結果

問題 No.856 増える演算
ユーザー vwxyz
提出日時 2024-04-08 06:32:15
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,830 ms / 3,153 ms
コード長 3,767 bytes
コンパイル時間 402 ms
コンパイル使用メモリ 82,388 KB
実行使用メモリ 306,500 KB
最終ジャッジ日時 2024-10-01 04:53:55
合計ジャッジ時間 59,033 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 80
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

def FFT(polynomial0,polynomial1,digit=10**5,round_to_int=True):
    assert digit==0 or round_to_int
    if len(polynomial0)*len(polynomial1)<=60:
        polynomial=[0]*(len(polynomial0)+len(polynomial1)-1)
        for i in range(len(polynomial0)):
            for j in range(len(polynomial1)):
                polynomial[i+j]+=polynomial0[i]*polynomial1[j]
        return polynomial
    def DFT(polynomial,n,inverse=False):
        if inverse:
            primitive_root=[math.cos(-i*2*math.pi/(1<<n))+math.sin(-i*2*math.pi/(1<<n))*1j for i in range(1<<n)]
        else:
            primitive_root=[math.cos(i*2*math.pi/(1<<n))+math.sin(i*2*math.pi/(1<<n))*1j for i in range(1<<n)]
        if inverse:
            for bit in range(1,n+1):
                a=1<<bit-1
                for i in range(1<<n-bit):
                    for j in range(a):
                        s=i*2*a+j
                        t=s+a
                        polynomial[s],polynomial[t]=polynomial[s]+polynomial[t]*primitive_root[j<<n-bit],polynomial[s]-polynomial[t]*primitive_root[j
                            <<n-bit]
        else:
            for bit in range(n,0,-1):
                a=1<<bit-1
                for i in range(1<<n-bit):
                    for j in range(a):
                        s=i*2*a+j
                        t=s+a
                        polynomial[s],polynomial[t]=polynomial[s]+polynomial[t],primitive_root[j<<n-bit]*(polynomial[s]-polynomial[t])
    def FFT_(polynomial0,polynomial1,round_to_int=True):
        N0=len(polynomial0)
        N1=len(polynomial1)
        N=N0+N1-1
        n=(N-1).bit_length()
        polynomial0=polynomial0+[0]*((1<<n)-N0)
        polynomial1=polynomial1+[0]*((1<<n)-N1)
        DFT(polynomial0,n)
        DFT(polynomial1,n)
        fft=[x*y for x,y in zip(polynomial0,polynomial1)]
        DFT(fft,n,inverse=True)
        if round_to_int:
            fft=[round((fft[i]/(1<<n)).real) for i in range(N)]
        else:
            fft=[(fft[i]/(1<<n)).real for i in range(N)]
        return fft
    if digit:
        N0=len(polynomial0)
        N1=len(polynomial1)
        N=N0+N1-1
        polynomial00,polynomial01=[None]*N0,[None]*N0
        polynomial10,polynomial11=[None]*N1,[None]*N1
        for i in range(N0):
            polynomial00[i],polynomial01[i]=divmod(polynomial0[i],digit)
        for i in range(N1):
            polynomial10[i],polynomial11[i]=divmod(polynomial1[i],digit)
        polynomial=[0]*N
        for i,x in enumerate(FFT_(polynomial00,polynomial10)):
            polynomial[i]+=x*(digit**2-digit)
        for i,x in enumerate(FFT_(polynomial01,polynomial11)):
            polynomial[i]-=x*(digit-1)
        for i,x in enumerate(FFT_([x1+x2 for x1,x2 in zip(polynomial00,polynomial01)],[x1+x2 for x1,x2 in zip(polynomial10,polynomial11)])):
            polynomial[i]+=x*digit
    else:
        polynomial=FFT_(polynomial0,polynomial1,round_to_int=round_to_int)
    return polynomial
import math
import sys
#sys.set_int_max_str_digits(10**7)
N=int(input())
mod=998244353
A=list(map(int,input().split()))
max_A=max(A)
cnt=[0]*(max_A+1)
for a in A:
    cnt[a]+=1
cnt=FFT(cnt,cnt)
mod=10**9+7
M=1
prod_A=1
for a in A:
    prod_A*=a
    prod_A%=mod
for a in A:
    cnt[a*2]-=1
ans=1
for a in range(1,max_A*2+1):
    ans*=pow(a,cnt[a]//2,mod)
    ans%=mod
cumsum=[0]+A
for i in range(1,N+1):
    cumsum[i]+=cumsum[i-1]
for i in range(N):
    ans*=pow(A[i],cumsum[N]-cumsum[i+1],mod)
    ans%=mod
j=A.index(min(A))
if j:
    i=A[:j].index(min(A[:j]))
else:
    i=None
if j<N-1:
    k=j+1+A[j+1:N].index(min(A[j+1:N]))
else:
    k=None
if i==None:
    mi=(A[j]+A[k])*A[j]**A[k]
elif k==None:
    mi=(A[i]+A[j])*A[i]**A[j]
else:
    mi=min((A[j]+A[k])*A[j]**A[k],(A[i]+A[j])*A[i]**A[j])
ans*=pow(mi,mod-2,mod)
ans%=mod
print(ans)
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