1 #include<bits/stdc++.h>
2 #define mod 998244353
3 #define Run(i,l,r) for(int i=l;i<=r;++i)
4 #define Don(i,l,r) for(int i=l;i>=r;--i)
5 const int N=1<<19;
6 using namespace std;
7 int n,a[N],fac[N],ans[N];
8 char s[N],ps[1000000],*pp=ps;
9 int pw(int x,int y){
10 if(y<0)y+=mod-1;
11 int re=1;
12 for(;y;y>>=1,x=1ll*x*x%mod)if(y&1)re=1ll*re*x%mod;
13 return re;
14 }
15 void push(char x){
16 if(pp==ps+1000000)fwrite(ps,1,1000000,stdout),pp=ps;
17 *pp++=x;
18 }
19 void write(int x){
20 static int top,sta[20];
21 if(!x){push('0'),push('
');return;}
22 while(x)sta[++top]=x%10,x/=10;
23 while(top)push(sta[top--]^'0');
24 push('
');
25 }
26 void flush(){fwrite(ps,1,pp-ps,stdout);}
27 namespace poly{
28 int g=3,iv[N],rev[N],L;
29 void init(int l){for(int i=1;i<=l;++i)iv[i]=pw(i,mod-2);}
30 void cls(int*A,int l,int r){for(int i=l;i<r;++i)A[i]=0;}
31 void cpy(int*A,int*B,int l){for(int i=0;i<l;++i)A[i]=B[i];}
32 void der(int*A,int l){Run(i,0,l-2)A[i]=1ll*(i+1)*A[i+1]%mod;A[l-1]=0;}
33 void dif(int*A,int l){Don(i,l-1,1)A[i]=1ll*iv[i]*A[i-1]%mod;A[0]=0;}
34 void ntt(int*A,int l,int f){
35 for(L=0;(1<<L)<l;++L);
36 for(int i=0;i<l;++i){
37 rev[i]=(rev[i>>1]>>1)|((i&1)<<(L-1));
38 if(i<rev[i])swap(A[i],A[rev[i]]);
39 }
40 for(int i=1;i<l;i<<=1){
41 int wn=pw(g,f*(mod-1)/(i<<1));
42 for(int j=0;j<l;j+=i<<1){
43 int w=1;
44 for(int k=0;k<i;++k,w=1ll*w*wn%mod){
45 int x=A[j+k],y=1ll*w*A[j+k+i]%mod;
46 A[j+k]=(x+y)%mod,A[j+k+i]=(x-y+mod)%mod;
47 }
48 }
49 }
50 if(!~f){for(int i=0;i<l;++i)A[i]=1ll*A[i]*iv[l]%mod;}
51 }
52 void inv(int*A,int*B,int l){
53 static int t[N];
54 if(l==1){B[0]=pw(A[0],mod-2);return;}
55 int len=l<<1;
56 inv(A,B,l>>1);cls(B,l,len);
57 cpy(t,A,l);cls(t,l,len);
58 ntt(t,len,1);ntt(B,len,1);
59 for(int i=0;i<len;++i)B[i]=1ll*B[i]*(2-1ll*t[i]*B[i]%mod+mod)%mod;
60 ntt(B,len,-1);cls(B,l,len);
61 }
62 void ln(int*A,int*B,int l){
63 static int t[N];
64 int len=l<<1;
65 inv(A,B,l);
66 cpy(t,A,l);cls(t,l,len);
67 der(t,l);
68 ntt(B,len,1);ntt(t,len,1);
69 for(int i=0;i<len;++i)B[i]=1ll*B[i]*t[i]%mod;
70 ntt(B,len,-1);cls(B,l,len);
71 dif(B,l);
72 }
73 void exp(int*A,int*B,int l){
74 static int t[N];
75 if(l==1){B[0]=1;return;}
76 int len=l<<1;
77 exp(A,B,l>>1);cls(B,l,len);
78 ln(B,t,l);
79 for(int i=0;i<l;++i)t[i]=(A[i]-t[i]+mod)%mod;
80 t[0]++;
81 ntt(B,len,1);ntt(t,len,1);
82 for(int i=0;i<len;++i)B[i]=1ll*B[i]*t[i]%mod;
83 ntt(B,len,-1);cls(B,l,len);
84 }
85 void solve(int*A,int l){
86 static int t[N],r[N];
87 if(l==1){A[0]=0;return;}
88 int len=l<<1;
89 solve(A,l>>1);cls(A,l,len);
90 cpy(t,a,l);cls(t,l,len);
91 ntt(A,len,1);ntt(t,len,1);
92 for(int i=0;i<len;++i){
93 int tmp=A[i];
94 A[i]=(mod-1ll*iv[2]*t[i]%mod*A[i]%mod*A[i]%mod)%mod;
95 t[i]=(mod-1ll*t[i]*tmp%mod)%mod;
96 }
97 ntt(A,len,-1);cls(A,l,len);A[0]++;
98 ntt(t,len,-1);cls(t,l,len);dif(t,l);
99 exp(t,r,l);inv(r,t,l);
100 ntt(A,len,1);ntt(r,len,1);
101 for(int i=0;i<len;++i)A[i]=1ll*A[i]*r[i]%mod;
102 ntt(A,len,-1);cls(A,l,len);
103 dif(A,l);
104 ntt(A,len,1);ntt(t,len,1);
105 for(int i=0;i<len;++i)A[i]=1ll*A[i]*t[i]%mod;
106 ntt(A,len,-1);cls(A,l,len);
107 }
108 }
109 int main(){
110 // freopen("uoj50.in","r",stdin);
111 // freopen("uoj50.out","w",stdout);
112 scanf("%d%s",&n,s+1);
113 for(int i=fac[0]=1;i<=n;++i){
114 fac[i]=1ll*fac[i-1]*i%mod;
115 if(s[i]-'0')a[i-1]=pw(fac[i-1],mod-2);
116 }
117 int len=1;for(;len<=n;len<<=1);
118 poly::init(len<<1);
119 poly::solve(ans,len);
120 for(int i=1;i<=n;++i)write(1ll*ans[i]*fac[i]%mod);
121 flush();
122 return 0;
123 }
