#include <algorithm>
#include <cassert>
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long ll;
const int N = 200003, B = 449;
const int P = 998244353;
int n, rk;
char s[N];
int fac[N], fiv[N], bn[N], fbn[N], sf[N];
int qp(int a, int b = P - 2) {
    int res = 1;
    while (b) {
        if (b & 1)
            res = (ll)res * a % P;
        a = (ll)a * a % P;
        b >>= 1;
    }
    return res;
}
inline void inc(int &x, int v) {
    if ((x += v) >= P)
        x -= P;
}
inline void dec(int &x, int v) {
    if ((x -= v) < 0)
        x += P;
}
inline int C(int a, int b) {
    return (ll)fac[a] * fiv[b] % P * fiv[a - b] % P;
}
int f[N], g[N];
int qa[N], qb[N], qc[N];
int main() {
    scanf("%s", s);
    n = strlen(s) - 1;
    fac[0] = 1;
    for (int i = 1; i <= n; ++i)
        fac[i] = (ll)fac[i - 1] * i % P;
    fiv[n] = qp(fac[n]);
    for (int i = n; i; --i)
        fiv[i - 1] = (ll)fiv[i] * i % P;
    bn[0] = 1;
    for (int i = 1; i <= n; ++i) {
        bn[i] = bn[i - 1] << 1;
        if (bn[i] >= P)
            bn[i] -= P;
    }
    for (int i = 0; i <= n; ++i) {
        fbn[i] = (ll)bn[i] * fiv[i] % P;
        if (i & 1)
            sf[i] = fiv[i];
        else
            sf[i] = P - fiv[i];
    }
    int ans = 0;
    for (int i = 0; i <= n; ++i)
        if (s[i] == '1')
            inc(ans, bn[n - i]);
    for (int i = 1; i <= n; ++i) {
        for (int x = 1; (i + 1) * x <= n; ++x) {
            int cur = (ll)C(n - i * x, x) * bn[n - i * x - x] % P;
            if (x & 1)
                inc(ans, cur);
            else
                dec(ans, cur);
        }
        for (int x = 1; (i + 1) * x - 1 <= n; ++x) {
            int cur = (ll)C(n - i * x, x - 1) * bn[n - i * x - x + 1] % P;
            if (x & 1)
                inc(ans, cur);
            else
                dec(ans, cur);
        }
    }
    int now = 1, mx = 0;
    for (int t = 1; t <= n; ++t) {
        ++now;
        if (s[t] == '1') {
            int lim = max(mx, now);
            int m = n - t;
            ans = (ans + (ll)lim * bn[m]) % P;
            ++rk, qa[rk] = m, qb[rk] = now, qc[rk] = lim;
            mx = max(mx, now - 1), now = 0;
        }
    }
    for (int x = 1; x < B; ++x) {
        for (int t = 0, t1 = -x, t2 = -2 * x; t <= n; ++t, ++t1, ++t2) {
            f[t] = g[t] = 0;
            if (t1 > 0) {
                inc(f[t] = f[t - 1], f[t - 1]);
                inc(f[t], bn[t1 - 1]);
                dec(f[t], f[t1 - 1]);
            }
            if (t2 >= 0)
                g[t] = (g[t1] + (ll)fac[t1] * fbn[t2] % P * sf[x]) % P;
        }
        for (int i = 1; i <= rk; ++i) {
            int m = qa[i], now = qb[i], lim = qc[i];
            int tlim = max(lim, B - 1);
            int ps = m - tlim * x;
            if (ps >= 2 * x)
                inc(ans, g[ps]);
            ps += now;
            if (ps >= 2 * x - 1)
                inc(ans, g[ps + 1]), dec(ans, g[ps]), dec(ans, g[ps]);
            if (x > lim) {
                inc(ans, f[m]);
                if (m - x + now >= 0) {
                    dec(ans, f[m - x + now]);
                    inc(ans, bn[m - x + now]);
                }
            }
        }
    }
    printf("%d\n", ans);
    return 0;
}