結果

問題 No.1529 Constant Lcm
ユーザー kyaneko999
提出日時 2021-06-04 20:27:00
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 783 ms / 3,000 ms
コード長 3,732 bytes
コンパイル時間 290 ms
コンパイル使用メモリ 82,128 KB
実行使用メモリ 259,336 KB
最終ジャッジ日時 2024-11-19 09:02:48
合計ジャッジ時間 11,021 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
sample AC * 2
other AC * 24
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

import sys
from sys import exit, stdin
from collections import deque, defaultdict
from copy import deepcopy
from bisect import bisect_left, bisect_right, insort_left, insort_right
from heapq import heapify, heappop, heappush
from itertools import product, permutations, combinations, combinations_with_replacement
from functools import reduce
from math import gcd, sin, cos, tan, asin, acos, atan, atan2, degrees, radians, ceil, floor
from math import pi as PI
from random import randint
# from decimal import Decimal
sys.setrecursionlimit(500000)
INF = (1<<61)-1
EPS = 1e-10
# MOD = 10**9+7
MOD = 998244353
def input():
    return stdin.readline()[:-1]
def intput():
    return int(stdin.readline())
def minput():
    return stdin.readline()[:-1].split()
def linput():
    return stdin.readline()[:-1].split()
def mint():
    return map(int,stdin.readline().split())
def lint():
    return list(map(int,stdin.readline().split()))
def ilint():
    return int(stdin.readline()), list(map(int,stdin.readline().split()))
def lcm(x,y):
    return x*y//gcd(x,y)
def lgcd(l):
    return reduce(gcd,l)
def llcm(l):
    return reduce(lcm,l)
def powmod(n,i,mod=MOD):
    return pow(n,mod-1+i,mod) if i<0 else pow(n,i,mod)
def div2(x):
    return x.bit_length()
def div10(x):
    return len(str(x))-(x==0)
def popcount(x):
    return bin(x).count('1')
def digit(x,i,max_len=None):
    s = str(x)
    if max_len:
        i -= max_len-len(s)
    return int(s[i-1]) if i>0 else 0
def digitsum(x):
    ans = 0
    for i in range(div10(x)):
        ans += digit(x,i+1)
    return ans
class counter(defaultdict):
    def __init__(self, *args):
        super().__init__(int)
    def add(self,x,d=1):
        self[x] += d
    def to_list(self):
        l = []
        for x in sorted(self.keys()):
            l.extend([x]*self[x])
        return l
def pf(x,mode='set'):
    C = counter()
    p = 2
    while x>1:
        k = 0
        while x%p==0:
            x //= p
            k += 1
        if k>0:
            C.add(p,k)
        p = p+2-(p==2) if p*p<x else x
    if mode=='counter':
        return C
    S = set([1])
    for k in C:
        T = deepcopy(S)
        for x in T:
            for i in range(1,C[k]+1):
                S.add(x*(k**i))
    if mode=='set':
        return S
    if mode=='list':
        return sorted(S)
def isprime(x):
    if x<2:
        return False
    return len(pf(x,'set'))==2
def matmul(A, B):
    # import numpy
    A1, A2 = A >> 15, A & (1 << 15) - 1
    B1, B2 = B >> 15, B & (1 << 15) - 1
    X = np.dot(A1, B1) % MOD
    Y = np.dot(A2, B2)
    Z = np.dot(A1 + A2, B1 + B2) - X - Y
    return ((X << 30) + (Z << 15) + Y) % MOD
def zash(S):
    lis = sorted(S)
    dic = {}
    for i,x in enumerate(lis):
        dic[x] = i
    return lis, dic
def pr(*x):
    print(x[0],end='') if len(x) else print('')
def lprint(l):
    for x in l:
        print(x)
def ston(c, c0='a'):
    return ord(c)-ord(c0)
def ntos(x, c0='a'):
    return chr(x+ord(c0))
def judge(x, l=['Yes', 'No']):
    print(l[0] if x else l[1])
######################################################
l=[1]*(10**6+1)
P=[]
for x in range(2,10**6+1):
    if l[x]:
        P.append(x)
        tmp=x
        while tmp<=10**6:
            l[tmp]=0
            tmp+=x
N=intput()
ans=1
for p in P:
    if p>=N:
        break
    if p*p>N:
        ans*=p
        ans%=MOD
        if not N%p and N>p:
            ans*=p
            ans%=MOD
        #print(p,1)
        continue
    cnt=[0]*N
    s=p
    while s<N:
        tmp=s
        while tmp<N:
            cnt[tmp]+=1
            tmp+=s
        s*=p
    tmp=0
    for i in range(1,N//2+1):
        tmp=max(tmp,cnt[i]+cnt[N-i])
    ans*=powmod(p,tmp)
    #print(p,tmp)
    ans%=MOD
print(ans)
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