package gioku2020day1; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class L { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(); int[] a = na(n); a = shrink(a); long inv = 0; { int[] ft = new int[n+5]; for(int i = n-1;i >= 0;i--){ inv += sumFenwick(ft, a[i]-1); addFenwick(ft, a[i], 1); } } long rinv = 0; { int[] ft = new int[n+5]; for(int i = 0;i < n;i++){ rinv += sumFenwick(ft, a[i]-1); addFenwick(ft, a[i], 1); } } int mod = 998244353; inv %= mod; rinv %= mod; long u = n; long s2 = u*(u-1)%mod*(u+1)%mod*(3*u+2)%mod*invl(24,mod)%mod; s2 = s2 % mod * invl(u*u%mod, mod) % mod; long S2 = s2; long mul = invl(u*(u-1)%mod, mod); long l = 0; for(int i = 1;i <= n;i++){ l += (long)i*(i-1); } S2 += l%mod*mul; S2 %= mod; int[][] fif = enumFIF(n, mod); long ans = s2*rinv + S2*inv; ans %= mod; for(int i = 1;i <= n;i++){ ans = ans * C(n, i, mod, fif) % mod; } out.println(ans); } public static long C(int n, int r, int mod, int[][] fif) { if (n < 0 || r < 0 || r > n) return 0; return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod; } public static int[][] enumFIF(int n, int mod) { int[] f = new int[n + 1]; int[] invf = new int[n + 1]; f[0] = 1; for (int i = 1; i <= n; i++) { f[i] = (int) ((long) f[i - 1] * i % mod); } long a = f[n]; long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } invf[n] = (int) (p < 0 ? p + mod : p); for (int i = n - 1; i >= 0; i--) { invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod); } return new int[][] { f, invf }; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static int sumFenwick(int[] ft, int i) { int sum = 0; for(i++;i > 0;i -= i&-i)sum += ft[i]; return sum; } public static void addFenwick(int[] ft, int l, int r, int v) { addFenwick(ft, l, v); addFenwick(ft, r, -v); } public static void addFenwick(int[] ft, int i, int v) { if(v == 0 || i < 0)return; int n = ft.length; for(i++;i < n;i += i&-i)ft[i] += v; } public static int[] shrink(int[] a) { int n = a.length; long[] b = new long[n]; for (int i = 0; i < n; i++) b[i] = (long) a[i] << 32 | i; Arrays.sort(b); int[] ret = new int[n]; int p = 0; for (int i = 0; i < n; i++) { if (i > 0 && (b[i] ^ b[i - 1]) >> 32 != 0) p++; ret[(int) b[i]] = p; } return ret; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new L().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }