namespace AtCoder; #nullable enable using System.Numerics; using System.Text; readonly record struct ModInt : IEqualityOperators, IAdditiveIdentity, IAdditionOperators, IUnaryNegationOperators, ISubtractionOperators, IMultiplicativeIdentity, IMultiplyOperators, IDivisionOperators { int V { get; init; } public const int Mod = 998244353; public ModInt(long value) { var v = value % Mod; if (v < 0) v += Mod; V = (int)v; } ModInt(int value) { V = value; } public static implicit operator ModInt(long v) => new(v); public static implicit operator int(ModInt modInt) => modInt.V; public static ModInt operator +(ModInt a, ModInt b) { var v = a.V + b.V; if (v >= Mod) v -= Mod; return new(v); } public static ModInt operator -(ModInt a) => new(a.V == 0 ? 0 : Mod - a.V); public static ModInt operator -(ModInt a, ModInt b) { var v = a.V - b.V; if (v < 0) v += Mod; return new(v); } public static ModInt operator *(ModInt a, ModInt b) => new((int)((long)a.V * b.V % Mod)); public static ModInt operator /(ModInt a, ModInt b) { if (b == 0) throw new DivideByZeroException(); var (d, x, _) = ExtendedGcd(b.V, Mod); if (d > 1) throw new DivideByZeroException(); return x * a.V; } public ModInt Power(long p) { if (p < 0) return (MultiplicativeIdentity / V).Power(-p); long res = 1; long k = V; while (p > 0) { if ((p & 1) > 0) res = res * k % Mod; k = k * k % Mod; p >>= 1; } return res; } static (long d, long x, long y) ExtendedGcd(long a, long b) { if (b == 0) return (a, 1, 0); var (d, x, y) = ExtendedGcd(b, a % b); return (d, y, x - a / b * y); } public static ModInt AdditiveIdentity => new(0); public static ModInt MultiplicativeIdentity => new(1); public override string ToString() => V.ToString(); } static class FactorialExtensions { static ModInt[] fac = Array.Empty(); static ModInt[] inv = Array.Empty(); const uint Capacity = 1 << 24; static void Resize(uint n) { if (n < fac.Length) return; var s = 1; while (s < n && s < Capacity) s <<= 1; fac = new ModInt[s + 1]; fac[0] = 1; for (var i = 1; i <= s; i++) fac[i] = fac[i - 1] * i; inv = new ModInt[s + 1]; inv[s] = fac[0] / fac[s]; for (var i = s; i > 0; i--) inv[i - 1] = inv[i] * i; } public static ModInt Factorial(this int n) { Resize((uint)Math.Abs(n)); return n < 0 ? inv[-n] : fac[n]; } public static ModInt C(this int n, int r) { if (r < 0 || n < r) return 0; if (n <= Capacity) return Factorial(n) * Factorial(r - n) * Factorial(-r); if (n - r < r) return C(n, n - r); var res = fac[0]; for (var i = n; i > n - r; i--) res *= i; return res * Factorial(-r); } public static ModInt P(this int n, int r) => C(n, r) * Factorial(-r); public static ModInt H(this int n, int r) => C(n + r - 1, r); } abstract class SegmentTree { public interface IOperator { TMonoid IdentityElement { get; } TMonoid Operation(TMonoid x, TMonoid y); } public interface IBinarySearchOperator { bool F(TMonoid value); } public class Body where TOperator : struct, IOperator { public int BaseSize { get; init; } protected int Height { get; init; } protected TOperator Op { get; init; } protected TMonoid[] Values { get; init; } public Body(TMonoid[] initial, TOperator op = default) { Op = op; (BaseSize, Height) = (1, 0); while (BaseSize < initial.Length) (BaseSize, Height) = (BaseSize << 1, Height + 1); var size = BaseSize << 1; Values = new TMonoid[size]; for (var i = 0; i < size; i++) Values[i] = op.IdentityElement; for (var i = 0; i < initial.Length; i++) Values[i + BaseSize] = initial[i]; for (var i = BaseSize - 1; i > 0; i--) Update(i); } public TMonoid Product(int l, int r) { (l, r) = (l + BaseSize, r + BaseSize); var (resL, resR) = (Op.IdentityElement, Op.IdentityElement); while (l < r) { if ((l & 1) == 1) resL = Op.Operation(resL, Values[l++]); if ((r & 1) == 1) resR = Op.Operation(Values[--r], resR); (l, r) = (l >> 1, r >> 1); } return Op.Operation(resL, resR); } public void Set(int index, TMonoid value) { var j = index + BaseSize; Values[j] = value; for (var i = 1; i <= Height; i++) Update(j >> i); } // the result might be greater than n public int MinIndex(TMinIndexOperator op = default) where TMinIndexOperator : struct, IBinarySearchOperator { if (!op.F(Values[1])) return BaseSize + 1; var product = Op.IdentityElement; var (res, w, i) = (0, BaseSize, 1); while (w > 0) { var p = Op.Operation(product, Values[i]); if (!op.F(p)) { res += w; i++; product = p; } w >>= 1; i <<= 1; } return res + 1; } protected void Update(int k) { Values[k] = Op.Operation(Values[k << 1], Values[(k << 1) + 1]); } } } struct Op : SegmentTree.IOperator { public int IdentityElement => 0; public int Operation(int x, int y) => x + y; } static class Extensions { public static T[] Repeat(this int time, Func F) => Enumerable.Range(0, time).Select(_ => F()).ToArray(); } class AtCoder { object? Solve() { var n = Int(); var q = new int[n]; for (var i = 0; i < n; i++) { var x = Int() - 1; q[x] = i; } var t0 = new SegmentTree.Body(n.Repeat(() => 0)); var t1 = new SegmentTree.Body(n.Repeat(() => 1)); ModInt ans = 0; for (var i = 0; i < n; i++) { var k = q[i]; ModInt bns = 1; for (var j = 0; j < 2; j++) { var x = t0.Product(0, k); var y = t1.Product(k + 1, n); var s = x + y; bns *= s.Factorial() / (x.Factorial() * y.Factorial()); (t0, t1) = (t1, t0); } ans += bns; t0.Set(k, 1); t1.Set(k, 0); } return ans; } public static void Main() => new AtCoder().Run(); public void Run() { var res = Solve(); if (res != null) { if (res is bool yes) res = yes ? "Yes" : "No"; sw.WriteLine(res); } sw.Flush(); } string[] input = Array.Empty(); int iter = 0; readonly StreamWriter sw = new(Console.OpenStandardOutput()) { AutoFlush = false }; #pragma warning disable IDE0051 string String() { while (iter >= input.Length) (input, iter) = (Console.ReadLine()!.Split(' '), 0); return input[iter++]; } T Input() where T : IParsable => T.Parse(String(), null); int Int() => Input(); void Out(object? x, string? separator = null) { separator ??= Environment.NewLine; if (x is System.Collections.IEnumerable obj and not string) { var firstLine = true; foreach (var item in obj) { if (!firstLine) sw.Write(separator); firstLine = false; sw.Write(item); } } else sw.Write(x); sw.WriteLine(); } #pragma warning restore IDE0051 }