// yuki 1529 Constant Lcm // 2021.8.15 #include #include #include #include typedef long long ll; const int mod = 998244353; #define MAX 1000005 int a[MAX]; ll ans = 1; int ptbl[] = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 0 }; int prime_factor(int *factor, int *power, int n) { int i, d, sz; int *pp; sz = 0; if ((n & 1) == 0) { factor[sz] = 2, power[sz] = 0; do n >>= 1, power[sz]++; while ((n & 1) == 0); sz++; } for (pp = ptbl; n > 1 && *pp > 0; pp++) { if (n % *pp) continue; d = *pp; factor[sz] = d, power[sz] = 0; do n /= d, power[sz]++; while (n % d == 0); sz++; } if (n > 1) { int b = (int)sqrt(n); for (i = 1009; n > 1; i += 2) { if (i > b) { factor[sz] = n, power[sz++] = 1; break; } if (n % i == 0) { factor[sz] = i, power[sz] = 0; do n /= i, power[sz]++; while (n % i == 0); sz++; } } } return sz; } int pow_mod(int x, int p) { int r = 1; while (p) { if (p & 1) r = (ll)r * x % mod; x = (ll)x * x % mod; p >>= 1; } return r; } inline static void mul_pow(int a) { ans = ans * a % mod; } inline static void chmax(int *a, int b) { if (*a < b) *a = b; } int f1[50], p1[50], f2[50], p2[50], w1, w2; void reg() { int i = 0, j = 0; while (i < w1 && j < w2) { if (f1[i] < f2[j]) chmax(a+f1[i], p1[i]), ++i; else if (f1[i] > f2[j]) chmax(a+f2[j], p2[j]), ++j; else chmax(a+f1[i], p1[i]+p2[j]), ++i, ++j; } while (i < w1) chmax(a+f1[i], p1[i]), ++i; while (j < w2) chmax(a+f2[j], p2[j]), ++j; } int main() { int N, i, j; int k; scanf("%d", &N); for (i = 1, j = N-1; i <= j; ++i, --j) { w1 = prime_factor(f1, p1, i); w2 = prime_factor(f2, p2, j); /* printf("i=%d, j=%d\n", i, j); printf("[%d] sz=%d: ", i, w1); for (k = 0; k < w1; ++k) printf("(%d,%d) ", f1[k],p1[k]); printf("\n"); printf(" [%d] sz=%d: ", j, w2); for (k = 0; k < w2; ++k) printf("(%d,%d) ", f2[k],p2[k]); printf("\n"); */ reg(); } if (a[2]) mul_pow(pow_mod(2, a[2])); for (i = 3; i < N; i+=2) if (a[i]) mul_pow(pow_mod(i, a[i])); printf("%d\n", (int)ans); return 0; }