#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using mint1 = modint998244353;
using mint2 = static_modint<998244352>;



template<class T, T (*add)(T, T), T (*zero)(), T (*mul)(T, T), T (*one)(), int N>
struct Mat : array<array<T, N>, N> {
  using M = Mat<T, add, zero, mul, one, N>;
  void make_identity() {
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        (*this)[i][j] = zero();
      }
    }
    for (int i = 0; i < N; i++) {
      (*this)[i][i] = one();
    }
  }
  M& operator+=(const M& rhs) {
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        (*this)[i][j] = add((*this)[i][j], rhs[i][j]);
      }
    }
    return *this;
  }
  M& operator*=(const M& rhs) {
    static M temp;
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        temp[i][j] = zero();
      }
    }
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        for (int k = 0; k < N; k++) {
          temp[i][k] = add(temp[i][k], mul((*this)[i][j], rhs[j][k]));
        }
      }
    }
    *this = temp;
    return *this;
  }
  template <class I>
  void inplace_pow(I k) {
    assert(k >= 0);
    static M temp;
    temp = *this;
    make_identity();
    while (k) {
      if (k & 1) *this *= temp;
      k >>= 1;
      if (k) temp *= temp;
    }
  }
  friend ostream& operator<<(ostream& os, const M& A) {
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        os << A[i][j] << " \n"[j + 1 == N];
      }
    }
    return os;
  }
};


// mint
mint1 add(mint1 x, mint1 y) { return x + y; }
mint1 zero() { return mint1(); }
mint1 mul(mint1 x, mint1 y) { return x * y; }
mint1 one() { return mint1::raw(1); }
using M = Mat<mint1, add, zero, mul, one, 2>;

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  string s;
  cin >> s;
  reverse(all(s));
  s += '0';
  rep(i, ssize(s)) {
    s[i] ^= '1' ^ '0';
    if (s[i] == '1') break;
  }
  int n = s.size();
  vector<mint2> u(n + 1);
  vector<char> is_zero(n + 1, true);
  rrep(i, n) {
    u[i] = 2 * u[i+1] + (s[i] - '0');
    is_zero[i] = is_zero[i+1] & (s[i] == '0');
  }
  mint1 ans;
  mint1 i3 = mint1(3).inv(), coeff = 1;
  mint2 p2i = 1, l;
  
  bool l_is_zero = true;
  rep(i, n) {
    M a;
    mint1 X = mint1(9).pow((p2i * u[i+1]).val());  // (9^(2^i))^u
    mint1 Y = is_zero[i+1] ? mint1(1) : mint1(0);  // (0^u)
    a[0][0] = i3 * (X + 2 * Y);
    a[0][1] = -2 * i3 * (Y - X);
    a[1][0] = i3 * (X - Y);
    a[1][1] = i3 * (2 * X + Y);
    M b;
    mint2 t = s[i] == '0' ? l : p2i;
    X = mint1(3).pow(t.val());
    Y = mint1(2).pow(t.val());
    b[0][0] = X;
    b[1][0] = X - Y;
    b[1][1] = Y;
    a *= b;
    if (s[i] == '1' && !l_is_zero) {
      M c;
      X = mint1(3).pow((l - 1).val());
      c[0][0] = X;
      c[0][1] = 2 * X;
      c[1][0] = X;
      c[1][1] = 2 * X;
      a *= c;
    }
    ans += coeff * a[0][1];
    l_is_zero &= s[i] == '0';
    l += (s[i] - '0') * p2i;
    p2i *= 2;
    coeff *= 2;
  }
  cout << (i3 * ans).val() << '\n';
}