
    template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
    template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
    template<class F> Iter when_true_to_false(F f) const {
        if(a == b) return a;
        return std::lower_bound(a, b, *a,
            [&](const Elem& x, const Elem&){ return f(x); });
    }
    seq_view same(Elem x) const { return { lb(x), ub(x) }; }
    template<class F> auto map(F f) const {
        vec<typename Iter::value_type> r;
        for(auto& x : *this) r.emp(f(x));
        return r;
    }
    Iter max() const { return std::max_element(a, b); }
    Iter min() const { return std::min_element(a, b); }
    template<class F = std::less<Elem>>
    Iter min(F f) const { return std::min_element(a, b, f); }
    seq_view rev() const { std::reverse(a, b); return *this; }
};

template<class Elem>
struct vec {
    using Base = typename std::vector<Elem>;
    using Iter = typename Base::iterator;
    using CIter = typename Base::const_iterator;
    using View = seq_view<Iter>;
    using CView = seq_view<CIter>;

    vec(){}
    explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
    template <class I2> vec(I2 first, I2 last) : a(first, last) {}
    vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
    vec(Base b) : a(std::move(b)) {}
    operator Base() const { return a; }

    Iter begin(){ return a.begin(); }
    CIter begin() const { return a.begin(); }
    Iter end(){ return a.end(); }
    CIter end() const { return a.end(); }
    int size() const { return a.size(); }
    bool empty() const { return a.empty(); }
    Elem& back(){ return a.back(); }
    const Elem& back() const { return a.back(); }
    vec sortunied(){ vec x = *this; x().sort(); x.a.erase(x().uni(), x.end()); return x; }
    Iter operator()(int x){ return a.begin() + x; }
    CIter operator()(int x) const { return a.begin() + x; }
    View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
    CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
    View operator()(){ return (*this)(0,size()); }
    CView operator()() const { return (*this)(0,size()); }
    Elem& operator[](int x){ return a[x]; }
    const Elem& operator[](int x) const { return a[x]; }
    Base& operator*(){ return a; }
    const Base& operator*() const { return a; }
    vec& push(Elem args){
        a.push_back(std::move(args));
        return *this;
    }
    template<class... Args>
    vec& emp(Args &&... args){
        a.emplace_back(std::forward<Args>(args) ...);
        return *this;
    }
    template<class Range>
    vec& app(Range& x){ for(auto& v : a) emp(v); }
    Elem pop(){
        Elem x = std::move(a.back());
        a.pop_back(); return x;
    }
    bool operator==(const vec& r) const { return a == r.a; }
    bool operator!=(const vec& r) const { return a != r.a; }
    bool operator<(const vec& r) const { return a < r.a; }
    bool operator<=(const vec& r) const { return a <= r.a; }
    bool operator>(const vec& r) const { return a > r.a; }
    bool operator>=(const vec& r) const { return a >= r.a; }
    vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
    template<class F> vec& filter(F f){
        int p = 0;
        for(int q=0; q<size(); q++) if(f(a[q])) std::swap(a[p++],a[q]);
        a.resize(p); return *this;
    }
private: Base a;
};

template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << v[i];
    } return os;
}
template<class OStr, class U, class T>
OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';
    } return os;
}
using namespace std;

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia
#include <cassert>

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia

namespace nachia{

struct HeavyLightDecomposition{
private:

    int N;
    std::vector<int> P;
    std::vector<int> PP;
    std::vector<int> PD;
    std::vector<int> D;
    std::vector<int> I;

    std::vector<int> rangeL;
    std::vector<int> rangeR;

public:

    HeavyLightDecomposition(const CsrArray<int>& E = CsrArray<int>::Construct(1, {}), int root = 0){
        N = E.size();
        P.assign(N, -1);
        I.assign(N, 0); I[0] = root;
        int iI = 1;
        for(int i=0; i<iI; i++){
            int p = I[i];
            for(int e : E[p]) if(P[p] != e){
                I[iI++] = e;
                P[e] = p;
            }
        }
        std::vector<int> Z(N, 1);
        std::vector<int> nx(N, -1);
        PP.resize(N);
        for(int i=0; i<N; i++) PP[i] = i;
        for(int i=N-1; i>=1; i--){
            int p = I[i];
            Z[P[p]] += Z[p];
            if(nx[P[p]] == -1) nx[P[p]] = p;
            if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p;
        }

        for(int p : I) if(nx[p] != -1) PP[nx[p]] = p;

        PD.assign(N,N);
        PD[root] = 0;
        D.assign(N,0);
        for(int p : I) if(p != root){
            PP[p] = PP[PP[p]];
            PD[p] = std::min(PD[PP[p]], PD[P[p]]+1);
            D[p] = D[P[p]]+1;
        }
        
        rangeL.assign(N,0);
        rangeR.assign(N,0);
        
        for(int p : I){
            rangeR[p] = rangeL[p] + Z[p];
            int ir = rangeR[p];
            for(int e : E[p]) if(P[p] != e) if(e != nx[p]){
                rangeL[e] = (ir -= Z[e]);
            }
            if(nx[p] != -1){
                rangeL[nx[p]] = rangeL[p] + 1;
            }
        }

        I.resize(N);
        for(int i=0; i<N; i++) I[rangeL[i]] = i;
    }
    
    HeavyLightDecomposition(const Graph& tree, int root = 0)
        : HeavyLightDecomposition(tree.getAdjacencyArray(true), root) {}

    int numVertices() const { return N; }
    int depth(int p) const { return D[p]; }
    int toSeq(int vtx) const { return rangeL[vtx]; }
    int toVtx(int seqidx) const { return I[seqidx]; }
    int toSeq2In(int vtx) const { return rangeL[vtx] * 2 - D[vtx]; }
    int toSeq2Out(int vtx) const { return rangeR[vtx] * 2 - D[vtx] - 1; }
    int parentOf(int v) const { return P[v]; }
    int heavyRootOf(int v) const { return PP[v]; }
    int heavyChildOf(int v) const {
        if(toSeq(v) == N-1) return -1;
        int cand = toVtx(toSeq(v) + 1);
        if(PP[v] == PP[cand]) return cand;
        return -1;
    }

    int lca(int u, int v) const {
        if(PD[u] < PD[v]) std::swap(u, v);
        while(PD[u] > PD[v]) u = P[PP[u]];
        while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; }
        return (D[u] > D[v]) ? v : u;
    }

    int dist(int u, int v) const {
        return depth(u) + depth(v) - depth(lca(u,v)) * 2;
    }

    struct Range{
        int l; int r;
        int size() const { return r-l; }
        bool includes(int x) const { return l <= x && x < r; }
    };

    std::vector<Range> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
        if(PD[c] < PD[r]) return {};
        std::vector<Range> res(PD[c]-PD[r]+1);
        for(int i=0; i<(int)res.size()-1; i++){
            res[i] = { rangeL[PP[c]], rangeL[c]+1 };
            c = P[PP[c]];
        }
        if(PP[r] != PP[c] || D[r] > D[c]) return {};
        res.back() = { rangeL[r]+(include_root?0:1), rangeL[c]+1 };
        if(res.back().l == res.back().r) res.pop_back();
        if(!reverse_path) std::reverse(res.begin(),res.end());
        else for(auto& a : res) a = { N - a.r, N - a.l };
        return res;
    }

    Range subtree(int p) const { return { rangeL[p], rangeR[p] }; }

    int median(int x, int y, int z) const {
        return lca(x,y) ^ lca(y,z) ^ lca(x,z);
    }

    int la(int from, int to, int d) const {
        if(d < 0) return -1;
        int g = lca(from,to);
        int dist0 = D[from] - D[g] * 2 + D[to];
        if(dist0 < d) return -1;
        int p = from;
        if(D[from] - D[g] < d){ p = to; d = dist0 - d; }
        while(D[p] - D[PP[p]] < d){
            d -= D[p] - D[PP[p]] + 1;
            p = P[PP[p]];
        }
        return I[rangeL[p] - d];
    }

    struct ChildrenIterRange {
    struct Iter {
        const HeavyLightDecomposition& hld; int s;
        int operator*() const { return hld.toVtx(s); }
        Iter& operator++(){
            s += hld.subtree(hld.I[s]).size();
            return *this;
        }
        Iter operator++(int) const { auto a = *this; return ++a; }
        bool operator==(Iter& r) const { return s == r.s; }
        bool operator!=(Iter& r) const { return s != r.s; }
    };
        const HeavyLightDecomposition& hld; int v;
        Iter begin() const { return { hld, hld.rangeL[v] + 1 }; }
        Iter end() const { return { hld, hld.rangeR[v] }; }
    };
    ChildrenIterRange children(int v) const {
        return ChildrenIterRange{ *this, v };
    }
};

} // namespace nachia
#include <map>

namespace nachia{

template<
    class S,
    S op(S l, S r)
>
struct Segtree {
private:
    int N;
    std::vector<S> A;
    int xN;

    void mergev(int i){
        if(i < N) A[i] = op(A[i*2], A[i*2+1]);
    }

    template<class E>
    int minLeft2(int r, E cmp, int a = 0, int b = 0, int i = -1) const {
        static S x;
        if(i == -1){ a=0; b=N; i=1; x=A[0]; }
        if(r <= a) return a;
        if(b <= r){
            S nx = op(A[i], x);
            if(cmp(nx)){ x = nx; return a; }
        }
        if(b - a == 1) return b;
        int q = minLeft2(r, cmp, (a+b)/2, b, i*2+1);
        if(q > (a+b)/2) return q;
        return minLeft2(r, cmp, a, (a+b)/2, i*2);
    }
    
    template<class E>
    int maxRight2(int l, E cmp, int a = 0, int b = 0, int i = -1) const {
        static S x;
        if(i == -1){ a=0; b=N; i=1; x=A[0]; }
        if(b <= l) return b;
        if(l <= a){
            S nx = op(x, A[i]);
            if(cmp(nx)){ x = nx; return b; }
        }
        if(b - a == 1) return a;
        int q = maxRight2(l, cmp, a, (a+b)/2, i*2);
        if(q < (a+b)/2) return q;
        return maxRight2(l, cmp, (a+b)/2, b, i*2+1);
    }

public:
    Segtree() : N(0) {}
    Segtree(int n, S e) : xN(n) {
        N = 1; while (N < n) N *= 2;
        A.assign(N * 2, e);
    }
    Segtree(const std::vector<S>& a, S e) : Segtree(a.size(), e){
        for(int i=0; i<(int)a.size(); i++) A[i + N] = a[i];
        for(int i=N-1; i>=1; i--) mergev(i);
    }

    void set(int p, S x){
        p += N; A[p] = x;
        for(int d=1; (1<<d)<=N; d++) mergev(p>>d);
    }

    S get(int p) const { return A[N+p]; }

    S prod(int l, int r) const {
        l += N; r += N;
        S ql = A[0], qr = A[0];
        while(l<r){
            if(l&1) ql = op(ql, A[l++]);
            if(r&1) qr = op(A[--r], qr);
            l /= 2;
            r /= 2;
        }
        return op(ql, qr);
    }

    S allProd() const { return A[1]; }

    // bool cmp(S)
    template<class E>
    int minLeft(int r, E cmp) const {
        return minLeft2(r, cmp);
    }

    // bool cmp(S)
    template<class E>
    int maxRight(int l, E cmp) const {
        int x = maxRight2(l, cmp);
        return x > xN ? xN : x;
    }
};

} // namespace nachia

namespace nachia {
    template<class T, class Cmp = std::less<T>>
    struct PointSetRangeMin{
    private:
        static T minop(T l, T r){ return std::min(l, r, Cmp()); }
        using Base = Segtree<T, minop>;
        Base base;
        Cmp cmpx;
    public:
        PointSetRangeMin() {}
        PointSetRangeMin(int len, T INF)
            : base(len, INF){}
        PointSetRangeMin(const std::vector<T>& init, T INF)
            : base(init, INF){}
        T min(int l, int r){ return base.prod(l, r); }
        T min(){ return base.allProd(); }
        void set(int pos, T val){ base.set(pos, val); }
        T get(int pos){ return base.get(pos); }
        void chmin(int pos, T val){ base.set(pos, minop(get(pos), val)); }
        int lBoundLeft(int from, T val){ return base.minLeft(from, [this,val](const T& x){ return cmpx(val, x); }); }
        int uBoundLeft(int from, T val){ return base.minLeft(from, [this,val](const T& x){ return !cmpx(x, val); }); }
        int lBoundRight(int from, T val){ return base.maxRight(from, [this,val](const T& x){ return cmpx(val, x); }); }
        int uBoundRight(int from, T val){ return base.maxRight(from, [this,val](const T& x){ return !cmpx(x, val); }); }
        template<class E>
        int minLeft(int r, E cmp){ return base.minLeft(r, cmp); }
        template<class E>
        int maxRight(int l, E cmp){ return base.maxRight(l, cmp); }
    };
} // namespace nachia


void testcase(){
    int N; cin >> N;
    vec<int> A(N); cin >> A;
    auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);
    auto hld = nachia::HeavyLightDecomposition(tree);
    map<int,vec<int>> Q;
    auto seg0 = nachia::PointSetRangeMin<int, greater<int>>(N, -1001001001);
    auto seg1 = nachia::PointSetRangeMin<int, greater<int>>(N, -1001001001);
    rep(i,N) Q[-A[i]].push(i);
    vec<int> ans(N);
    for(auto &[aaaa,q] : Q){
        for(auto v : q){
            int d = hld.depth(v);
            for(auto [l,r] : hld.path(0,v)) if(l < r){
                seg1.chmin(r-1, d);
                seg0.chmin(r-1, d - hld.depth(hld.toVtx(r-1)) * 2);
            }
        }
        for(auto v : q){
            int t = 0;
            int d = hld.depth(v);
            for(auto [l,r] : hld.path(0,v)) if(l < r){
                int w = hld.toVtx(r-1);
                if(hld.heavyChildOf(w) >= 0){
                    int x = hld.heavyChildOf(w);
                    auto [sl,sr] = hld.subtree(x);
                    chmax(t, seg1.min(sl, sr) + d - hld.depth(w) * 2);
                }
                chmax(t, seg0.min(l, r-1) + d);
            }
            ans[v] = t;
        }
    }
    cout << ans << '\n';
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    #ifdef NACHIA
    int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
    #endif
    testcase();
    return 0;
}