#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>#define rcy(x) ((x)%2==0?1:-1)
using namespace std;
typedef long long LL;
const int _=100;
const int maxn=2*1e3+_;
const LL mod=998244353;LL C[maxn][maxn],S[maxn][maxn],A[maxn][maxn];//i的降j次幂
void yu()
{C[0][0]=S[0][0]=A[0][0]=1;for(int i=1;i<maxn;i++){C[i][0]=A[i][0]=1;for(int j=1;j<=i;j++)C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod,S[i][j]=(S[i-1][j-1]+(i-1)*S[i-1][j])%mod,A[i][j]=A[i][j-1]*(i-j+1)%mod;}
}//------------------------------------------def-------------------------------------------------------bool vis[maxn*2];int n,nxt[maxn*2],cnt[4];//0-x,x-0,x-x,0-0
void dfs(int x,int st)
{vis[x]=true;if(nxt[x]==0){if(x>n&&st>n)cnt[3]++;else if(x<=n&&st>n)cnt[0]++;else if(x>n&&st<=n)cnt[1]++;}else{if(!vis[nxt[x]])dfs(nxt[x],st);else cnt[2]++;}
}//-------------------------------------------分类讨论---------------------------------------------- void calc(LL *u,int k)
{for(int x=0;x<=k;x++)for(int i=x;i<=k;i++)u[x]=(u[x]+C[k][i]*S[i][x]%mod*A[cnt[3]+k-i][k-i])%mod;for(int i=0;i<=k;i++){for(int j=i+1;j<=k;j++)u[i]=(u[i]+rcy(j-i)*u[j]*C[j][i])%mod;u[i]=(u[i]+mod)%mod;}
}
LL f[maxn],g[maxn],h[maxn],as[maxn];
void solve()
{calc(f,cnt[0]),calc(g,cnt[1]);for(int i=0;i<=n;i++)for(int j=0;j<=i;j++)h[i]=(h[i]+f[j]*g[i-j])%mod;        for(int i=0;i<=n;i++)for(int j=0;j<=i;j++)as[i]=(as[i]+h[j]*S[cnt[3]][i-j])%mod;for(int i=0;i<=n;i++)as[i]=as[i]*A[cnt[3]][cnt[3]]%mod;
}//--------------------------------------------solve-------------------------------------------------int a[maxn],b[maxn]; bool ru[maxn*2];
int main()
{freopen("gift.in","r",stdin);freopen("gift.out","w",stdout);yu();scanf("%d",&n);for(int i=1;i<=n;i++)scanf("%d",&a[i]);for(int i=1;i<=n;i++)scanf("%d",&b[i]);memset(vis,true,sizeof(vis));for(int i=1;i<=n;i++){if(a[i]==0)a[i]=i+n;if(b[i]==0)b[i]=i+n;vis[a[i]]=vis[b[i]]=false;if(a[i]<=n||b[i]<=n)nxt[a[i]]=b[i],ru[b[i]]=true;}for(int i=1;i<=2*n;i++)if(!vis[i]&&!ru[i])dfs(i,i);for(int i=1;i<=2*n;i++)if(!vis[i])dfs(i,i);solve();for(int i=0;i<n;i++)printf("%lld ",n-cnt[2]-i>=0?as[n-cnt[2]-i]:0);puts("");return 0;
}