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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#61538#1262. Justice For EveryoneAppleblue17AC ✓2932ms38788kbC++148.2kb2022-11-13 22:00:582022-11-13 22:00:59

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2022-11-13 22:00:59]
  • 评测
  • 测评结果:AC
  • 用时:2932ms
  • 内存:38788kb
  • [2022-11-13 22:00:58]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
const long long N=66,V=220,O=2e5+5,mod=998244353,inv2=499122177,g=3;

long long mul[O],inv[O];
long long ksm(long long f,long long x){
	long long tot=1;
	while(x){
		if(x & 1ll) tot=tot*f%mod;
		f=f*f%mod;
		x>>=1ll;
	}
	return tot;
}
void init(long long lim){
	mul[0]=inv[0]=1;
	for(long long i=1;i<=lim;i++) mul[i]=mul[i-1]*i%mod;
	inv[lim]=ksm(mul[lim],mod-2);
	for(long long i=lim-1;i>=1;i--) inv[i]=inv[i+1]*(i+1)%mod;
}

long long C(long long m,long long n){
	if(m<0 || n<0 || m<n) return 0;
	return mul[m]*inv[n]%mod*inv[m-n]%mod;
}

long long ID(long long x){
	if(x & 1ll) return mod-1;
	else return 1;
}




long long qmod(long long x){
	if(x>=mod) x-=mod;
	return x;
}
void qmo(long long &x){x += x >> 31 & mod;}
long long pr[O];
namespace NTT{
	long long A[O],B[O],rev[O];
	void pre(){
		for(long long mid = 1;mid < O;mid <<= 1){
			long long Wn = ksm(3, (mod-1)/(mid<<1)); pr[mid] = 1;
			for(long long i = 1;i < mid && mid+i<O;++ i) pr[mid+i] = 1ll*pr[mid+i-1] * Wn % mod;
		}
	}
	long long init(long long n,long long m){
		long long lim=0;
		while((1ll<<lim)<=n+m) lim++;
		for(long long i=0;i<=(1<<lim)-1;i++)
			rev[i]=(rev[i>>1ll]>>1ll) | ((i & 1ll)<<(lim-1));
		return lim;
	}
	void ntt(long long *A,long long lim, long long op){
		for(long long i = 0;i < lim;++ i)
			if(i < rev[i]) swap(A[i], A[rev[i]]);
		for(long long mid = 1;mid < lim;mid <<= 1)
			for(long long i = 0;i < lim;i += mid<<1)
				for(long long j = 0;j < mid;++ j){
					long long y = 1ll*A[mid+i+j] * pr[mid+j] % mod;
					
					qmo(A[mid+i+j] = A[i+j] - y); 
					qmo(A[i+j] += y - mod);
				}
		if(op==-1){ reverse(A+1, A+lim); long long inv = ksm(lim, mod-2);
			for(long long i = 0;i < lim;++ i) A[i] = 1ll*A[i] * inv % mod;}
	}	
	void solve(long long *s,long long* f,long long* g,long long n,long long m){
		long long S[O];
		if(n+m<=100){
			for(long long i=0;i<=n+m;i++) S[i]=0;
			for(long long i=0;i<=n;i++){
				for(long long j=0;j<=m;j++){
					S[i+j]=qmod(S[i+j]+1ll*f[i]*g[j]%mod);
				}
			}
			for(long long i=0;i<=n+m;i++) s[i]=S[i];
			return ;
		}
		
		long long lim=init(n,m);
		for(long long i=0;i<=n;i++) A[i]=f[i];
		for(long long i=0;i<=m;i++) B[i]=g[i];
		for(long long i=n+1;i<=(1ll<<lim);i++) A[i]=0;
		for(long long i=m+1;i<=(1ll<<lim);i++) B[i]=0;
		ntt(A,(1<<lim),1);
		ntt(B,(1<<lim),1);
		for(long long i=0;i<=(1<<lim)-1;i++) S[i]=1ll*A[i]*B[i]%mod;
		ntt(S,(1<<lim),-1);
		for(long long i=0;i<=n+m;i++) s[i]=S[i];
	}
}

namespace INV{
	long long A[O],B[O],S[O];
	void solve(long long *s,long long *f,long long n){
		S[0]=ksm(f[0],mod-2);
		S[1]=0;
		long long len;
		for(len=2;len<=(n<<1ll);len<<=1ll){
			long long lim=len<<1ll;
			for(long long i=0;i<len;i++) A[i]=f[i],B[i]=S[i];
			for(long long i=len;i<lim;i++) A[i]=B[i]=0;
			NTT::init(len,0);
			NTT::ntt(A,lim,1);
			NTT::ntt(B,lim,1);
			for(long long j=0;j<lim;j++)
				S[j]=(2ll*B[j]+mod-1ll*A[j]*B[j]%mod*B[j]%mod)%mod;
			NTT::ntt(S,lim,-1);
			for(long long j=len;j<lim;j++) S[j]=0;
		}
		for(long long i=0;i<=n;i++) s[i]=S[i];
	}
}
namespace poly{
	void Rev(long long *s,long long *f,long long n){
		for(long long i=0;i<=n/2;i++) swap(f[i],f[n-i]);
	}
	//翻转 
	void Deriv(long long *s,long long *f,long long n){
		long long A[O];
		A[n]=0;
		for(long long i=1;i<=n;i++) A[i-1]=1ll*f[i]*i%mod;
		for(long long i=0;i<=n;i++) s[i]=A[i];
	}
	//求导 
}



namespace Evaluation{
	long long tmp[O];
	vector <long long> P[O],Q[O],Qn[O];
	long long lenp[O],lenq[O];
	void init(long long o,long long l,long long r){
		long long len=r-l+1,mid=(l+r)>>1ll;
		lenp[o]=len;
		lenq[o]=len-1;
		P[o].resize(2*lenp[o]+2);
		Q[o].resize(2*lenq[o]+2);
		if(l==r) return ;
		init(o<<1,l,mid);
		init(o<<1|1,mid+1,r);
	}
	
	void solve1(long long *a,long long o,long long l,long long r){	
		if(l==r){
			P[o][0]=1,P[o][1]=(mod-a[l])%mod;
			return ;
		}
		long long mid=(l+r)>>1;
		solve1(a,o<<1,l,mid);
		solve1(a,o<<1|1,mid+1,r);
		NTT::solve(P[o].data(),P[o<<1].data(),P[o<<1|1].data(),lenp[o<<1],lenp[o<<1|1]);
	}
	
	void solve2(long long *s,long long *a,long long o,long long l,long long r){
		if(l==r){
			s[l]=Q[o][0];
			return ;
		}
		long long mid=(l+r)>>1;
		long long len1=mid-l+1,len2=r-mid;
		
		NTT::solve(tmp,Q[o].data(),P[o<<1|1].data(),lenq[o],lenp[o<<1|1]);
		for(long long i=0;i<len1;i++) Q[o<<1][i]=tmp[i+len2];
		
		NTT::solve(tmp,Q[o].data(),P[o<<1].data(),lenq[o],lenp[o<<1]);
		for(long long i=0;i<len2;i++) Q[o<<1|1][i]=tmp[i+len1];
		
		solve2(s,a,o<<1,l,mid);
		solve2(s,a,o<<1|1,mid+1,r);
	}
	void solve(long long *s,long long *f,long long *a,long long n,long long m){
		m=max(n,m);
		n=max(n,m);
		init(1,1,m);
		solve1(a,1,1,m);
		poly::Rev(f,f,n);
		
		INV::solve(P[1].data(),P[1].data(),lenp[1]);
		
		NTT::solve(tmp,f,P[1].data(),n,lenp[1]);
		for(long long i=0;i<=m;i++) Q[1][i]=tmp[i];
		
		solve2(s,a,1,1,m);
		for(long long i=1;i<=m;i++){
			s[i]=(f[n]+1ll*s[i]*a[i]%mod)%mod;
		}
	}
}

namespace Interpolation{
	long long tmp[O];
	vector <long long> P[O],Q[O];
	long long lenp[O],lenq[O];
	long long g[O],gv[O];
	void init(long long o,long long l,long long r){
		long long len=r-l+1,mid=(l+r)>>1ll;
		lenp[o]=len;
		lenq[o]=len-1;
		P[o].resize(2*lenp[o]+2);
		Q[o].resize(2*lenq[o]+2);
		if(l==r) return ;
		init(o<<1,l,mid);
		init(o<<1|1,mid+1,r);
	}
	
	void solve1(long long *x,long long o,long long l,long long r){	
		if(l==r){
			P[o][0]=(mod-x[l])%mod,P[o][1]=1;
			return ;
		}
		long long mid=(l+r)>>1;
		solve1(x,o<<1,l,mid);
		solve1(x,o<<1|1,mid+1,r);
		NTT::solve(P[o].data(),P[o<<1].data(),P[o<<1|1].data(),lenp[o<<1],lenp[o<<1|1]);
	}
	
	void solve2(long long *x,long long *y,long long o,long long l,long long r){
		if(l==r){
			Q[o][0]=1ll*y[l]*ksm(gv[l],mod-2)%mod;
			return ;
		}
		long long mid=(l+r)>>1;
		solve2(x,y,o<<1,l,mid);
		solve2(x,y,o<<1|1,mid+1,r);
		long long tmp[O];
		NTT::solve(Q[o].data(),Q[o<<1].data(),P[o<<1|1].data(),lenq[o<<1],lenp[o<<1|1]);
		NTT::solve(tmp,Q[o<<1|1].data(),P[o<<1].data(),lenq[o<<1|1],lenp[o<<1]);
		for(long long i=0;i<=lenq[o];i++) Q[o][i]=(Q[o][i]+tmp[i])%mod;
	}
	void solve(long long *s,long long *x,long long *y,long long n){
		init(1,1,n);
		solve1(x,1,1,n);
		poly::Deriv(g,P[1].data(),lenp[1]);
		Evaluation::solve(gv,g,x,lenp[1]-1,n);
		solve2(x,y,1,1,n);
		for(long long i=0;i<=n;i++) s[i]=Q[1][i];
	}
}

long long det(long long a[N][N],long long n){
	long long tot=1;
	for(long long k=1;k<=n;k++){
		long long st=0;
		for(long long i=k;i<=n;i++){
			if(a[i][k]){
				st=i;
				break;
			}
		}
		if(!st) return 0;
		for(long long j=1;j<=n;j++) swap(a[k][j],a[st][j]);
		if(st!=k) tot=mod-tot;
		for(long long i=k+1;i<=n;i++){
			long long t=a[i][k]*ksm(a[k][k],mod-2)%mod;
			for(long long j=k;j<=n;j++) a[i][j]=(a[i][j]+mod-a[k][j]*t%mod)%mod;
		}
		tot=tot*a[k][k]%mod;
	}
	return tot;
}

pair <int,int> P[N];
long long n,s,anss,A[N],B[N];
long long f[N][N][V],G[N][N];
long long id[O],val[O],ans[O];

int main(){
	NTT::pre();
	init(O-5);
	cin>>n;
	for(long long i=1;i<=n;i++) cin>>A[i],s-=A[i];
	for(long long i=1;i<=n;i++) cin>>B[i],s+=B[i];
	for(int i=1;i<=n;i++) P[i]=make_pair(A[i],B[i]);
	sort(P+1,P+n+1);
	for(int i=1;i<n;i++){
		if(P[i].second>P[i+1].second)
			return puts("0"),0;
	}
	if(s<0 || s%2==1) return puts("0"),0;
	s/=2;
	
	for(long long i=1;i<=n;i++){
		for(long long j=1;j<=n;j++){
			long long d=B[j]-A[i];
			for(long long t=0;t<=d/2;t++)
				f[i][j][t]=(f[i][j][t]+inv[t]*inv[d-2*t]%mod)%mod;
//				,cout<<f[i][j][t]<<"/";
//			cout<<"  ";
		}
//		cout<<endl;
	}
	
	for(long long x=0;x<=s;x++){
//		cout<<x<<": "<<endl;
		for(long long i=1;i<=n;i++){
			for(long long j=1;j<=n;j++){
				long long d=B[j]-A[i],tot=0;
				for(long long t=0;t<=d/2;t++) tot=(tot+ksm(x,t)*f[i][j][t]%mod)%mod;
				G[i][j]=tot;
//				cout<<tot<<" ";
			}
//			cout<<endl;
		}
		
		val[x+1]=det(G,n);
	}
	
	for(long long i=0;i<=s;i++) id[i+1]=i;
	
	Interpolation::solve(ans,id,val,s+1);
	
	for(long long i=0;i<=s;i++)
		anss=(anss+ans[i]*C(s,i)%mod*ID(i)%mod*mul[i]%mod*mul[2*s-2*i]%mod)%mod;
	cout<<anss*ksm(inv2,s)%mod;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 16ms
memory: 31712kb

input:

3
1 2 3
3 4 5

output:

1

result:

ok answer is '1'

Test #2:

score: 0
Accepted
time: 8ms
memory: 32612kb

input:

3
1 2 3
7 8 9

output:

42

result:

ok answer is '42'

Test #3:

score: 0
Accepted
time: 17ms
memory: 32796kb

input:

3
1 4 7
3 6 9

output:

6

result:

ok answer is '6'

Test #4:

score: 0
Accepted
time: 4ms
memory: 32088kb

input:

1
1
3

output:

0

result:

ok answer is '0'

Test #5:

score: 0
Accepted
time: 8ms
memory: 31984kb

input:

1
1
1

output:

1

result:

ok answer is '1'

Test #6:

score: 0
Accepted
time: 7ms
memory: 31996kb

input:

2
1 4
4 7

output:

1

result:

ok answer is '1'

Test #7:

score: 0
Accepted
time: 9ms
memory: 33176kb

input:

10
10 9 8 7 6 1 2 3 4 5
11 12 13 114 115 120 129 128 127 126

output:

0

result:

ok answer is '0'

Test #8:

score: 0
Accepted
time: 7ms
memory: 32312kb

input:

30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 131

output:

0

result:

ok answer is '0'

Test #9:

score: 0
Accepted
time: 961ms
memory: 38788kb

input:

30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

output:

936606510

result:

ok answer is '936606510'

Test #10:

score: 0
Accepted
time: 11ms
memory: 32748kb

input:

30
16 21 33 44 51 60 71 81 91 100 110 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 199
110 111 112 113 114 115 116 117 118 119 120 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 199

output:

0

result:

ok answer is '0'

Test #11:

score: 0
Accepted
time: 93ms
memory: 34180kb

input:

30
16 21 33 44 51 60 71 81 91 100 110 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 199
110 111 112 113 114 115 116 117 118 119 120 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 200

output:

836228983

result:

ok answer is '836228983'

Test #12:

score: 0
Accepted
time: 48ms
memory: 33140kb

input:

10
10 9 8 7 6 5 4 3 2 1
110 109 108 107 106 105 104 103 102 101

output:

422463757

result:

ok answer is '422463757'

Test #13:

score: 0
Accepted
time: 2932ms
memory: 37744kb

input:

30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

output:

575061951

result:

ok answer is '575061951'