class PrimeFactor(): def __init__(self, n): """ エラトステネス O(N loglog N) """ self.n = n self.table = list(range(n+1)) # 最小素因数のリスト self.table[2::2] = [2]*(n//2) for p in range(3, int(n**0.5) + 2, 2): if self.table[p] == p: for q in range(p * p, n + 1, 2 * p): if self.table[q] == q: self.table[q] = p def is_prime(self, x): """ 素数判定 O(1) """ if x < 2: return False return self.table[x] == x def prime_factors(self, x): """ 素因数分解 O(logN) (試し割りだとO(sqrt(N))) """ res = [] if x < 2: return res while self.table[x] != 1: res.append(self.table[x]) x //= self.table[x] return res def divisors(self, x): """ 約数列挙 x=[1,10**6]の約数全列挙も間に合う """ primes=self.prime_counter(x) P=set([1]) for key, value in primes.items(): Q=[] for p in P: for k in range(value+1): Q.append(p*pow(key,k)) P|=set(Q) P = list(P) P.sort() return P def prime_counter(self, x): """ 素因数分解(個数のリスト) O(logN) {素因数: 個数} の形で返す """ res = dict() if x < 2: return res while self.table[x] != 1: res[self.table[x]] = res.get(self.table[x], 0) + 1 x //= self.table[x] return res def divisors_counter(self, x): """ 約数の個数 O((logN)^2) """ res = 1 for value in self.prime_counter(x).values(): res *= (value+1) return res def prime_gcd(self,X,MOD=None): """ n個の最大公約数 X:n個のリスト (O((logN)^2)) """ exponents = self.prime_counter(X[0]) for x in X[1:]: Y = self.prime_counter(x) for prime, exp in exponents.items(): if Y[prime] < exp: exponents[prime] = Y[prime] res = 1 for prime, exp in exponents.items(): res *= pow(prime,exp,MOD) if MOD == None: return res else: return res%MOD def prime_lcm(self,X,MOD=None): """ n個の最小公倍数 X:n個のリスト (O((logN)^2)) """ exponents = dict() for x in X: for prime, exp in self.prime_counter(x).items(): if exp > exponents.get(prime, 0): exponents[prime] = exp res = 1 for prime, exp in exponents.items(): res *= pow(prime,exp,MOD) if MOD == None: return res else: return res%MOD ##################################################################################################### import sys input = sys.stdin.readline from math import gcd MOD=998244353 N=int(input()) PF = PrimeFactor(N) flg=0 P=[] for i in range(1,N+1)[::-1]: if PF.is_prime(i) and flg==0: flg=1 elif PF.is_prime(i): P.append(i) res=1 for p in P: n=p while n<=N: res*=p res%=MOD n*=p print(res)