#include <bits/stdc++.h>
#define rep(i, a, b) for (int i = a; i <= b; i++)
#define per(i, a, b) for (int i = a; i >= b; i--)
using namespace std;
 
typedef unsigned long long ull;
typedef pair <int, int> pii;
typedef long long ll;
 
template <typename T>
inline void read(T &f) {
    f = 0; T fu = 1; char c = getchar();
    while (c < '0' || c > '9') { if (c == '-') { fu = -1; } c = getchar(); }
    while (c >= '0' && c <= '9') { f = (f << 3) + (f << 1) + (c & 15); c = getchar(); }
    f *= fu;
}

template <typename T>
void print(T x) {
    if (x < 0) putchar('-'), x = -x;
    if (x < 10) putchar(x + 48);
    else print(x / 10), putchar(x % 10 + 48);
}
 
template <typename T>
void print(T x, char t) {
    print(x); putchar(t);
}

const int N = 260;

long double a[N][N], ans[N];
void gauss() {
    for (int i = 0; i < 256; i++) {
        int pos = i;
        for (int j = i; j < 256; j++) {
            if (fabs(a[j][i]) > fabs(a[pos][i])) {
                pos = j;
            }
        }
        swap(a[pos], a[i]);
        for (int j = i + 1; j < 256; j++) {
            long double coef = a[j][i] / a[i][i];
            for (int k = i; k <= 256; k++) a[j][k] -= coef * a[i][k];
        }
    }
    for (int i = 255; i >= 0; i--) {
        ans[i] = a[i][256];
        for (int j = i + 1; j < 256; j++) ans[i] += ans[j] * a[i][j];
        ans[i] /= -a[i][i];
    }
}

int T;

int main() {
    for (int i = 0; i < 256; i++) {
        static int seq[8];
        for (int j = 0; j < 8; j++) seq[j] = (i >> j) & 1;
        int len = 0, sum = 0;
        while (1) {
            int cando = 0;
            // for (int j = 0; j < 8 - len; j++) cout << seq[j];
            // cout << endl;
            for (int l = 0, r; l < 8 - len; l = r + 1) {
                r = l;
                while (r + 1 < 8 - len && seq[l] == seq[r + 1]) ++r;
                if (r - l + 1 >= 3) {
                    for (int j = r + 1; j < 8 - len; j++) seq[j - (r - l + 1)] = seq[j];
                    len += r - l + 1; sum += (r - l + 1) * (r - l + 1);
                    cando = 1;
                    break;
                }
            }
            if (!cando) break;
        }
        // fprintf(stderr, "len = %d\n", len);
        a[i][i] = -1;
        if (len) {
            a[i][256] += sum;
            long double inv = (long double)1 / (1 << len);
            for (int j = 0; j < (1 << len); j++) {
                for (int k = 0; k < len; k++) seq[7 - k] = (j >> k) & 1;
                int go = 0;
                for (int k = 0; k < 8; k++) go |= (seq[k] << k);
                a[i][go] += inv;
            }
        }
    }
    gauss();
    read(T);
    while (T--) {
        static char c[10];
        scanf("%s", c);
        int now = 0;
        for (int i = 0; i < 8; i++) now |= (c[i] - '0') << i;
        printf("%.7lf\n", (double)ans[now]);
    }
    return 0;
}