// Skyqwq
#include <bits/stdc++.h>

#define pb push_back
#define fi first
#define se second
#define mp make_pair

using namespace std;

typedef long long LL;

template <typename T> void chkMax(T &x, T y) { if (y > x) x = y; }
template <typename T> void chkMin(T &x, T y) { if (y < x) x = y; }

template <typename T> void inline read(T &x) {
    int f = 1; x = 0; char s = getchar();
    while (s < '0' || s > '9') { if (s == '-') f = -1; s = getchar(); }
    while (s <= '9' && s >= '0') x = x * 10 + (s ^ 48), s = getchar();
    x *= f;
}

const int N = (1 << 8) + 5;

int a[8], b[8], c, len;

bool inline clear() {
    int ans = 0;
    for (int i = 0; i < len; i++) {
        int j = i;
        while (j + 1 < len && a[j + 1] == a[i]) ++j;
        int l = j - i + 1;
        if (l >= 3) {
            c += l * l;
            memcpy(b, a, sizeof b);
            for (int k = j + 1; k < len; k++)
                a[k - l] = b[k];
            len -= l;
            for (int k = len; k < len + l; k++) a[k] = 0;
            return 1;
        }
        i = j;
    }
    return 0;
}

void inline out(int x) {
    for (int i = 0; i < 8; i++) printf("%d", x >> i & 1);
}

double w[N][N];

int n = (1 << 8);

void gauss() {
    for (int i = 0; i < n; i++) {
        if (!w[i][i]) {
            for (int j = i + 1; j < n; j++) {
                if (w[j][i]) {
                    swap(w[i], w[j]);
                    break;
                }
            }
        }
        double o = w[i][i];
        for (int j = 0; j <= n; j++) w[i][j] /= o;
        for (int j = 0; j < n; j++) {
            if (i != j && w[j][i]) {
                double t = w[j][i];
                for (int k = 0; k <= n; k++)
                    w[j][k] -= w[i][k] * t;
            } 
        }
    }
}

void inline prework() {
    for (int i = 0; i < (1 << 8); i++) {
        for (int j = 0; j < 8; j++) a[j] = i >> j & 1;
        c = 0; len = 8;
        while (clear());
        int r = 8 - len;
        int v = 0;
        for (int j = 7; ~j; j--)
            v = v * 2 + a[j];
        double p = 1.0 / (1 << r);
        w[i][i] = 1, w[i][n] = c;
        if (r) for (int j = 0; j < (1 << r); j++) {
            int t = v + (j << len);
            w[i][t] += -p;
        }
    }
}

char s[10];
 
int main() {
    prework();
    gauss();
    int T; read(T);
    while (T--) {
        scanf("%s", s);
        int v = 0;
        for (int i = 7; ~i; i--) v = v * 2 + s[i] - '0';
        printf("%.14lf\n", w[v][n]);
    }
    return 0;
}