#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
//#include <unordered_map>
//#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 2e5 + 7;
int N, head[maxN], cnt, a[maxN], Lsan[maxN], _UP;
struct Eddge
{
    int nex, to;
    Eddge(int a=-1, int b=0):nex(a), to(b) {}
} edge[maxN << 1];
inline void addEddge(int u, int v)
{
    edge[cnt] = Eddge(head[u], v);
    head[u] = cnt++;
}
inline void _add(int u, int v) { addEddge(u, v); addEddge(v, u); }
int ans[maxN], dp[maxN];
int tree[maxN << 2] = {0};
struct heap
{
    priority_queue<int> Que, Del;
    inline bool empty()
    {
        while(!Que.empty() && !Del.empty() && Que.top() == Del.top()) { Que.pop(); Del.pop(); }
        return Que.empty();
    }
    inline void push(int val) { Que.push(val); }
    inline void clear(int val) { Del.push(val); }
    inline int size() { return (int)(Que.size() - Del.size()); }
    inline int top()
    {
        while(!Que.empty() && !Del.empty() && Que.top() == Del.top()) { Que.pop(); Del.pop(); }
        return Que.top();
    }
    inline void pop()
    {
        while(!Que.empty() && !Del.empty() && Que.top() == Del.top()) { Que.pop(); Del.pop(); }
        Que.pop();
    }
} st[maxN];
inline void pushup(int rt) { tree[rt] = max(tree[lsn], tree[rsn]); }
void Add(int rt, int l, int r, int qx, int val)
{
    if(l == r)
    {
        st[l].push(val);
        tree[rt] = st[l].top();
        return;
    }
    int mid = HalF;
    if(qx <= mid) Add(Lson, qx, val);
    else Add(Rson, qx, val);
    pushup(rt);
}
void Del(int rt, int l, int r, int qx, int val)
{
    if(l == r)
    {
        st[l].clear(val);
        if(st[l].empty()) tree[rt] = 0;
        else tree[rt] = st[l].top();
        return;
    }
    int mid = HalF;
    if(qx <= mid) Del(Lson, qx, val);
    else Del(Rson, qx, val);
    pushup(rt);
}
int query(int rt, int l, int r, int ql, int qr)
{
    if(ql <= l && qr >= r) return tree[rt];
    int mid = HalF;
    if(qr <= mid) return query(QL);
    else if(ql > mid) return query(QR);
    else return max(query(QL), query(QR));
}
void dfs(int u, int fa)
{
    Add(1, 1, _UP, a[u], dp[u]);
    ans[u] = max(dp[u], ans[fa]);
    for(int i=head[u], v; ~i; i=edge[i].nex)
    {
        v = edge[i].to;
        if(v == fa) continue;
        dp[v] = ((a[v] - 1) > 0 ? query(1, 1, _UP, 1, a[v] - 1) : 0) + 1;
        dfs(v, u);
    }
    Del(1, 1, _UP, a[u], dp[u]);
}
inline void init()
{
    cnt = 0;
    for(int i=1; i<=N; i++) head[i] = -1;
}
int main()
{
    scanf("%d", &N);
    init();
    for(int i=1; i<=N; i++) { scanf("%d", &a[i]); Lsan[i] = a[i]; }
    sort(Lsan + 1, Lsan + N + 1);
    _UP = (int)(unique(Lsan + 1, Lsan + N + 1) - Lsan - 1);
    for(int i=1; i<=N; i++) a[i] = (int)(lower_bound(Lsan + 1, Lsan + _UP + 1, a[i]) - Lsan);
    for(int i=1, u, v; i<N; i++)
    {
        scanf("%d%d", &u, &v);
        _add(u, v);
    }
    dp[1] = 1;
    dfs(1, 0);
    for(int i=1; i<=N; i++) printf("%d\n", ans[i]);
    return 0;
}


Measured memory_bytes: 47280