using System; using System.ComponentModel; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.Diagnostics.Contracts; using System.IO; using System.Linq; using System.Numerics; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Text; using static Functions; using static OutputLib; using ModInt = StaticModInt; static class Program { static public void Main(string[] args) { Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); new Solver(); Console.Out.Flush(); } } public class Solver { public Solver() { Solve(); } void Solve() { int n = ri; var a = new long[n + 1]; for (int i = 0; i <= n; i++) a[i] = rl; var g = new List[n + 1]; for (int i = 0; i <= n; i++) g[i] = new List(); for (int i = 0; i < n; i++) { int u = ri, v = ri; g[u].Add(v); g[v].Add(u); } var xs = new long[n + 1]; for (int i = 0; i <= n; i++) xs[i] = a[i] * (n + 1) + i; Array.Sort(xs); var id = new int[n + 1]; var dic = new Dictionary(); for (int i = 0; i <= n; i++) { id[i] = (int)xs[i] % (n + 1); dic.Add(id[i], i); } var seg_cnt = new SegTree(n + 1); var seg_val = new SegTree(n + 1); var ans = new long[n]; Array.Fill(ans, -1); void DFS(int x, int dep = 0, int p = -1) { int idx = dic[x]; seg_cnt.Set(idx, 1); seg_val.Set(idx, a[x]); if (dep >= 2) { int min = seg_cnt.MaxRight(0, v => v == 0); int max = seg_cnt.MinLeft(n + 1, v => v == 0) - 1; ans[x - 1] = INF; for (int shift = 0; shift < 2; shift++) { long del_val = shift == 0 ? a[id[min]] : a[id[max]]; int l = min + shift, r = max + shift; if (dep % 2 == 1) { int mid_cnt = (dep + 1) / 2; int mid = seg_cnt.MaxRight(l, v => v < mid_cnt); long val = seg_val.Prod(mid + 1, r) - seg_val.Prod(l, mid); if (a[id[mid]] == del_val) val++; Chmin(ref ans[x - 1], val); } else { int mid_cnt = dep / 2; int mid1 = seg_cnt.MaxRight(l, v => v < mid_cnt); int mid2 = seg_cnt.MaxRight(mid1 + 1, v => v == 0); long val = seg_val.Prod(mid2, r) - seg_val.Prod(l, mid2); if (a[id[mid1]] == a[id[mid2]] && a[id[mid1]] == del_val) val++; Chmin(ref ans[x - 1], val); } } } foreach (var y in g[x]) { if (y == p) continue; DFS(y, dep + 1, x); } seg_cnt.Set(idx, 0); seg_val.Set(idx, 0); } DFS(0); WriteJoin("\n", ans); } const long INF = 1L << 60; int ri { [MethodImpl(256)] get => (int)sc.Integer(); } (int, int) ri2 { [MethodImpl(256)] get => (ri, ri); } (int, int, int) ri3 { [MethodImpl(256)] get => (ri, ri, ri); } (int, int, int, int) ri4 { [MethodImpl(256)] get => (ri, ri, ri, ri); } (int, int, int, int, int) ri5 { [MethodImpl(256)] get => (ri, ri, ri, ri, ri); } long rl { [MethodImpl(256)] get => sc.Integer(); } (long, long) rl2 { [MethodImpl(256)] get => (rl, rl); } (long, long, long) rl3 { [MethodImpl(256)] get => (rl, rl, rl); } (long, long, long, long) rl4 { [MethodImpl(256)] get => (rl, rl, rl, rl); } (long, long, long, long, long) rl5 { [MethodImpl(256)] get => (rl, rl, rl, rl, rl); } uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); } ulong rul { [MethodImpl(256)] get => sc.UInteger(); } double rd { [MethodImpl(256)] get => sc.Double(); } string rs { [MethodImpl(256)] get => sc.Scan(); } string rline { [MethodImpl(256)] get => sc.Line(); } public StreamScanner sc = new StreamScanner(Console.OpenStandardInput()); } public static class Functions { [MethodImpl(256)] public static int Popcount(ulong x) { x = (x & 0x5555555555555555UL) + ((x >> 1) & 0x5555555555555555UL); x = (x & 0x3333333333333333UL) + ((x >> 2) & 0x3333333333333333UL); x = (x & 0x0f0f0f0f0f0f0f0fUL) + ((x >> 4) & 0x0f0f0f0f0f0f0f0fUL); x = (x & 0x00ff00ff00ff00ffUL) + ((x >> 8) & 0x00ff00ff00ff00ffUL); x = (x & 0x0000ffff0000ffffUL) + ((x >> 16) & 0x0000ffff0000ffffUL); x = (x & 0x00000000ffffffffUL) + ((x >> 32) & 0x00000000ffffffffUL); return (int)x; } [MethodImpl(256)] public static int Popcount(long x) { x = (x & 0x5555555555555555L) + ((x >> 1) & 0x5555555555555555L); x = (x & 0x3333333333333333L) + ((x >> 2) & 0x3333333333333333L); x = (x & 0x0f0f0f0f0f0f0f0fL) + ((x >> 4) & 0x0f0f0f0f0f0f0f0fL); x = (x & 0x00ff00ff00ff00ffL) + ((x >> 8) & 0x00ff00ff00ff00ffL); x = (x & 0x0000ffff0000ffffL) + ((x >> 16) & 0x0000ffff0000ffffL); x = (x & 0x00000000ffffffffL) + ((x >> 32) & 0x00000000ffffffffL); return (int)x; } [MethodImpl(256)] public static int Popcount(int x) { x = (x & 0x55555555) + ((x >> 1) & 0x55555555); x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x & 0x0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f); x = (x & 0x00ff00ff) + ((x >> 8) & 0x00ff00ff); x = (x & 0x0000ffff) + ((x >> 16) & 0x0000ffff); return x; } [MethodImpl(256)] public static int Ctz(long x) { if (x == 0) return -1; return Popcount((ulong)((x & -x) - 1)); } [MethodImpl(256)] public static int CeilPow2(int n) { int x = 0; while ((1 << x) < n) x++; return x; } [MethodImpl(256)] public static int SafeMod(int x, int m) { int r = x % m; return r < 0 ? r + Math.Abs(m) : r; } [MethodImpl(256)] public static long SafeMod(long x, long m) { long r = x % m; return r < 0 ? r + Math.Abs(m) : r; } [MethodImpl(256)] public static int Sign(long x) => x == 0 ? 0 : (x < 0 ? -1 : 1); [MethodImpl(256)] public static int Sign(double x) => x == 0 ? 0 : (x < 0 ? -1 : 1); [MethodImpl(256)] public static int DigitSum(long n, int d = 10) { long s = 0; while (n > 0) { s += n % d; n /= d; } return (int)s; } [MethodImpl(256)] public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1; [MethodImpl(256)] public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b; [MethodImpl(256)] public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b); [MethodImpl(256)] public static uint Gcd(uint a, uint b) => b == 0 ? a : Gcd(b, a % b); [MethodImpl(256)] public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b); [MethodImpl(256)] public static ulong Gcd(ulong a, ulong b) => b == 0 ? a : Gcd(b, a % b); [MethodImpl(256)] public static (long x, long y, long g) ExtGcd(long a, long b) { if (b == 0) return (Sign(a), 0, Math.Abs(a)); long c = SafeMod(a, b); var (x2, y2, g) = ExtGcd(b, c); long x = SafeMod(y2, b); long y = (g - a * x) / b; return (x, y, g); } [MethodImpl(256)] public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; } [MethodImpl(256)] public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; } [MethodImpl(256)] public static void Swap(ref T x, ref T y) { T t = y; y = x; x = t; } [MethodImpl(256)] public static T Clamp(T x, T l, T r) where T : IComparable => x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); [MethodImpl(256)] public static T Clamp(ref T x, T l, T r) where T : IComparable => x = x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); [MethodImpl(256)] public static void Chmin(ref T x, T y) where T : IComparable { if (x.CompareTo(y) > 0) x = y; } [MethodImpl(256)] public static void Chmax(ref T x, T y) where T : IComparable { if (x.CompareTo(y) < 0) x = y; } [MethodImpl(256)] public static int LowerBound(long[] arr, long val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => Sign(t - val), l, r); [MethodImpl(256)] public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => t - val, l, r); [MethodImpl(256)] public static int LowerBound(T[] arr, T val, int l = -1, int r = -1) where T : IComparable => LowerBound(arr.AsSpan(), t => t.CompareTo(val), l, r); [MethodImpl(256)] public static int LowerBound(T[] arr, Func comp, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), comp, l, r); [MethodImpl(256)] public static int LowerBound(Span data, Func comp, int l = -1, int r = -1) { if (data.Length == 0) return -1; if (l == -1) l = 0; if (r == -1) r = data.Length; while (l < r) { int x = (l + r) / 2; if (comp(data[x]) < 0) l = x + 1; else r = x; } return l; } [MethodImpl(256)] public static int RangeCount(T[] arr, T geq, T lt, int l = -1, int r = -1) where T : IComparable => Math.Max(0, LowerBound(arr.AsSpan(), t => t.CompareTo(lt), l, r) - LowerBound(arr.AsSpan(), t => t.CompareTo(geq), l, r)); [MethodImpl(256)] public static string ToBase2(long v, int digit = -1) { if (digit == -1) { digit = 0; while ((v >> digit) > 0) digit++; } var c = new string[digit]; for (int i = 0; i < digit; i++) c[digit - 1 - i] = ((v >> i) & 1) == 0 ? "0" : "1"; return string.Join("", c); } [MethodImpl(256)] public static string ToBaseN(long v, int n, int digit = -1) { if (digit == -1) { digit = 0; long pow = 1; while (v >= pow) { digit++; pow *= n; } } var c = new int[digit]; for (int i = 0; i < digit; i++, v /= n) c[digit - 1 - i] = (int)(v % n); return string.Join("", c); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } private readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } [MethodImpl(256)] private 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++]; } [MethodImpl(256)] public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } [MethodImpl(256)] public string Line() { var sb = new StringBuilder(); for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b); return sb.ToString(); } [MethodImpl(256)] public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } [MethodImpl(256)] public long Integer() { 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'; } } [MethodImpl(256)] public ulong UInteger() { ulong ret = 0; byte b = 0; do b = read(); while (b < '0' || '9' < b); for (; true; b = read()) { if (b < '0' || '9' < b) return ret; else ret = ret * 10 + b - '0'; } } [MethodImpl(256)] public double Double() => double.Parse(Scan()); } public static class OutputLib { [MethodImpl(256)] public static void WriteJoin(string s, IEnumerable t) => Console.WriteLine(string.Join(s, t)); [MethodImpl(256)] public static void WriteMat(T[,] a, string sep = " ") { int sz1 = a.GetLength(0), sz2 = a.GetLength(1); var b = new T[sz2]; for (int i = 0; i < sz1; i++) { for (int j = 0; j < sz2; j++) b[j] = a[i, j]; WriteJoin(sep, b); } } [MethodImpl(256)] public static void WriteMat(T[][] a, string sep = " ") { for (int i = 0; i < a.Length; i++) WriteJoin(sep, a[i]); } [MethodImpl(256)] public static void WriteMat(T[][] a, Func map, string sep = " ") { for (int i = 0; i < a.Length; i++) WriteJoin(sep, a[i].Select(x => map(x))); } [MethodImpl(256)] public static void Write(object t) => Console.WriteLine(t.ToString()); [MethodImpl(256)] public static void Write(params object[] arg) => Console.WriteLine(string.Join(" ", arg.Select(x => x.ToString()))); [MethodImpl(256)] public static void Write(string str) => Console.WriteLine(str); [MethodImpl(256)] public static void WriteFlush(object t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); } [MethodImpl(256)] public static void WriteError(object t) => Console.Error.WriteLine(t.ToString()); [MethodImpl(256)] public static void Flush() => Console.Out.Flush(); [MethodImpl(256)] public static void YN(bool t) => Console.WriteLine(t ? "YES" : "NO"); [MethodImpl(256)] public static void Yn(bool t) => Console.WriteLine(t ? "Yes" : "No"); [MethodImpl(256)] public static void yn(bool t) => Console.WriteLine(t ? "yes" : "no"); [MethodImpl(256)] public static void DeleteLine() => Console.Write("\x1b[1A\x1b[2K"); [MethodImpl(256)] public static void ProgressBar(long now, long total, int blocks = 50) { int x = (int)((2 * now * blocks + 1) / (2 * total)); Console.Write($"\x1b[G{now} / {total} : [\x1b[42m{string.Concat(Enumerable.Repeat("_", x))}\x1b[0m{string.Concat(Enumerable.Repeat("_", blocks - x))}]"); } } public interface IStaticMod { uint Mod { get; } bool IsPrime { get; } } public readonly struct Mod1000000007 : IStaticMod { public uint Mod => 1000000007; public bool IsPrime => true; } public readonly struct Mod998244353 : IStaticMod { public uint Mod => 998244353; public bool IsPrime => true; } public readonly struct StaticModInt : IEquatable> where T : struct, IStaticMod { internal readonly uint _v; private static readonly T op = default; public int Value => (int)_v; public static int Mod => (int)op.Mod; public static StaticModInt Zero => default; public static StaticModInt One => new StaticModInt(1u); [MethodImpl(256)] public static StaticModInt Raw(int v) { var u = unchecked((uint)v); return new StaticModInt(u); } [MethodImpl(256)] public StaticModInt(long v) : this(Round(v)) { } [MethodImpl(256)] public StaticModInt(ulong v) : this((uint)(v % op.Mod)) { } [MethodImpl(256)] private StaticModInt(uint v) => _v = v; [MethodImpl(256)] private static uint Round(long v) { var x = v % op.Mod; if (x < 0) x += op.Mod; return (uint)x; } [MethodImpl(256)] public static StaticModInt operator ++(StaticModInt v) { var x = v._v + 1; if (x == op.Mod) x = 0; return new StaticModInt(x); } [MethodImpl(256)] public static StaticModInt operator --(StaticModInt v) { var x = v._v; if (x == 0) x = op.Mod; return new StaticModInt(x - 1); } [MethodImpl(256)] public static StaticModInt operator +(StaticModInt lhs, StaticModInt rhs) { var v = lhs._v + rhs._v; if (v >= op.Mod) v -= op.Mod; return new StaticModInt(v); } [MethodImpl(256)] public static StaticModInt operator -(StaticModInt lhs, StaticModInt rhs) { unchecked { var v = lhs._v - rhs._v; if (v >= op.Mod) v += op.Mod; return new StaticModInt(v); } } [MethodImpl(256)] public static StaticModInt operator *(StaticModInt lhs, StaticModInt rhs) => new StaticModInt((uint)((ulong)lhs._v * rhs._v % op.Mod)); [MethodImpl(256)] public static StaticModInt operator /(StaticModInt lhs, StaticModInt rhs) => new StaticModInt((uint)((ulong)lhs._v * Inv(rhs._v) % op.Mod)); [MethodImpl(256)] public static StaticModInt operator +(StaticModInt v) => v; [MethodImpl(256)] public static StaticModInt operator -(StaticModInt v) => new StaticModInt(v._v == 0 ? 0 : op.Mod - v._v); [MethodImpl(256)] public static bool operator ==(StaticModInt lhs, StaticModInt rhs) => lhs._v == rhs._v; [MethodImpl(256)] public static bool operator !=(StaticModInt lhs, StaticModInt rhs) => lhs._v != rhs._v; [MethodImpl(256)] public static implicit operator StaticModInt(int v) => new StaticModInt(v); [MethodImpl(256)] public static implicit operator StaticModInt(uint v) => new StaticModInt((long)v); [MethodImpl(256)] public static implicit operator StaticModInt(long v) => new StaticModInt(v); [MethodImpl(256)] public static implicit operator StaticModInt(ulong v) => new StaticModInt(v); [MethodImpl(256)] public static implicit operator long(StaticModInt v) => v._v; [MethodImpl(256)] public static implicit operator ulong(StaticModInt v) => v._v; [MethodImpl(256)] public StaticModInt Pow(long n) { var x = this; var r = new StaticModInt(1U); while (n > 0) { if ((n & 1) > 0) r *= x; x *= x; n >>= 1; } return r; } [MethodImpl(256)] public StaticModInt Inv() => new StaticModInt(Inv(_v)); [MethodImpl(256)] static ulong Inv(ulong x) { long u = op.Mod, xu = 1, yu = 0, v = (long)x, xv = 0, yv = 1; while (v != 0) { long w = SafeMod(u, v); long q = (u - w) / v; long xw = xu - xv * q; long yw = yu - yv * q; u = v; xu = xv; yu = yv; v = w; xv = xw; yv = yw; } return (ulong)(yu < 0 ? yu + op.Mod : yu); } [MethodImpl(256)] static long SafeMod(long x, long m) { long r = x % m; if (r < 0) r += m; return r; } [MethodImpl(256)] public override string ToString() => _v.ToString(); [MethodImpl(256)] public string ToString(string format, IFormatProvider formatProvider) => _v.ToString(format, formatProvider); [MethodImpl(256)] public override bool Equals(object? obj) => obj is StaticModInt m && Equals(m); [MethodImpl(256)] public bool Equals(StaticModInt other) => _v == other._v; [MethodImpl(256)] public override int GetHashCode() => _v.GetHashCode(); } public interface IGroup : IMonoid, IInvertible { } public struct IntAddGroup : IGroup { public int Identity => 0; public int Operate(int x, int y) => x + y; public int Inverse(int x) => -x; } public struct LongAddGroup : IGroup { public long Identity => 0; public long Operate(long x, long y) => x + y; public long Inverse(long x) => -x; } public struct ModIntAddGroup : IGroup> where T : struct, IStaticMod { public StaticModInt Identity => 0; public StaticModInt Operate(StaticModInt x, StaticModInt y) => x + y; public StaticModInt Inverse(StaticModInt x) => -x; } public class SegTree where Op : struct, IMonoid { private static readonly Op op = default; public int Length { get; } readonly int log, size; public readonly T[] d; public SegTree(int sz) { Length = sz; log = 0; while ((1 << log) < Length) log++; size = 1 << log; d = new T[2 * size]; Array.Fill(d, op.Identity); } public SegTree(T[] v) : this(v.Length) { for (int i = 0; i < Length; i++) d[size + i] = v[i]; for (int i = size - 1; i > 0; i--) Update(i); } [MethodImpl(256)] internal void SetWithoutUpdate(int p, T v) => d[p + size] = v; [MethodImpl(256)] internal void AllUpdate() { for (int i = size - 1; i > 0; i--) Update(i); } [MethodImpl(256)] private void Update(int p) => d[p] = op.Operate(d[2 * p], d[2 * p + 1]); [MethodImpl(256)] public T Get(int p) => d[p + size]; [MethodImpl(256)] public void Set(int p, T v) { p += size; d[p] = v; for (int i = 1; i <= log; i++) Update(p >> i); } public T AllProd() => d[1]; [MethodImpl(256)] public T Prod(int l, int r) { T sl = op.Identity, sr = op.Identity; l += size; r += size; while (l < r) { if ((l & 1) != 0) sl = op.Operate(sl, d[l++]); if ((r & 1) != 0) sr = op.Operate(d[--r], sr); l >>= 1; r >>= 1; } return op.Operate(sl, sr); } [MethodImpl(256)] public int MaxRight(int l, Predicate f) { Debug.Assert(0 <= l && l <= Length); Debug.Assert(f(op.Identity)); if (l == Length) return Length; l += size; var s = op.Identity; do { while (l % 2 == 0) l >>= 1; if (!f(op.Operate(s, d[l]))) { while (l < size) { l <<= 1; if (f(op.Operate(s, d[l]))) { s = op.Operate(s, d[l]); l++; } } return l - size; } s = op.Operate(s, d[l]); l++; } while ((l & -l) != l); return Length; } [MethodImpl(256)] public int MinLeft(int r, Predicate f) { if (r == 0) return 0; r += size; var s = op.Identity; do { r--; while (r > 1 && (r % 2) != 0) r >>= 1; if (!f(op.Operate(d[r], s))) { while (r < size) { r = (2 * r + 1); if (f(op.Operate(d[r], s))) { s = op.Operate(d[r], s); r--; } } return r + 1 - size; } s = op.Operate(d[r], s); } while ((r & -r) != r); return 0; } } public interface IMonoid : IOperation, IIdentity { } public struct IntMinMonoid : IMonoid { public int Identity => int.MaxValue; public int Operate(int x, int y) => Math.Min(x, y); } public struct IntMaxMonoid : IMonoid { public int Identity => int.MinValue; public int Operate(int x, int y) => Math.Max(x, y); } public struct LongMinMonoid : IMonoid { public long Identity => long.MaxValue; public long Operate(long x, long y) => Math.Min(x, y); } public struct LongMaxMonoid : IMonoid { public long Identity => long.MinValue; public long Operate(long x, long y) => Math.Max(x, y); } public interface IInvertible { T Inverse(T x); } public interface IOperation { T Operate(T x, T y); } public interface IIdentity { T Identity { get; } }