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 Main { InputStream is; PrintWriter out; String INPUT = ""; public static int mod = 1012924417; static int[][] fif = enumFIF(2200005, mod); void solve() { int N = ni(); long[] cos0 = new long[N / 2 + 5]; long[] sin0 = new long[N / 2 + 5]; for (int i = 0; i < cos0.length; i++) { cos0[i] = (long) fif[1][2 * i] * (i % 2 == 0 ? 1 : mod - 1) % mod; } for (int i = 0; i < sin0.length; i++) { sin0[i] = (long) fif[1][2 * i + 1] * (i % 2 == 0 ? 1 : mod - 1) % mod; } cos0 = inv(cos0); sin0 = convolute(sin0, cos0, 3, mod); long[] ret = new long[N + 1]; for (int i = 0; i < sin0.length && 2 * i + 1 < ret.length; ++i) { ret[2 * i + 1] = sin0[i]; } for (int i = 0; i < cos0.length && 2 * i < ret.length; ++i) { ret[2 * i] += cos0[i]; ret[2 * i] %= mod; } out.println(2 * ret[N] * fif[0][N] % mod); } public static long[] mul(long[] a, long[] b) { if (Math.max(a.length, b.length) >= 3000) { return Arrays.copyOf(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(convolute(a, b, 3, mod), lim); } else { return mulnaive(a, b, lim); } } public static long[] mulnaive(long[] a, long[] b) { long[] c = new long[a.length + b.length - 1]; long big = 8L * mod * mod; 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]; long big = 8L * mod * mod; 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) { long[] ret = i(mul(d(f), inv(f))); ret[0] = f[0]; return ret; } // ln F(x) - k ln P(x) = 0 public static long[] pow(long[] p, int K) { int n = p.length; long[] lnp = ln(p); for (int i = 1; i < lnp.length; i++) lnp[i] = lnp[i] * K % mod; lnp[0] = pow(p[0], K, mod); // go well for some reason return exp(Arrays.copyOf(lnp, n)); } // destructive public static long[] divf(long[] a, int[][] fif) { for (int i = 0; i < a.length; i++) a[i] = a[i] * fif[1][i] % mod; return a; } // destructive public static long[] mulf(long[] a, int[][] fif) { for (int i = 0; i < a.length; i++) a[i] = a[i] * fif[0][i] % mod; return a; } public static long[] transformExponentially(long[] a, int[][] fif) { return mulf(exp(divf(Arrays.copyOf(a, a.length), fif)), fif); } public static long[] transformLogarithmically(long[] a, int[][] fif) { return mulf(Arrays.copyOf(ln(divf(Arrays.copyOf(a, a.length), fif)), a.length), fif); } // 1/(1-F)-1 static long[] transformInvertly(long[] a) { long[] b = new long[a.length]; for (int i = 0; i < a.length; i++) { b[i] = mod - a[i]; if (b[i] == mod) b[i] = 0; } if (++b[0] == mod) b[0] = 0; long[] ret = inv(b); if (--ret[0] < 0) ret[0] += mod; return ret; } // -1/(1+F)+1 static long[] transformInverseOfInvertly(long[] a) { long[] b = new long[a.length]; for (int i = 0; i < a.length; i++) { b[i] = a[i]; } if (++b[0] == mod) b[0] = 0; long[] ret = inv(b); for (int i = 0; i < a.length; i++) { ret[i] = mod - ret[i]; if (ret[i] == mod) ret[i] = 0; } if (++ret[0] == mod) ret[0] = 0; return ret; } public static long[] reverse(long[] p) { long[] ret = new long[p.length]; for (int i = 0; i < p.length; i++) { ret[i] = p[p.length - 1 - i]; } return ret; } public static long[] reverse(long[] p, int lim) { long[] ret = new long[lim]; for (int i = 0; i < lim && i < p.length; i++) { ret[i] = p[p.length - 1 - i]; } return ret; } // [quotient, remainder] // remainder can be empty. // // deg(f)=n, deg(g)=m, f=gq+r, f=gq+r. // f* = x^n*f(1/x), // t=g*^-1 mod x^(n-m+1), q=(tf* mod x^(n-m+1))* public static long[][] div(long[] f, long[] g) { int n = f.length, m = g.length; if (n < m) return new long[][] { new long[0], Arrays.copyOf(f, n) }; long[] rf = reverse(f, n - m + 1); long[] rg = reverse(g, n - m + 1); long[] rq = mul(rf, inv(rg), n - m + 1); long[] q = reverse(rq, n - m + 1); long[] r = sub(f, mul(q, g, m - 1), m - 1); return new long[][] { q, r }; } // public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681}; // public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17}; public static final int[] NTTPrimes = { 1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033 }; public static final int[] NTTPrimitiveRoots = { 5, 3, 3, 3, 17, 7, 7, 7, 3, 5 }; 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); } public static long[] convolute(long[] a, long[] b) { int USE = 2; int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2); long[][] fs = new long[USE][]; for (int k = 0; k < USE; k++) { int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; 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; } fs[k] = nttmb(fa, m, true, P, g); } int[] mods = Arrays.copyOf(NTTPrimes, USE); long[] gammas = garnerPrepare(mods); int[] buf = new int[USE]; for (int i = 0; i < fs[0].length; i++) { for (int j = 0; j < USE; j++) buf[j] = (int) fs[j][i]; long[] res = garnerBatch(buf, mods, gammas); long ret = 0; for (int j = res.length - 1; j >= 0; j--) ret = ret * mods[j] + res[j]; fs[0][i] = ret; } return fs[0]; } public static long[] convolute(long[] a, long[] b, int USE, int mod) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2); long[][] fs = new long[USE][]; for (int k = 0; k < USE; k++) { int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; 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; } fs[k] = nttmb(fa, m, true, P, g); } int[] mods = Arrays.copyOf(NTTPrimes, USE); long[] gammas = garnerPrepare(mods); int[] buf = new int[USE]; for (int i = 0; i < fs[0].length; i++) { for (int j = 0; j < USE; j++) buf[j] = (int) fs[j][i]; long[] res = garnerBatch(buf, mods, gammas); long ret = 0; for (int j = res.length - 1; j >= 0; j--) ret = (ret * mods[j] + res[j]) % mod; fs[0][i] = ret; } return fs[0]; } // 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 << h - 1]; long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P); long w = (1L << 32) % P; for (int k = 0; k < 1 << h - 1; k++) { wws[k] = (int) w; w = modh(w * dw, M, H, P); } long J = invl(P, 1L << 32); for (int i = 0; i < h; i++) { for (int j = 0; j < 1 << i; j++) { for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++, s++, t++) { long u = (dst[s] - dst[t] + 2 * P) * wws[k]; dst[s] += dst[t]; if (dst[s] >= 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 << h - i - 2; k++) wws[k] = wws[k * 2]; } } for (int i = 0; i < n; i++) { if (dst[i] >= 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 << h - 1]; long[] ws = new long[1 << h - 1]; long w = 1; for (int k = 0; k < 1 << h - 1; k++) { wws[k] = (w << 32) / P; ws[k] = w; w = modh(w * dw, M, H, P); } for (int i = 0; i < h; i++) { for (int j = 0; j < 1 << i; j++) { for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++, s++, t++) { long ndsts = dst[s] + dst[t]; if (ndsts >= 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 << h - i - 2; k++) { wws[k] = wws[k * 2]; ws[k] = ws[k * 2]; } } } for (int i = 0; i < n; i++) { if (dst[i] >= 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; } private 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; } private 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 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 }; } 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 Main().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)); } }