#include<iostream>
#include<cstdio>
#include<cmath>
#include<vector>
#define N 400002
#define mod 998244353
using namespace std;
struct reads
{
	int num,data;
};
string s;
int ps,F[N+1],delta[N+1],delta2[N+1],fac[N+1],invfac[N+1],pw2[N+1],sz,Base,ans;
vector<int>v[N+1];
vector<int>v2[N+1];
vector<reads>v3[N+1];
vector<reads>v4[N+1];
int fast_pow(int a,int b)
{
	int res=1,mul=a;
	while (b)
	{
		if (b&1) res=1ll*res*mul%mod;
		mul=1ll*mul*mul%mod,b>>=1;
	}
	return res;
}
int C(int x,int y)
{
	return 1ll*fac[x]*invfac[y]%mod*invfac[x-y]%mod;
}
int MD(int x)
{
	return x>=mod?x-mod:x;
}
int MD2(int x)
{
	return x<0?x+mod:x;
}
void Adder(int &x,int d)
{
	x=x+d>=mod?x+d-mod:x+d;
	return;
}
void Adder2(int &x,int d)
{
	x=x+d<0?x+d+mod:x+d;
	return;
}
int calc(int a,int n)
{
	int d,res=0;
	for (int i=0;(a+2)*i<=n;++i)
	{
		d=n-(a+2)*i;
		if (!(i&1)) Adder(res,1ll*C(d+i,d)*pw2[d]%mod);
		else Adder2(res,-1ll*C(d+i,d)*pw2[d]%mod);
	}
	return res;
}
int solve(int a,int b,int n)
{
	int res=0;
	Adder(res,calc(a,n));
	if (n>=b+1) Adder2(res,-calc(a,n-b-1));
	return res;
}
void get(int a,int b,int n)
{
	Adder(ans,1ll*pw2[n]*(sz+1)%mod),a=max(a,b);
	if (a<=Base) v[a].push_back(n),v2[a].push_back(n+b-1);
	if (max(a,Base+1)+2<=n) v3[n/(max(a,Base+1)+2)].push_back((reads){max(a,Base+1),n});
	if ((max(a,Base+1)<<1)+2<=n+b-1) v4[(n+b-1-max(a,Base+1))/(max(a,Base+1)+2)].push_back((reads){max(a,Base+1),n+b-1});
	if (max(a,Base+1)<=sz-1) Adder2(ans,-1ll*(sz-max(a,Base+1))*pw2[n]%mod);
	if (max(a,Base+1)<=min(sz-1,n+b-1)) Adder(ans,MD2(pw2[n+b-max(a,Base+1)]-pw2[n+b-1-min(sz-1,n+b-1)]));
	return;
}
int main()
{
	int d,maxn;
	fac[0]=1;
	for (int i=1;i<=N;++i) fac[i]=1ll*fac[i-1]*i%mod;
	invfac[N]=fast_pow(fac[N],mod-2);
	for (int i=N-1;i>=0;--i) invfac[i]=1ll*invfac[i+1]*(i+1)%mod;
	pw2[0]=1;
	for (int i=1;i<=N;++i) pw2[i]=2ll*pw2[i-1]%mod;
	cin>>s,ans=1ll*pw2[s.length()-1]*s.length()%mod;
	for (int i=0;i+1<s.length();++i) Adder2(ans,-solve(i,i,s.length()-1));
	d=maxn=1,sz=s.length()+1,Base=sqrt(sz);
	for (int i=1;i<s.length();++i)
	{
		if (s[i]=='1') get(maxn,d+1,s.length()-i-1),d=0;
		else maxn=max(maxn,++d);
	}
	for (int i=Base;i>=0;--i)
	{
		F[0]=1;
		for (int j=1;j<=(sz<<1)-i;++j) F[j]=j<=i+1?2ll*F[j-1]%mod:(2ll*F[j-1]-F[j-i-2]+mod)%mod;
		for (int j=0;j<=(sz<<1)-i;++j) Adder(delta[j],F[j]),Adder(delta2[j+i],F[j]);
		for (int j=0;j<v[i].size();++j) Adder2(ans,-delta[v[i][j]]);
		for (int j=0;j<v2[i].size();++j) Adder(ans,delta2[v2[i][j]]);
	}
	for (int i=0;i<=sz;++i) delta[i]=pw2[i];
	for (int i=1;i<=sz/(Base+3);++i)
	{
		for (int j=0;j<=sz;++j) delta[j]=1ll*delta[j]*(j+i)%mod,F[j]=delta[j];
		for (int j=i;j<=sz;++j) Adder(F[j],F[j-i]);
		if (!(i&1))
		{
			for (int j=i;j<=sz/(Base+3);++j)
				for (int k=0;k<v3[j].size();++k)
					Adder2(ans,-1ll*F[v3[j][k].data-(v3[j][k].num+2)*i]*invfac[i]%mod);
		}
		else
		{
			for (int j=i;j<=sz/(Base+3);++j)
				for (int k=0;k<v3[j].size();++k)
					Adder(ans,1ll*F[v3[j][k].data-(v3[j][k].num+2)*i]*invfac[i]%mod);
		}
	}
	for (int i=0;i<=(sz<<1);++i) delta[i]=pw2[i];
	for (int i=1;i<=(sz<<1)/(Base+3);++i)
	{
		for (int j=0;j<=(sz<<1);++j) delta[j]=1ll*delta[j]*(j+i)%mod,F[j]=delta[j];
		for (int j=i+1;j<=(sz<<1);++j) Adder(F[j],F[j-i-1]);
		if (!(i&1))
		{
			for (int j=i;j<=(sz<<1)/(Base+3);++j)
				for (int k=0;k<v4[j].size();++k)
					Adder(ans,1ll*F[v4[j][k].data-(v4[j][k].num+2)*i-v4[j][k].num]*invfac[i]%mod);
		}
		else
		{
			for (int j=i;j<=(sz<<1)/(Base+3);++j)
				for (int k=0;k<v4[j].size();++k)
					Adder2(ans,-1ll*F[v4[j][k].data-(v4[j][k].num+2)*i-v4[j][k].num]*invfac[i]%mod);
		}
	}
	printf("%d\n",ans);
	return 0;
}