#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
#define int long long
const int mod=998244353;
const int N=2e5+9,M=5e5+9,B=450;
int cf[M];
int fac[M],inv[M],ifac[M];
void ycl(int lim=5e5)
{
	cf[0]=1;cf[1]=2;
	fac[0]=fac[1]=inv[0]=inv[1]=ifac[0]=ifac[1]=1;
	for(int i=2;i<=lim;i++)
	{
		fac[i]=fac[i-1]*i%mod;
		inv[i]=(mod-mod/i)*inv[mod%i]%mod;
		ifac[i]=ifac[i-1]*inv[i]%mod;
		cf[i]=cf[i-1]*2%mod;
	}
}
inline int ksm(int x,int y){int z=1;for(;y;x=x*x%mod,y>>=1) if(y&1) z=z*x%mod;return z;}
inline int C(int x,int y){return x>=y&&y>=0?fac[x]*ifac[y]%mod*ifac[x-y]%mod:0;}
inline int cf2(int x){return x>=0?cf[x]:0;}
int js(int n)
{
	int res=0;
	for(int j=1;j<=n;j++)
	for(int k=1;k<=n/j;k++)
	{
		res+=C(n-j*k,k)*cf2(n-j*k-k)%mod*((k&1)?1:mod-1)%mod;
		res+=C(n-j*k,k-1)*cf2(n-j*k-k+1)%mod*((k&1)?1:mod-1)%mod;
		res%=mod;
	}
	return res;
}
char s[N];
int n,ans=0;
int f[N<<1],g[N<<1];
signed main()
{
	scanf("%s",s+1);
	n=strlen(s+1);
	ycl();
	int num=0;
	for(int i=1;i<=n;i++) num=(num*2+(s[i]-'0'))%mod;
	ans=(js(n-1)+num)%mod;
	cerr<<ans<<endl;
	for(int k=1;k<=B;k++)
	{
		for(int i=0;i<=n;i++)
		if(i<k) f[i]=g[i]=0;
		else
		{
			f[i]=(f[i-k]+C(i-k,k)*cf2(i-k-k)%mod)%mod;
			g[i]=(g[i-k]+C(i-k,k-1)*cf2(i-k-k+1)%mod)%mod;
		}
		int mxlen=0,hzlen=0;
		for(int i=1;i<=n;i++)
		{
			if(i>1&&s[i]=='1')
			{
				int len=hzlen+1;
				int mx=max(mxlen,len);
				if(k==1) (ans+=mx*cf[n-i]%mod)%=mod;
				if(n-i-max(mx,B)*k>=0) (ans+=f[n-i-max(mx,B)*k]*((k&1)?1:(mod-1))%mod)%=mod;
				if(n-i+len-max(mx,B)*k>=0) (ans+=g[n-i+len-max(mx,B)*k]*((k&1)?1:(mod-1))%mod)%=mod;
			}
			if(i==1) hzlen++,mxlen=max(mxlen,hzlen);
			else
			{
				if(s[i]=='1') hzlen=0;
				else hzlen++,mxlen=max(mxlen,hzlen);
			}
		}
	}
	cerr<<ans<<endl;
	for(int j=1;j<=B;j++)
	{
		for(int i=1;i<=n;i++)
		if(i<=j) f[i]=0,g[i]=(i==j);
		else
		{
			f[i]=(f[i-1]*2+mod-f[i-j-1]+cf2(i-j-1))%mod;
			g[i]=(g[i-1]*2+mod-g[i-j-1])%mod;
		}
		int mxlen=0,hzlen=0;
		for(int i=1;i<=n;i++)
		{
			if(i>1&&s[i]=='1')
			{
				int len=hzlen+1;
				int mx=max(mxlen,len);
				if(j>mx)
				{
					if(n-i>=0) (ans+=f[n-i])%=mod;
					if(n-i+len>=0) (ans+=g[n-i+len])%=mod;
				}
			}
			if(i==1) hzlen++,mxlen=max(mxlen,hzlen);
			else
			{
				if(s[i]=='1') hzlen=0;
				else hzlen++,mxlen=max(mxlen,hzlen);
			}
		}
	}
	printf("%lld\n",ans);
}