#include <bits/stdc++.h>
using namespace std;
const int N = 260;
const double eps = 1e-8;

double a[N][N];
double x[N];
 
int gauss(int equ,int var){
    for(int i=0;i<=var;i++)x[i]=0;
    int col=0;
    int row;
    for(row=0;row<equ&&col<var;row++,col++){
        int maxRow=row;
        for(int i=row+1;i<equ;i++){
            if(abs(a[i][col])>abs(a[maxRow][col]))
                maxRow=i;
        }
        if(maxRow!=row){
            for(int j=row;j<var+1;j++)
                swap(a[row][j],a[maxRow][j]);
        }
        if(abs(a[row][col])<eps){
            row--;
            continue;
        }
 
        for(int i=row+1;i<equ;i++){
            if(abs(a[i][col]) > eps){
                double temp=a[i][col]/a[row][col];
                for(int j=col;j<var+1;j++) 
                    a[i][j]-=a[row][j]*temp;
                a[i][col]=0;
            }
        }
    }
 
    for(int i=row;i<equ;i++)
        if(abs(a[i][col])>eps)
            return -1;
 
    int temp=var-row;
    if(row<var)
        return temp;
 
    for(int i=var-1;i>=0;i--){
        double temp=a[i][var];
        for(int j=i+1;j<var;j++)
            temp-=a[i][j]*x[j];
        x[i]=temp/a[i][i];
    }
    return 0;
}

int score;
bool reduce(vector<int> &b)
{
    for (int i = 0; i + 2 < (int)b.size(); ++i)
    {
        if (b[i] != b[i + 1] || b[i] != b[i + 2]) continue;
        int val = b[i], cnt = 0;
        vector<int>::iterator it = b.begin() + i;
        while (it != b.end() && *it == val)
        {
            it = b.erase(it);
            ++cnt;
        }
        score += cnt * cnt;
        return true;
    }
    return false;
}

void init(int n)
{
    vector<int> b;
    b.reserve(8);
    for (int i = 0; i < 8; ++i)
        b.push_back(n >> (7 - i) & 1);
    score = 0;
    while (reduce(b)) ;
    a[n][n] = 1;
    a[n][256] = score;
    if (b.size() == 8) return;
    int num = 0;
    for (int x : b) num = num << 1 | x;
    num <<= 8 - (int)b.size();
    int end = 1 << (8 - (int)b.size());
    double val = 1.0 / end;
    for (int i = 0; i < end; ++i)
        a[n][num + i] -= val;
}

int main()
{
    for (int i = 0; i < 256; ++i) init(i);
    assert(!gauss(256, 256));
    int T;
    char s[11];
    scanf("%d", &T);
    while (T--)
    {
        scanf("%s", s);
        int n = 0;
        for (int i = 0; i < 8; ++i)
            n = n << 1 | (s[i] - '0');
        printf("%.11f\n", x[n]);
    }
    return 0;
}