#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = long long;
#define all(s) (s).begin(),(s).end()
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define rep(i, n) rep2(i, 0, n)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define P pair<ll,ll>
#define REP(i, n) for (int i = 0; i < (n); ++i)
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 2000000000000000000ll;
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
void YesNo(bool a){if(a){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}}
void YESNO(bool a){if(a){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}}
template<class T,class U> void chmax(T& t,const U& u){if(t<u) t=u;}
template<class T,class U> void chmin(T& t,const U& u){if(t>u) t=u;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
ll modPow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }

void gbjsmzmfuuvdf(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(20);
}
using mint = modint998244353;
struct S{
    mint value;
    int size;
};
using F = mint;
S op(S a, S b){ return {a.value+b.value, a.size+b.size}; }
S e(){ return {mint(0),1}; }
S mapping(F f, S x){ return {x.value+x.size*f, x.size}; }
F composition(F f, F g){ return f+g; }
F id(){ return mint(0); }
mint k[200100];
void com(){
  k[0]=1;
  for(int i=1;i<200100;i++){
    k[i]=k[i-1]*i;
  }
}
mint g(ll a,ll b){
  if(a==1){
    return mint(1);
  }
  if(b==1){
    return mint(1)/mint(2);
  }
  if(a==b){
    return mint(1)/mint(mint(2).pow(a-1)*k[a-1]);
  }
  return mint(1)/mint(mint(2).pow(b))*(mint(2)/mint(k[b-1])-mint(1)/mint(k[b]));
}
int main()  {
  gbjsmzmfuuvdf();
  com();
  int n;
  cin>>n;
  assert(2<=n&&n<=100000);
  mint h=mint(4).pow(n-1);
  for(int i=1;i<=n-1;i++){
    h*=i;
  }
  vector<mint> a(n),b(n);
  lazy_segtree<S, op, e, F, mapping, composition, id> seg(n);
  for(int i=0;i<n;i++){
    seg.apply(i,g(n-i,1));
  }
  for(int i=2;i<n;i++){
    seg.apply(i-1,n-1,g(n,i));
  }
  for(int i=2;i<=n;i++){
    seg.apply(n-1,g(i,i));
  }
  for(int i=0;i<n;i++){
    int x;
    cin>>x;
    assert(0<=x&&x<=2);
    a[i]=x;
  }
  mint ans=0;
  for(int i=0;i<n;i++){
    ans+=a[i]*seg.prod(i,i+1).value;
    b[i]=seg.prod(i,i+1).value;
  }
  for(int i=n-1;i>=0;i--){
    a.push_back(a[i]);
    b.push_back(b[i]);
  }
  n*=2;
  rever(b);
  vector<mint> c=convolution(a,b);
  for(int i=n;i<int(c.size());i++){
    c[i%n]+=c[i];
  }
  c.resize(n);
  rever(c);
  cout<<(c[0]*h/mint(2)).val()<<endl;
  int k=min(int(sqrt(n/2)*4),int(n));
  vector<vector<pair<int,mint>>> F(k+1);
  vector<mint> p;
  F[0]={{0,mint(1)}};
  for(int i=1;i<=n/2;i++){
    ll v=i%k;
    if(v==i){
      unordered_map<int,mint> M;
      for(int j=0;j<int(F[i-1].size());j++){
        M[F[i-1][j].fi]+=(n/2-3)*F[i-1][j].se;
        M[(F[i-1][j].fi-1+n)%n]+=F[i-1][j].se;
        M[(F[i-1][j].fi+1)%n]+=F[i-1][j].se;
      }
      for(auto e:M){
        F[i].push_back({e.fi,e.se});
      }
      mint ans=0;
      for(int j=0;j<int(F[i].size());j++){
        ans+=F[i][j].se*c[F[i][j].fi];
      }
      cout<<(ans*h/mint(2)).val()<<endl;
    }
    else{
      mint ans=0;
      for(int j=0;j<int(F[v].size());j++){
        ans+=F[v][j].se*c[F[v][j].fi];
      }
      cout<<(ans*h/mint(2)).val()<<endl;
    }
    if(i%k==k-1){
      if(int(p.size())==0){
        unordered_map<int,mint> M;
        for(int j=0;j<int(F[k-1].size());j++){
          M	[F[k-1][j].fi]+=(n/2-3)*F[k-1][j].se;
          M[(F[k-1][j].fi-1+n)%n]+=F[k-1][j].se;
          M[(F[k-1][j].fi+1)%n]+=F[k-1][j].se;
        }
        vector<pair<int,int>> S(int(M.size()));
        int now=0;
        for(auto e:M){
          if(e.fi>=n/2){
            S[now]={e.fi-n,e.se.val()};
          }
          else{
            S[now]={e.fi,e.se.val()};
          }
          now++;
        }
        sor(S);
        for(int j=0;j<int(S.size());j++){
          p.push_back(S[j].se);
        }
      }
      auto d=convolution(c,p);
      for(int j=0;j<int(c.size());j++){
        c[j]=0;
      }
      for(int j=0;j<int(d.size());j++){
        c[(j-k+n)%n]+=d[j];
      }
    }
  }
}