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 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(); } int[] len; static ModInt[] pow; void Solve() { int n = ri; var a = new long[n]; len = new int[n]; pow = new ModInt[n]; for (int i = 0; i < n; i++) { a[i] = rl; long t = a[i]; pow[i] = 1; while (t > 0) { len[i]++; t /= 10; pow[i] *= 10; } } var powinv = new ModInt[100]; powinv[powinv.Length - 1] = new ModInt(10).Pow(powinv.Length - 1).Inv(); for (int i = powinv.Length - 1; i > 0; i--) powinv[i - 1] = powinv[i] * 10; var dp = new ReRootingDP(n); var g = new List[n]; for (int i = 0; i < n; i++) g[i] = new List(); for (int i = 0; i < n - 1; i++) { int u = ri - 1, v = ri - 1; dp.AddEdge(u, v); g[u].Add(v); g[v].Add(u); } dp.Calc(); ModInt ans = 0; for (int i = 0; i < n; i++) { foreach (var j in g[i]) { var t = dp[i, j]; ans += (n - t.count) * a[i] * t.sum * powinv[len[i]]; } ans += a[i] * dp[i].sum * powinv[len[i]]; } Write(ans); } struct T { public int count; public ModInt sum; public T(int cnt, ModInt sm) { count = cnt; sum = sm; } } struct S { public int count; public ModInt sum; public S(int cnt, ModInt sm) { count = cnt; sum = sm; } } struct Op : IReRootingDPOperator { public S SIdentity => new S(0, 0); public S TtoS(T t) => new S(t.count, t.sum); public S Merge(S x, S y) => new S(x.count + y.count, x.sum + y.sum); public T AddRoot(int i, int j, S x) => new T(x.count + 1, (x.sum + 1) * pow[i]); } const long INF = 1L << 60; int ri { get { return (int)sc.Integer(); } } long rl { get { return sc.Integer(); } } ulong rul { get { return sc.UInteger(); } } double rd { get { return sc.Double(); } } string rs { get { return sc.Scan(); } } string rline { get { return sc.Line(); } } public StreamScanner sc = new StreamScanner(Console.OpenStandardInput()); [MethodImpl(MethodImplOptions.AggressiveInlining)] T[] RepArray(T t, int count) => Enumerable.Repeat(t, count).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] void WriteJoin(string s, IEnumerable t) => Console.WriteLine(string.Join(s, t)); [MethodImpl(MethodImplOptions.AggressiveInlining)] void WriteMat(T[,] a) { int sz1 = a.GetLength(0); int sz2 = a.GetLength(1); for (int i = 0; i < sz1; i++) { var s = new List(); for (int j = 0; j < sz2; j++) s.Add(a[i, j].ToString()); WriteJoin(" ", s); } } [MethodImpl(MethodImplOptions.AggressiveInlining)] void Write(object t) => Console.WriteLine(t.ToString()); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Write(string str) => Console.WriteLine(str); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Write(string str, object arg1) => Console.WriteLine(str, arg1); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Write(string str, object arg1, object arg2) => Console.WriteLine(str, arg1, arg2); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Write(string str, object arg1, object arg2, object arg3) => Console.WriteLine(str, arg1, arg2, arg3); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Write(string str, params object[] arg) => Console.WriteLine(str, arg); [MethodImpl(MethodImplOptions.AggressiveInlining)] void WriteFlush(object t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] void WriteError(object t) => Console.Error.WriteLine(t.ToString()); [MethodImpl(MethodImplOptions.AggressiveInlining)] void YN(bool t) => Console.WriteLine(t ? "YES" : "NO"); [MethodImpl(MethodImplOptions.AggressiveInlining)] void Yn(bool t) => Console.WriteLine(t ? "Yes" : "No"); [MethodImpl(MethodImplOptions.AggressiveInlining)] void yn(bool t) => Console.WriteLine(t ? "yes" : "no"); } 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>, IFormattable 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) => lhs * rhs.Inv(); [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() { var (x, y, g) = ExtGcd(_v, op.Mod); return new StaticModInt(x); } [MethodImpl(256)] static (long x, long y, long g) ExtGcd(long a, long b) { if (b == 0) return a >= 0 ? (1, 0, a) : (-1, 0, -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)] 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 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(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 long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b); [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; } public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => t - val, l, r); public static int LowerBound(T[] arr, Func comp, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), comp, l, r); 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(MethodImplOptions.AggressiveInlining)] 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(MethodImplOptions.AggressiveInlining)] 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; } } 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++]; } public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } public string Line() { var sb = new StringBuilder(); for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b); return sb.ToString(); } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } 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'; } } 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'; } } public double Double() { return double.Parse(Scan()); } } interface IReRootingDPOperator { S SIdentity { get; } S TtoS(T t); S Merge(S x, S y); T AddRoot(int i, int j, S x); } class ReRootingDP where Op : IReRootingDPOperator { int n; Op op = default; List[] edges; T[] ans; Dictionary[] dp; public T this[int i, int j] { get => dp[i][j]; } public T this[int i] { get => ans[i]; } public ReRootingDP(int _n) { n = _n; edges = new List[n]; for (int i = 0; i < n; i++) edges[i] = new List(); } public void AddEdge(int u, int v) { edges[u].Add(v); edges[v].Add(u); } public void Calc() { dp = new Dictionary[n]; for (int i = 0; i < n; i++) dp[i] = new Dictionary(); seen = new bool[n]; for (int i = 0; i < n; i++) if (!seen[i]) DFS1(i); seen = new bool[n]; for (int i = 0; i < n; i++) if (!seen[i]) DFS2(i); ans = new T[n]; for (int i = 0; i < n; i++) ans[i] = dp[i][-1]; } bool[] seen; private void DFS1(int x, int p = -1) { seen[x] = true; S val = op.SIdentity; foreach (var y in edges[x]) { if (y == p) continue; DFS1(y, x); val = op.Merge(val, op.TtoS(dp[y][x])); } dp[x].Add(p, op.AddRoot(x, p, val)); } private void DFS2(int x, int p = -1) { seen[x] = true; int deg = edges[x].Count; var dp_r = new S[deg + 1]; dp_r[deg] = op.SIdentity; for (int i = deg - 1; i >= 0; i--) dp_r[i] = op.Merge(dp_r[i + 1], op.TtoS(dp[edges[x][i]][x])); if (p != -1) dp[x].Add(-1, op.AddRoot(x, -1, dp_r[0])); S sum_l = op.SIdentity; for (int i = 0; i < deg; i++) { int y = edges[x][i]; if (y != p) { dp[x].Add(y, op.AddRoot(x, y, op.Merge(sum_l, dp_r[i + 1]))); DFS2(y, x); } sum_l = op.Merge(sum_l, op.TtoS(dp[edges[x][i]][x])); } } }