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

double A[300][300], x[300];

void solveLinear() {
    int n = 256;
    for (int i = 0; i < n; i++) {
        int piv = i;
        for (int j = i; j < n; j++)
            if (fabs(A[j][i]) > fabs(A[piv][i])) piv = j;
        for (int j = 0; j <= n; j++)
            swap(A[i][j], A[piv][j]);
        for (int j = i + 1; j <= n; j++)
            A[i][j] /= A[i][i];
        for (int j = 0; j < n; j++) if (i != j)
            for (int k = i + 1; k <= n; k++) A[j][k] -= A[j][i] * A[i][k];
    }
}

pair <int, pair <int, int> > nxt(int state, int len, int score) {
    for (int i = 0; i < len; i++) {
        for (int l = len; l >= 3; l--) {
            if (i + l > len) continue ;
            int f = 1, t = -1;
            for (int j = 0; j < l; j++) {
                int c = state >> (i + j) & 1;
                if (t == -1) t = c;
                if (t != c) f = 0;
            }
            if (!f) continue ;
            int x = 0;
            for (int j = len - 1; j >= 0; j--)
                if (j - i < 0 || j - i >= l)
                    x = (x << 1) | (state >> j & 1);
            return nxt(x, len - l, score + l * l);
        }
    }
    return make_pair(state, make_pair(len, score));
}

int main() {
    for (int state = 0; state < 256; state++) {
        A[state][state] -= 1.0;
        pair <int, pair <int, int> > pr = nxt(state, 8, 0);
        int L = 8 - pr.second.first;
        if (L) for (int d = 0; d < (1 << L); d++) {
            int nxt = (d << (8 - L)) | pr.first;
            A[state][nxt] += 1.0 / (1 << L);
        }
        A[state][256] -= pr.second.second;
    }
    solveLinear();
    
    int t;
    scanf("%d", &t);
    while (t--) {
        char s[20];
        scanf(" %s", s);
        int num = 0;
        for (int i = 7; i >= 0; i--)
            num = num * 2 + (s[i] - '0');
        printf("%.12lf\n", fabs(A[num][256]));
    }
    return 0;
}