/* -*- coding: utf-8 -*- * * 1529.cc: No.1529 Constant Lcm - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_P = 1000000; const int MOD = 998244353; /* typedef */ typedef long long ll; typedef pair pii; typedef vector vi; typedef vector vpii; /* global variables */ bool primes[MAX_P + 1]; vpii pds[MAX_P]; int es[MAX_P]; /* subroutines */ int gen_primes(int maxp, vi &pnums) { memset(primes, true, sizeof(primes)); primes[0] = primes[1] = false; int p; for (p = 2; p * p <= maxp; p++) if (primes[p]) { pnums.push_back(p); for (int q = p * p; q <= maxp; q += p) primes[q] = false; } for (; p <= maxp; p++) if (primes[p]) pnums.push_back(p); return (int)pnums.size(); } bool prime_decomp(int n, vi &pnums, vpii& pds) { pds.clear(); int pn = pnums.size(); for (int i = 0; i < pn; i++) { int pi = pnums[i]; if (pi * pi > n) { if (n > 1) { int k = lower_bound(pnums.begin(), pnums.end(), n) - pnums.begin(); pds.push_back(pii(k, 1)); } return true; } if (n % pi == 0) { int fi = 0; while (n % pi == 0) n /= pi, fi++; pds.push_back(pii(i, fi)); } } return false; } int powmod(int a, int n) { // a^n % MOD int pm = 1; while (n > 0) { if (n & 1) pm = (ll)pm * a % MOD; a = (ll)a * a % MOD; n >>= 1; } return pm; } inline void setmax(int &a, int b) { if (a < b) a = b; } /* main */ int main() { vi pnums; int pn = gen_primes(MAX_P, pnums); //printf("pn=%d\n", pn); int n; scanf("%d", &n); for (int i = 2; i < n; i++) prime_decomp(i, pnums, pds[i]); for (int i = 1; i < n; i++) { vpii &pd0 = pds[i], &pd1 = pds[n - i]; int m0 = pd0.size(), m1 = pd1.size(); int i0 = 0, i1 = 0; while (i0 < m0 && i1 < m1) { if (pd0[i0].first < pd1[i1].first) { setmax(es[pd0[i0].first], pd0[i0].second); i0++; } else if (pd0[i0].first > pd1[i1].first) { setmax(es[pd1[i1].first], pd1[i1].second); i1++; } else { setmax(es[pd0[i0].first], pd0[i0].second + pd1[i1].second); i0++, i1++; } } while (i0 < m0) { setmax(es[pd0[i0].first], pd0[i0].second); i0++; } while (i1 < m1) { setmax(es[pd1[i1].first], pd1[i1].second); i1++; } } int p = 1; for (int i = 0; i < pn; i++) if (es[i] > 0) p = (ll)p * powmod(pnums[i], es[i]) % MOD; printf("%d\n", p); return 0; }