#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using pi=pair<int,int>;
#define fi first
#define se second
const int N=2e5+5,mod=998244353;
int n,to[N],mxt[N];
ll ans,fc[N],inv[N],pw[N],f[N],g[N];
string a;
ll qp(ll a,int b){ll ans=1;for(;b;b>>=1,a=a*a%mod)if(b&1)ans=ans*a%mod;return ans;}
ll C(int n,int m){return n<m||m<0?0:fc[n]*inv[m]%mod*inv[n-m]%mod;}
ll P(int n){return n<0?0:pw[n];}
ll S(ll*f,int x){return x<0?0:f[x];}
void init(int n) {
    fc[0]=pw[0]=1;
    for(int i=1;i<=n;i++)fc[i]=fc[i-1]*i%mod,pw[i]=pw[i-1]*2%mod;
    inv[n]=qp(fc[n],mod-2);
    for(int i=n-1;~i;i--)inv[i]=inv[i+1]*(i+1)%mod;
}
int main() {
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    cin>>a,n=a.size(),init(n),a=' '+a;
    for(int i=1;i<=n;i++)ans=(ans*2+a[i]-'0')%mod; 
    int sq=sqrt(n);a[1]='0';
    for(int i=1;i<=n;i++)to[i]=(a[i]=='0'?to[i-1]+1:0),mxt[i]=max(mxt[i-1],to[i]);
    for(int i=2;i<=n;i++)if(a[i]=='1')ans=(ans+pw[n-i]*max(mxt[i],to[i-1]+1))%mod;
    for(int K=1;K<=sq;K++) {
        for(int i=0;i<K;i++)f[i]=g[i]=0;g[K-1]=1;
        for(int i=K;i<=n;i++)f[i]=(f[i-K]+C(i,K)*P(i-K))%mod,g[i]=(g[i-K]+C(i,K-1)*P(i-K+1))%mod;
        for(int i=2;i<=n;i++)if(a[i]=='1') {
            int m=n-i,nt=to[i-1]+1,mx=max(nt,mxt[i]);
            ans=(ans+(K&1?1:-1)*(S(f,m-(max(sq,mx)+1)*K)+S(g,m+nt-(max(sq,mx)+1)*K)))%mod;
        }
        ans=(ans+(K&1?1:-1)*(S(f,n-1-(sq+1)*K)+S(g,n-1-(sq+1)*K)))%mod;
    }
    for(int J=1;J<=sq;J++) {
        for(int i=0;i<=J;i++)f[i]=g[i]=0;g[J]=1;
        for(int i=J+1;i<=n;i++)f[i]=(f[i-1]*2-f[i-1-J]-P(i-1-J))%mod,g[i]=(g[i-1]*2-g[i-1-J])%mod;
        for(int i=2;i<=n;i++)if(a[i]=='1') {
            int m=n-i,nt=to[i-1]+1;
            if(J>max(nt,mxt[i]))ans=(ans-f[m]+g[m+nt])%mod;
        }ans=(ans-f[n-1]+g[n-1])%mod;
    }
    cout<<(ans+mod)%mod<<'\n';
    return 0;
}