#include <bits/stdc++.h>
using namespace std;
using ll=long long;
const ll ILL=2167167167167167167;
const int INF=2100000000;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> int UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(b<a){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
    if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
    else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}

#include <atcoder/modint>
using mint = atcoder::modint998244353;
const int MOD1 = 998244352;

void solve();
// CITRUS CURIO CITY / FREDERIC
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
    // cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    string S;
    cin >> S;
    reverse(all(S));
    S += "0";
    for (auto &c : S){
        if (c == '0'){
            c = '1';
            break;
        }
        c = '0';
    }
    if (S.back() == '0') S.pop_back();
    int N = S.size();
    using F = array<array<mint, 2>, 2>;
    auto e = [&]() -> F {
        F res;
        rep(i, 0, 2) rep(j, 0, 2) res[i][j] = 1 - abs(i - j);
        return res;
    };
    auto mul = [&](F l, F r) -> F {
        F res;
        rep(i, 0, 2) rep(j, 0, 2) rep(k, 0, 2){
            res[i][k] += l[i][j] * r[j][k];
        }
        return res;
    };
    auto pow = [&](F l, ll times) -> F {
        F res = e();
        while (times){
            if (times & 1) res = mul(res, l);
            times /= 2;
            l = mul(l, l);
        }
        return res;
    };
    vector dp(N, vector<F>(2));
    rep(i, 0, 2) rep(j, 0, 2){
        dp[0][i][j][i | j] += 1;
        dp[0][i][j][i & j] += 1;
        dp[0][i][j][i ^ j] += 1;
    }
    rep(i, 1, N) rep(a, 0, 2){
        dp[i][a] = mul(dp[i - 1][a], dp[i - 1][a]);
    }
    vector<F> snuke(2, e());
    vector<ll> fr_mod(N);
    {
        ll tmp = 0;
        for (int i = N - 1; i >= 0; i--){
            fr_mod[i] = tmp;
            tmp *= 2;
            if (S[i] == '1') tmp++;
            tmp %= MOD1;
        }
    }
    mint ans = 0;
    mint p2 = 1;
    rep(i, 0, N){
        if (S[i] == '0'){
            auto tmp = mul(pow(mul(dp[i][0], dp[i][1]), min(i, 1) * MOD1 + fr_mod[i]), snuke[0]);
            ans += p2 * tmp[0][1];
        }
        else{
            auto tmp = pow(mul(dp[i][0], dp[i][1]), min(i, 1) * MOD1 + fr_mod[i]);
            tmp = mul(tmp, dp[i][0]);
            tmp = mul(tmp, snuke[1]);
            ans += p2 * tmp[0][1];
            snuke[0] = mul(snuke[0], dp[i][0]);
            snuke[1] = mul(snuke[1], dp[i][1]);
        }
        p2 *= 2;
    }
    ans /= 3;
    cout << ans.val() << "\n";
}