#include <bits/stdc++.h>
 
#define FOR(i, a, b) for(auto i=a; i<=b; ++i)
#define REP(i, a, b) for(auto i=a; i<b; ++i)
#define FORI(i, a, b) for(auto i=a; i!=b+1-2*(a>b); i+=1-2*(a>b))
#define REPI(i, a, b) for(auto i=a-(a>b); i!=b-(a>b); i+=1-2*(a>b))
#define ALL(v) v.begin(),v.end()
#define mp(a, b) make_pair(a, b)
#define pb(a) push_back(a)
#define pf(a) push_front(a)
#define eb(a, b) emplace_back(a, b)
#define fir first
#define sec second
#define what_is(x) cout<<#x<<" is "<<x<<endl;
#define type(x) typeid(x).name()
#define ms(arr, val) memset(arr, val, sizeof(arr))
#define min3(a,b,c) min(min(a,b),c)
#define max3(a,b,c) max(max(a,b),c)
#define PI acos(-1)
#define open_read freopen("christmas.in", "r", stdin)
#define open_write freopen("christmas.out", "w", stdout)
 
using namespace std;
 
typedef long long LL;
typedef long double LD;
typedef unsigned long long ULL;
typedef pair<double, double> PDD;
typedef pair<int, int> PII;
typedef pair<int, PII> PIPII;
typedef pair<PII, PII> PPIIPII;
typedef pair<LL, LL> PLL;
typedef pair<ULL, ULL> PUU;
typedef pair<LL, PLL> PLPLL;
typedef pair<PLL, PLL> PPLLPLL;
typedef pair<int, LL> PIL;
typedef pair<LL, int> PLI;
 
template<typename T, typename T1>
ostream& operator << (ostream &out, pair<T, T1> obj) {
    out << "(" << obj.first << ", " << obj.second << ")";
    return out;
}
 
template<typename T, typename T1>
ostream& operator << (ostream &out, map<T, T1> cont) {
    typename map<T, T1>::const_iterator itr = cont.begin();
    typename map<T, T1>::const_iterator ends = cont.end();
 
    for(; itr != ends; ++itr) {
        out << *itr << " ";
    }
 
    out<<endl;
    return out;
} 

template<typename T>
ostream& operator << (ostream &out, set<T> cont) {
    typename set<T>::const_iterator itr = cont.begin();
    typename set<T>::const_iterator ends = cont.end();
    
    for(; itr != ends; ++itr) {
        out << *itr << " ";
    }
 
    out << endl;
    return out;
}
  
template<typename T>
ostream& operator << (ostream &out, multiset<T> cont) {
    typename multiset<T>::const_iterator itr = cont.begin();
    typename multiset<T>::const_iterator ends = cont.end();
 
    for (; itr != ends; ++itr) {
        out << *itr << " ";
    }
 
    out << endl;
    return out;
}

template<typename T, template<typename ELEM, typename ALLOC=allocator<ELEM>> class CONT>
ostream& operator << (ostream &out, CONT<T> cont) {
    typename CONT<T>::const_iterator itr = cont.begin();
    typename CONT<T>::const_iterator ends = cont.end();
 
    for (; itr != ends; ++itr) {
        out << *itr << " ";
    }
 
    out << endl;
    return out;
}
 
template<typename T, unsigned int N, typename CTy, typename CTr>
typename enable_if<!is_same<T, char>::value, basic_ostream<CTy, CTr> &>::type
operator << (basic_ostream<CTy, CTr> &out, const T (&arr)[N]) {
    REP (i, 0, N) {
        out << arr[i] << " ";
    }
 
    out << endl;
    return out;
}
  
template<typename T>
T GCD(T a, T b) {
    T min_v = min(a, b);
    T max_v = max(a, b);
 
    while (min_v) {
        T temp = max_v % min_v;
        max_v = min_v;
        min_v = temp;
    }
 
    return max_v;
}
 
template<typename T>
T LCM(T a, T b) {
    return (a * b) / gcd(a, b);
}
 
template<typename T>
T fastExpPow(T base, T exp, T mod) {
    T res = 1;
 
    while (exp) {
        if (exp & 1) {
            res *= base;
            res %= mod;
        }
 
        exp >>= 1;
        base *= base;
        base %= mod;
    }
 
    return res % mod;
}
 
/*#################################################################################################################
###################################################################################################################
###################################################################################################################
#################################################################################################################*/

#define SIZE 200010

int N;
int numbers[SIZE], segTree[4 * SIZE], lis[SIZE];
vector<int> tree[SIZE], order[SIZE];


int getMax(int Qbeg, int Qend, int Tbeg = 0, int Tend = N - 1, int ind = 0) { 
    if (Tbeg > Qend - 1 || Tend < Qbeg - 1) {
        return 0;
    }

    if (Qbeg - 1 <= Tbeg && Tend <= Qend - 1) {
        return segTree[ind];
    }

    int Tmid = (Tbeg + Tend) >> 1;

    int max1 = getMax(Qbeg, Qend, Tbeg, Tmid, 2 * ind + 1);
    int max2 = getMax(Qbeg, Qend, Tmid + 1, Tend, 2 * ind + 2);
    
    return max(max1, max2); 
} 
  
void update(int pos, int val, int Tbeg = 0, int Tend = N - 1, int ind = 0) { 
    if (Tbeg > pos - 1 || Tend < pos - 1) {
        return;
    }

    if (Tbeg == pos - 1 && Tbeg == Tend) {
        segTree[ind] = val;
        return;
    }

    int Tmid = (Tbeg + Tend) >> 1;

    update(pos, val, Tbeg, Tmid, 2 * ind + 1);
    update(pos, val, Tmid + 1, Tend, 2 * ind + 2);
    
    segTree[ind] = max(segTree[2 * ind + 1], segTree[2 * ind + 2]);
}

void dfs(int node = 1, int par = 0) {
    int num = numbers[node];
    int val = getMax(0, num - 1) + 1;
    
    order[num].pb(val);
    update(num, order[num].back());
    lis[node] = getMax(1, N);

    for (auto connNode: tree[node]) {
        if (connNode != par) {
            dfs(connNode, node);
        }
    }
    
    order[num].pop_back();

    if (order[num].empty()) {
        update(num, 0);
    } else {
        update(num, order[num].back());
    }
}


int main() {
    scanf("%d", &N);
    vector<PII> sorted;

    FOR (i, 1, N) {
        scanf("%d", numbers + i);
        sorted.eb(numbers[i], i);
    }
    
    sort(ALL(sorted));

    int cnt = 1;
    numbers[sorted[0].sec] = cnt;
    
    REP (i, 1, N) {
        if (sorted[i].fir > sorted[i - 1].fir) {
            ++cnt;
        }

        numbers[sorted[i].sec] = cnt;
    }

    FOR (i, 1, N - 1) {
        int U, V;
        scanf("%d%d", &U, &V);

        tree[U].pb(V);
        tree[V].pb(U);
    }
    
    dfs();

    FOR (i, 1, N) {
        printf("%d\n", lis[i]);
    }
    
    return 0;
}  


Measured memory_bytes: 39900