#ifdef LOCAL
#include "stdafx.h"
#else
#include <bits/stdc++.h>
#define IL inline
#define LL long long
#define eb emplace_back
#define sz(v) ((int) (v).size())
#define me(f, x) memset(f, x, sizeof(f))
#define mc(f, g) memcpy(f, g, sizeof(g))
#define L(i, j, k) for (int i = (j); i <= (k); ++i)
#define R(i, j, k) for (int i = (j); i >= (k); --i)
#define FIO(FILE) freopen(FILE".in", "r", stdin), freopen(FILE".out", "w", stdout)
using namespace std;

using vi = vector<int>;
#endif

constexpr int P = 998244353;
constexpr int N = 2e5 + 9;
constexpr int M = 450;

IL constexpr int qpow (int b, int k = P - 2) {
  int r = 1;
  for (; k; k >>= 1, b = (LL)b * b % P) if (k & 1) r = (LL)r * b % P;
  return r;
}

int fc[N], ifc[N], p2[N];

void init (int Z) {
  fc[0] = 1;
  L (i, 1, Z) {
    fc[i] = (LL)fc[i - 1] * i % P;
  }
  ifc[Z] = qpow(fc[Z]);
  R (i, Z - 1, 0) {
    ifc[i] = (LL)ifc[i + 1] * (i + 1) % P;
  }
  p2[0] = 1;
  L (i, 1, Z) {
    p2[i] = 2LL * p2[i - 1] % P;
  }
}

IL int C (int n, int m) {
  return n < m || m < 0 ? 0 : (LL)fc[n] * ifc[m] % P * ifc[n - m] % P;
}

IL int sgn (int x) {
  return x & 1 ? 1 : -1;
}

int n, B, p[N], L[N];
char s[N];

int f[N], g[N];

int main () {
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> s;
  n = strlen(s) - 1;
  init(n);
  B = sqrt(n);
  LL ns = p2[n];
  L (i, 1, n) {
    L (t, 1, n / i) {
      LL x = C(n - i * t, t) * (LL)p2[n - (i + 1) * t];
      LL y = C(n - i * t, t - 1) * (LL)p2[n - (i + 1) * t + 1];
      ns = (ns + (x + y) * sgn(t)) % P;
    }
  }
  p[n] = n + 1;
  R (i, n - 1, 0) {
    p[i] = s[i + 1] == '1' ? i + 1 : p[i + 1];
  }
  int cur = 1, mx = 0;
  L (i, 0, n - 1) {
    if (p[i] > n) {
      break;
    }
    if (i) {
      if (s[i] == '0') {
        cur += 1;
      } else {
        mx = max(mx, cur);
        cur = 0;
      }
    }
    if (i > 0 && cur > 0) {
      p[i] = n + 1;
      continue;
    }
    L[i] = max(mx, cur + p[i] - i);
    ns = (ns + p2[n - p[i]] * (LL)(L[i] + 1)) % P;
  }
  L (k, 1, B) {
    L (i, 0, k - 1) {
      f[i] = g[i] = 0;
    }
    L (i, k, n + 1) {
      f[i] = f[i - k];
      if (i - 2 * k + 1 >= 0) {
        f[i] = (f[i] + C(i - k, k - 1) * (LL)p2[i - 2 * k + 1] * sgn(k)) % P;
      }
      g[i] = (2LL * g[i - 1] + P - g[i - 1 - k] + (i == k)) % P;
    }
    L (i, 0, n - 1) {
      if (p[i] <= n) {
        if (L[i] < k) {
          ns += g[n - i + (i == 0)];
        }
        int m = n - i + (i == 0) - max(L[i], B) * k;
        if (m >= 0) {
          ns += f[m];
        }
      }
    }
  }
  L (k, 1, B) {
    L (i, 0, k - 1) {
      f[i] = g[i] = 0;
    }
    L (i, k, n) {
      f[i] = f[i - k];
      if (i - 2 * k >= 0) {
        f[i] = (f[i] + C(i - k, k) * (LL)p2[i - 2 * k] * sgn(k)) % P;
      }
      g[i] = (2LL * g[i - 1] + P - g[i - 1 - k]) % P;
      if (i - k - 1 >= 0) {
        g[i] = (g[i] + p2[i - k - 1]) % P;
      }
    }
    L (i, 0, n - 1) {
      if (p[i] <= n) {
        if (L[i] < k) {
          ns += g[n - p[i]];
        }
        int m = n - p[i] - max(L[i], B) * k;
        if (m >= 0) {
          ns += f[m];
        }
      }
    }
  }
  ns %= P;
  if (ns < 0) {
    ns += P;
  }
  cout << ns << '\n';
}
// I love WHQ!