#include <bits/stdc++.h>
using namespace std;

double f(int len) {
    if (len & 1) return (len + 1) / 2;
    return len/2 - 1 + sqrt(2);
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);

    string s;
    cin >> s;
    int n = s.size();

    double ans = 0;
    int pre = -1;
    for (int i = 0; i < n; i++) {
        if (s[i] == '1') {
            if (pre == -1) pre = i;
        } else {
            if (pre != -1) ans += f(i - pre);
            pre = -1;
        }
    }
    if (pre != -1) ans += f(n - pre);
    cout << fixed << setprecision(10) << ans << endl;

    return 0;
}