using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ABC165F
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var aList = NNList(N);
            var uv = Repeat(0, N - 1).Select(_ => new { u = NN - 1, v = NN - 1 }).ToArray();
            var tree = new LIB_Tree(N);
            foreach (var item in uv)
            {
                tree.AddPath(item.u, item.v);
            }
            var dp = new List<long>();
            var dpoldval = new long[N];
            var dpupdidx = new long[N];
            var ans = new long[N];
            foreach (var item in tree.EulerTour(0))
            {
                if (item.direction == 1)
                {
                    var left = -1;
                    var right = dp.Count;
                    while (right - left > 1)
                    {
                        var mid = (int)(right + left) / 2;
                        if (dp[mid] >= aList[item.node]) right = mid;
                        else left = mid;
                    }
                    if (right >= dp.Count)
                    {
                        dpupdidx[item.node] = right;
                        dpoldval[item.node] = -1;
                        dp.Add(aList[item.node]);
                    }
                    else
                    {
                        dpupdidx[item.node] = right;
                        dpoldval[item.node] = dp[right];
                        dp[right] = aList[item.node];
                    }
                    ans[item.node] = dp.Count;
                }
                else
                {
                    if (dpoldval[item.node] == -1)
                    {
                        dp.RemoveAt(dp.Count - 1);
                    }
                    else
                    {
                        dp[(int)dpupdidx[item.node]] = dpoldval[item.node];
                    }
                }
            }
            foreach (var item in ans)
            {
                Console.WriteLine(item);
            }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    class LIB_FastIO
    {
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[1024];
        int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        public LIB_FastIODebug() { }
        public override string Scan() => NextString();
        public override long Long() => long.Parse(NextString());
        public override double Double() => double.Parse(NextString());
    }
    class LIB_Tree
    {
        int N;
        List<int>[] path;
        public struct EulerRes
        {
            public long node;
            public long parent;
            public long direction;
        }
        List<EulerRes> eulerList;
        public struct BFSRes
        {
            public long node;
            public long parent;
        }
        List<BFSRes> bfsList;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_Tree(long n)
        {
            N = (int)n;
            path = Enumerable.Repeat(0, N).Select(_ => new List<int>()).ToArray();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void AddPath(long u, long v)
        {
            if (u >= N || v >= N) throw new Exception();
            path[u].Add((int)v);
            path[v].Add((int)u);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int[] GetSurround(long u) => path[u].ToArray();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public List<BFSRes> BFSFromRoot(long root)
        {
            bfsList = new List<BFSRes>();
            var q = new Queue<int>();
            var done = new bool[N];
            bfsList.Add(new BFSRes { node = root, parent = -1 });
            done[root] = true;
            q.Enqueue((int)root);
            while (q.Count > 0)
            {
                var w = q.Dequeue();
                foreach (var i in path[w])
                {
                    if (done[i]) continue;
                    done[i] = true;
                    q.Enqueue(i);
                    bfsList.Add(new BFSRes { node = i, parent = w });
                }
            }
            return bfsList;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public List<BFSRes> BFSFromLeaf(long root) => BFSFromRoot(root).ToArray().Reverse().ToList();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public List<EulerRes> EulerTour(long root)
        {
            eulerList = new List<EulerRes>();
            var s = new Stack<Tuple<int, int>>();
            var done = new bool[N];
            done[root] = true;
            s.Push(Tuple.Create((int)root, -1));
            while (s.Count > 0)
            {
                var w = s.Peek();
                var ad = true;
                foreach (var i in path[w.Item1])
                {
                    if (done[i]) continue;
                    done[i] = true;
                    ad = false;
                    s.Push(Tuple.Create(i, w.Item1));
                }
                if (!ad || path[w.Item1].Count == 1) eulerList.Add(new EulerRes { node = w.Item1, parent = w.Item2, direction = 1 });
                if (ad)
                {
                    s.Pop();
                    eulerList.Add(new EulerRes { node = w.Item1, parent = w.Item2, direction = -1 });
                }
            }
            return eulerList;
        }
        public class LCAResult
        {
            int[] depth;
            int l;
            int[][] pr;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public LCAResult(int[] depth, int l, int[][] pr)
            {
                this.depth = depth;
                this.l = l;
                this.pr = pr;
            }
            public long this[long u, long v]
            {
                [MethodImpl(MethodImplOptions.AggressiveInlining)]
                get
                {
                    if (depth[u] > depth[v])
                    {
                        var t = u; u = v; v = t;
                    }
                    for (var k = 0; k < l; k++)
                    {
                        if ((((depth[v] - depth[u]) >> k) & 1) != 0) v = pr[k][v];
                    }
                    if (u == v) return u;
                    for (var k = l - 1; k >= 0; k--)
                    {
                        if (pr[k][u] != pr[k][v])
                        {
                            u = pr[k][u];
                            v = pr[k][v];
                        }
                    }
                    return pr[0][u];
                }
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LCAResult BuildLCA(long root)
        {
            var depth = new int[N];
            var l = 0;
            while (N > (1 << l)) l++;
            var pr = Enumerable.Repeat(0, l).Select(_ => new int[N]).ToArray();
            depth[root] = 0;
            pr[0][root] = -1;
            var q = new Stack<int>();
            q.Push((int)root);
            while (q.Count > 0)
            {
                var w = q.Pop();
                foreach (var i in path[w])
                {
                    if (i == pr[0][w]) continue;
                    q.Push(i);
                    depth[i] = depth[w] + 1;
                    pr[0][i] = w;
                }
            }
            for (var k = 0; k + 1 < l; k++)
            {
                for (var w = 0; w < N; w++)
                {
                    if (pr[k][w] < 0) pr[k + 1][w] = -1;
                    else pr[k + 1][w] = pr[k][pr[k][w]];
                }
            }
            return new LCAResult(depth, l, pr);
        }
        /// <summary>
        /// 蜈ｨ譁ｹ菴肴惠DP
        /// </summary>
        /// <param name="idxToVal">鬆らせ逡ｪ蜿ｷ縺九ｉ蛟､繧貞叙蠕・/param>
        /// <param name="mergeSubTrees">驛ｨ蛻・惠縺ｨ驛ｨ蛻・惠縺ｮ繝槭・繧ｸ (subtree, subtree)</param>
        /// <returns>2谺｡蜈・・蛻夕node, parent]縺ｮ驛ｨ蛻・惠縺ｮDP蛟､縲Ｑarent=-1縺ｯnode繧偵Ν繝ｼ繝医→縺励◆譛ｨ縺ｮ蛟､</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public CReRooting<T> ReRooting<T>(Func<long, T> idxToVal, Func<T, T, T> mergeSubTrees) => new CReRooting<T>(this, idxToVal, mergeSubTrees);
        public class CReRooting<T>
        {
            LIB_Tree tree;
            Dictionary<int, T>[] dp;
            Func<T, T, T> f;
            Func<long, T> g;
            Func<long, long, T, T> g2;
            Func<T, T, T> h;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public CReRooting(LIB_Tree tree, Func<long, T> idxToVal, Func<T, T, T> mergeSubTrees)
            {
                this.tree = tree;
                dp = Enumerable.Repeat(0, tree.N).Select(_ => new Dictionary<int, T>()).ToArray();
                f = mergeSubTrees;
                g = idxToVal;
                g2 = (r, p, v) => v;
                h = (v, t) => t;
            }
            public T this[long vtx, long parent]
            {
                [MethodImpl(MethodImplOptions.AggressiveInlining)]
                get { return dp[vtx][(int)parent]; }
            }
            /// <summary>
            /// 鬆らせ逡ｪ蜿ｷ(root, parent)縺ｧ陦ｨ縺呵ｾｺ縺ｨroot繧偵Ν繝ｼ繝医→縺吶ｋ驛ｨ蛻・惠繧偵・繝ｼ繧ｸ縺吶ｋ繝｡繧ｽ繝・ラ繧定ｨｭ螳・            /// </summary>
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public void SetMergeEdgeAndSubtree(Func<long, long, T, T> mergeEdgeAndSubtree) { g2 = mergeEdgeAndSubtree; }
            /// <summary>
            /// 鬆らせ縺ｨ驛ｨ蛻・惠縺ｮ邨先棡繧偵・繝ｼ繧ｸ(vertex, subtrees)縺吶ｋ繝｡繧ｽ繝・ラ繧定ｨｭ螳・            /// </summary>
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public void SetMergeVertexAndSubtree(Func<T, T, T> mergeVertexAndSubtree) { h = mergeVertexAndSubtree; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public void Build()
            {
                var done = new bool[tree.N];
                Action<long, long, T> upd = (vtx, rt, val) =>
                {
                    if (vtx == -1) return;
                    if (done[vtx]) dp[vtx][-1] = f(dp[vtx][-1], g2(rt, vtx, val));
                    else dp[vtx][-1] = g2(rt, vtx, val);
                    done[vtx] = true;
                };
                foreach (var item in tree.BFSFromLeaf(0))
                {
                    var ary = tree.path[item.node].Where(e => e != item.parent).ToArray();
                    var val = g(item.node);
                    if (ary.Length > 0)
                    {
                        var acc = g2(ary[0], item.node, dp[ary[0]][(int)item.node]);
                        foreach (var item2 in ary.Skip(1)) acc = f(acc, g2(item2, item.node, dp[item2][(int)item.node]));
                        val = h(val, acc);
                    }
                    upd(item.parent, item.node, dp[item.node][(int)item.parent] = val);
                }
                var swag = new LIB_SlidingWindowAggregation<T>(f);
                Action<int, int> process = (node, parent) =>
                {
                    var val = g(node);
                    if (tree.path[node].Count == 1)
                    {
                        var x = tree.path[node][0];
                        if (x != parent) upd(x, node, dp[node][x] = val);
                    }
                    else if (tree.path[node].Count == 2)
                    {
                        var x = tree.path[node][0]; var y = tree.path[node][1];
                        if (x != parent) upd(x, node, dp[node][x] = h(val, g2(y, node, dp[y][node])));
                        if (y != parent) upd(y, node, dp[node][y] = h(val, g2(x, node, dp[x][node])));
                    }
                    else if (tree.path[node].Count == 3)
                    {
                        var x = tree.path[node][0]; var y = tree.path[node][1]; var z = tree.path[node][2];
                        if (x != parent) upd(x, node, dp[node][x] = h(val, f(g2(y, node, dp[y][node]), g2(z, node, dp[z][node]))));
                        if (y != parent) upd(y, node, dp[node][y] = h(val, f(g2(x, node, dp[x][node]), g2(z, node, dp[z][node]))));
                        if (z != parent) upd(z, node, dp[node][z] = h(val, f(g2(x, node, dp[x][node]), g2(y, node, dp[y][node]))));
                    }
                    else if (tree.path[node].Count == 4)
                    {
                        var x = tree.path[node][0]; var y = tree.path[node][1]; var z = tree.path[node][2]; var w = tree.path[node][3];
                        var xy = f(g2(x, node, dp[x][node]), g2(y, node, dp[y][node]));
                        var zw = f(g2(z, node, dp[z][node]), g2(w, node, dp[w][node]));
                        if (x != parent) upd(x, node, dp[node][x] = h(val, f(g2(y, node, dp[y][node]), zw)));
                        if (y != parent) upd(y, node, dp[node][y] = h(val, f(g2(x, node, dp[x][node]), zw)));
                        if (z != parent) upd(z, node, dp[node][z] = h(val, f(xy, g2(w, node, dp[w][node]))));
                        if (w != parent) upd(w, node, dp[node][w] = h(val, f(xy, g2(z, node, dp[z][node]))));
                    }
                    else
                    {
                        swag.Clear();
                        var pre = new T[tree.path[node].Count];
                        for (var i = 0; i < pre.Length; ++i) swag.PushBack(pre[i] = g2(tree.path[node][i], node, dp[tree.path[node][i]][node]));
                        for (var i = 0; i < pre.Length; ++i)
                        {
                            var item2 = tree.path[node][i];
                            swag.PopFront();
                            if (item2 != parent) upd(item2, node, dp[node][item2] = h(val, swag.Aggregate()));
                            swag.PushBack(pre[i]);
                        }
                    }
                };
                foreach (var item in tree.BFSFromRoot(0)) process((int)item.node, (int)item.parent);
                for (var i = 1; i < tree.N; i++) dp[i][-1] = done[i] ? h(g(i), dp[i][-1]) : g(i);
            }
        }
    }
    class LIB_SlidingWindowAggregation<T>
    {
        T[][] list;
        T[][] agg;
        int[] size;
        Func<T, T, T> fun;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_SlidingWindowAggregation(IEnumerable<T> ary, Func<T, T, T> f)
        {
            list = new T[2][]; agg = new T[2][]; size = new int[2];
            fun = f;
            list[0] = new T[16]; agg[0] = new T[16]; size[0] = 0;
            if (ary.Any())
            {
                var temp = ary.ToArray();
                size[1] = temp.Length;
                list[1] = new T[size[1]];
                agg[1] = new T[size[1]];
                for (var i = 0; i < list[1].Length; i++)
                {
                    list[1][i] = temp[i];
                    if (i == 0) agg[1][i] = temp[i];
                    else agg[1][i] = fun(agg[1][i - 1], temp[i]);
                }
            }
            else
            {
                list[1] = new T[16]; agg[1] = new T[16]; size[1] = 0;
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_SlidingWindowAggregation(Func<T, T, T> f) : this(new T[0], f) { }
        public int Count => size[0] + size[1];
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Clear()
        {
            size[0] = size[1] = 0;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Push(int lista, T val)
        {
            if (list[lista].Length == size[lista])
            {
                var newAry = new T[size[lista] * 2];
                var newAgg = new T[size[lista] * 2];
                Array.Copy(list[lista], newAry, size[lista]);
                Array.Copy(agg[lista], newAgg, size[lista]);
                list[lista] = newAry;
                agg[lista] = newAgg;
            }
            if (size[lista] == 0) agg[lista][0] = val;
            else if (lista == 0) agg[lista][size[lista]] = fun(val, agg[lista][size[lista] - 1]);
            else agg[lista][size[lista]] = fun(agg[lista][size[lista] - 1], val);
            list[lista][size[lista]++] = val;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void PushBack(T val) => Push(1, val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void PushFront(T val) => Push(0, val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        T Pop(int lista)
        {
            var listb = 1 - lista;
            if (size[lista] == 0)
            {
                if (size[listb] == 0) throw new Exception();
                var mid = (size[listb] - 1) / 2;
                if (list[lista].Length <= mid)
                {
                    list[lista] = new T[mid + 1];
                    agg[lista] = new T[mid + 1];
                }
                size[lista] = 0;
                for (var i = mid; i >= 0; i--)
                {
                    if (size[lista] == 0) agg[lista][size[lista]] = list[listb][i];
                    else if (lista == 0) agg[lista][size[lista]] = fun(list[listb][i], agg[lista][size[lista] - 1]);
                    else agg[lista][size[lista]] = fun(agg[lista][size[lista] - 1], list[listb][i]);
                    list[lista][size[lista]++] = list[listb][i];
                }
                for (var i = mid + 1; i < size[listb]; i++)
                {
                    var idx = i - mid - 1;
                    if (idx == 0) agg[listb][idx] = list[listb][i];
                    else if (lista == 0) agg[listb][idx] = fun(list[listb][i], agg[listb][idx - 1]);
                    else agg[listb][idx] = fun(agg[listb][idx - 1], list[listb][i]);
                    list[listb][idx] = list[listb][i];
                }
                size[listb] -= size[lista];
            }
            return list[lista][--size[lista]];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T PopBack() => Pop(1);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T PopFront() => Pop(0);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T Aggregate()
        {
            if (size[0] == 0 && size[1] == 0) throw new Exception();
            else if (size[1] == 0) return agg[0][size[0] - 1];
            else if (size[0] == 0) return agg[1][size[1] - 1];
            else return fun(agg[0][size[0] - 1], agg[1][size[1] - 1]);
        }
    }
}


Measured memory_bytes: 87628