package contest201127; import java.io.*; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; public class E2 { InputStream is; FastWriter out; String INPUT = ""; public void solve() { int n = ni(); final int mod = 998244353; int[][] fif = enumFIF(n); long[] a = new long[n-1]; for(int i = 1;i <= n-1;i++){ a[i-1] = (long)fif[1][i-1] * i % mod; } // 2n-2 - n long[] b = pow(a, n); out.println(b[n-2] * fif[0][n-2] % mod * invl(pow(n, n-2, mod), mod) % mod); } public static long[] powNaive(long[] a, int K) { int n = a.length; long[] ret = {1}; for(int d = 31-Integer.numberOfLeadingZeros(K);d >= 0;d--) { ret = mul(ret, ret, n); if(K<<~d<0) { ret = mul(ret, a, n); } } return ret; } 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 long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } public static final int mod = 998244353; public static final int G = 3; // only 998244353 public static long[] mul(long[] a, long[] b) { return Arrays.copyOf(convoluteSimply(a, b, mod, 3), a.length+b.length-1); } public static long[] mul(long[] a, long[] b, int lim) { return Arrays.copyOf(convoluteSimply(a, b, mod, 3), lim); } // public static final int mod = 1000000007; // public static long[] mul(long[] a, long[] b) // { // if(Math.max(a.length, b.length) >= 3000){ // return Arrays.copyOf(NTTCRT.convolute(a, b, 3, mod), a.length+b.length-1); // }else{ // return mulnaive(a, b); // } // } // public static long[] mul(long[] a, long[] b, int lim) // { // if(Math.max(a.length, b.length) >= 3000){ // return Arrays.copyOf(NTTCRT.convolute(a, b, 3, mod), lim); // }else{ // return mulnaive(a, b, lim); // } // } public static final long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod; public static long[] mulnaive(long[] a, long[] b) { long[] c = new long[a.length+b.length-1]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length;j++){ c[i+j] += a[i]*b[j]; if(c[i+j] >= big)c[i+j] -= big; } } for(int i = 0;i < c.length;i++)c[i] %= mod; return c; } public static long[] mulnaive(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length && i+j < lim;j++){ c[i+j] += a[i]*b[j]; if(c[i+j] >= big)c[i+j] -= big; } } for(int i = 0;i < c.length;i++)c[i] %= mod; return c; } public static long[] mul_(long[] a, long k) { for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod; return a; } public static long[] mul(long[] a, long k) { a = Arrays.copyOf(a, a.length); for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod; return a; } public static long[] add(long[] a, long[] b) { long[] c = new long[Math.max(a.length, b.length)]; for(int i = 0;i < a.length;i++)c[i] += a[i]; for(int i = 0;i < b.length;i++)c[i] += b[i]; for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod; return c; } public static long[] add(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i]; for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i]; for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod; return c; } public static long[] sub(long[] a, long[] b) { long[] c = new long[Math.max(a.length, b.length)]; for(int i = 0;i < a.length;i++)c[i] += a[i]; for(int i = 0;i < b.length;i++)c[i] -= b[i]; for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod; return c; } public static long[] sub(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i]; for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i]; for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod; return c; } // F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x) // if want p-destructive, comment out flipping p just before returning. public static long[] inv(long[] p) { int n = p.length; long[] f = {invl(p[0], mod)}; for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } for(int i = 1;i < 2*n;i*=2){ long[] f2 = mul(f, f, Math.min(n, 2*i)); long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i)); for(int j = 0;j < f.length;j++){ f2p[j] += 2L*f[j]; if(f2p[j] >= mod)f2p[j] -= mod; if(f2p[j] >= mod)f2p[j] -= mod; } f = f2p; } for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } return f; } // differentiate public static long[] d(long[] p) { long[] q = new long[p.length]; for(int i = 0;i < p.length-1;i++){ q[i] = p[i+1] * (i+1) % mod; } return q; } // integrate public static long[] i(long[] p) { long[] q = new long[p.length]; for(int i = 0;i < p.length-1;i++){ q[i+1] = p[i] * invl(i+1, mod) % mod; } return q; } static long[] exp(long[] a) { return exp(a, a.length); } /** * https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf * @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series * @param a * @param lim * @return */ static long[] exp(long[] a, int lim) { long[] F = {1L}; long[] G = {1L}; long[] da = d(a); for(int m = 1;;m *= 2) { long[] G2 = mul(G, G, m); G = sub(mul_(G, 2), mul(F, G2, m)); long[] Q = Arrays.copyOf(da, m-1); long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m-1))); F = mul(F, add(new long[] {1}, sub(Arrays.copyOf(a, m), i(W))), m); if(m >= lim)break; } return Arrays.copyOf(F, lim); } // // // F_{t+1}(x) = F_t(x)-(ln F_t(x) - P(x)) * F_t(x) // public static long[] exp(long[] p) // { // int n = p.length; // long[] f = {p[0]}; // for(int i = 1;i < 2*n;i*=2){ // long[] ii = ln(f); // long[] sub = sub(ii, p, Math.min(n, 2*i)); // if(--sub[0] < 0)sub[0] += mod; // for(int j = 0;j < 2*i && j < n;j++){ // sub[j] = mod-sub[j]; // if(sub[j] == mod)sub[j] = 0; // } // f = mul(sub, f, Math.min(n, 2*i)); //// f = sub(f, mul(sub(ii, p, 2*i), f, 2*i)); // } // return f; // } // \int f'(x)/f(x) dx public static long[] ln(long[] f) { return i(mul(d(f), inv(f))); } // ln F(x) - k ln P(x) = 0 public static long[] pow(long[] p, long K) { int n = p.length; int tz = trailingZeros(p); if((long)tz*K >= n)return new long[n]; long[] pa = Arrays.copyOfRange(p, tz, n); int m = pa.length; // pa[0] must be 1 long base = pa[0]; long scale = invl(base, mod); for(int i = 0;i < m;i++)pa[i] = pa[i] * scale % mod; long[] lnp = Arrays.copyOf(ln(pa), m); for(int i = 0;i < m;i++)lnp[i] = lnp[i] * K % mod; long[] reta = exp(lnp); long kscale = pow(base, K, mod); for(int i = 0;i < m;i++)reta[i] = reta[i] * kscale % mod; long[] ret = new long[n]; System.arraycopy(reta, 0, ret, (int)(tz*K), (int)(n-tz*K)); return ret; } public static int trailingZeros(long[] a) { int ret = 0; for(long v : a) { if(v == 0) { ret++; }else { break; } } return ret; } public static long[] convoluteSimply(long[] a, long[] b, int P, int g) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2); long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i]%P; } return nttmb(fa, m, true, P, g); } // static int[] wws = new int[270000]; // outer faster // Modifed Montgomery + Barrett private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; int[] wws = new int[1<= 2*P)dst[s] -= 2*P; // long Q = (u&(1L<<32)-1)*J&(1L<<32)-1; long Q = (u<<32)*J>>>32; dst[t] = (u>>>32)-(Q*P>>>32)+P; } } if(i < h-1){ for(int k = 0;k < 1<= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P); } return dst; } // Modified Shoup + Barrett private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P); long[] wws = new long[1<= 2*P)ndsts -= 2*P; long T = dst[s] - dst[t] + 2*P; long Q = wws[k]*T>>>32; dst[s] = ndsts; dst[t] = ws[k]*T-Q*P&(1L<<32)-1; } } // dw = dw * dw % P; if(i < h-1){ for(int k = 0;k < 1<= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++){ dst[i] = modh(dst[i] * in, M, H, P); } } return dst; } static final long mask = (1L<<31)-1; public static long modh(long a, long M, int h, int mod) { long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod; return r < mod ? r : r-mod; } private static long[] garnerPrepare(int[] m) { int n = m.length; assert n == m.length; if(n == 0)return new long[0]; long[] gamma = new long[n]; for(int k = 1;k < n;k++){ long prod = 1; for(int i = 0;i < k;i++){ prod = prod * m[i] % m[k]; } gamma[k] = invl(prod, m[k]); } return gamma; } private static long[] garnerBatch(int[] u, int[] m, long[] gamma) { int n = u.length; assert n == m.length; long[] v = new long[n]; v[0] = u[0]; for(int k = 1;k < n;k++){ long temp = v[k-1]; for(int j = k-2;j >= 0;j--){ temp = (temp * m[j] + v[j]) % m[k]; } v[k] = (u[k] - temp) * gamma[k] % m[k]; if(v[k] < 0)v[k] += m[k]; } return v; } public static int[][] enumFIF(int n) { 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 void main(String[] args) { new E2().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-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(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){ 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 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[] 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 int ni() { int num = 0, 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 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(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln(); return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }