#include<bits/stdc++.h>
#define LL long long
#define LLL __int128
#define uint unsigned
#define ldb long double
#define uLL unsigned long long
using namespace std;
const int N=2e5+5,Mod=998244353;
int n,q,ans,BL;
string s;
int F[N],f[N],g[N];
tuple<int,int,int>Q[N];
int frc[N],ivf[N],pw2[N];
inline int qpow(int x,int y,int z=1){
	for(;y;(y>>=1)&&(x=(LL)x*x%Mod))if(y&1)z=(LL)z*x%Mod;return z;
}
inline int add(int x,const int&y){
    return ((x+=y)-Mod)>=0?x-Mod:x;
}
inline int sub(int x,const int&y){
    return (x-=y)<0?x+Mod:x;
}
inline int neg(const int&x){
	return x?Mod-x:0;
}
inline int div2(const int&x){
    return x&1?(x+Mod)>>1:x>>1;
}
inline void Init(const int&n){
    frc[0]=1;
    for(int i=1;i<=n;++i)frc[i]=1ll*frc[i-1]*i%Mod;
    ivf[n]=qpow(frc[n],Mod-2);
    for(int i=n;i>=1;--i)ivf[i-1]=1ll*ivf[i]*i%Mod;
    pw2[0]=1;
    for(int i=1;i<=n;++i)pw2[i]=add(pw2[i-1],pw2[i-1]);
}
signed main(){
    cin.tie(0)->sync_with_stdio(0);
	cin>>s,n=s.length()-1,Init(n),BL=sqrtl(n)+1;
    for(int i=0;i<=n;++i)
        F[i]=1ll*pw2[i]*ivf[i]%Mod;
    for(int i=0;i<=n;++i)if(s[i]=='1')ans=add(ans,pw2[n-i]);
    Q[0]=make_tuple(n,0,0);
    for(int i=1,cur=1,mx=0;i<=n;++i)
        if(s[i]=='1')Q[++q]=make_tuple(n-i,cur+1,max(mx,cur+1)),mx=max(mx,cur),cur=0;
        else ++cur;
    for(int i=1;i<=q;++i){
        const auto [qx,qy,qz]=Q[i];
        ans=(ans+1ll*qz*pw2[qx])%Mod;
    }
    for(int x=1;x<BL;++x){
        for(int i=0;i<=n;++i){
            f[i]=0,g[i]=0;
            if(i-x>0)f[i]=sub(add(add(f[i-1],f[i-1]),pw2[i-x-1]),f[i-x-1]);
            if(i-x-x>=0)g[i]=(g[i-x]+1ll*frc[i-x]*F[i-x-x]%Mod*(x&1?ivf[x]:Mod-ivf[x]))%Mod;
        }
        for(int i=0;i<=q;++i){
            const auto [qx,qy,qz]=Q[i];
            int len=max(qz,BL-1),p=qx-len*x;
            if(p>=x+x)ans=add(ans,g[p]);
            if((p+=qy)>=x+x-1)ans=add(ans,sub(g[p+1],add(g[p],g[p])));
            if(x>qz){
                ans=add(ans,f[qx]);
                if(qx+qy-x>=0)ans=add(ans,sub(pw2[qx+qy-x],f[qx+qy-x]));
            }
        }
    }
    cout<<ans;
    return 0;
}
/*

*/