#include<bits/stdc++.h>
using namespace std;
#define eps (1e-9)

double a[520][520],ans[520];
int id[10][310],len[520],t,tt;
char s[110];

inline int rd()
{
    int x=0;char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar());
    for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
    return x;
}

int num[110],tot;
bool bo[110];

inline int gao(int x,int y)
{
    tot=0;
    for (int i=1;i<=x;i++) num[++tot]=y&1,y>>=1;
    reverse(num+1,num+tot+1);
    for (int i=1;i<=x;i++) bo[i]=false;
    bool flag=false;
    for (int i=1,j;i<=tot;i=j+1)
    {
        for (j=i;j<=x&&num[j]==num[i];j++);j--;
        if (j-i+1>=3) { for (int k=i;k<=j;k++) bo[k]=true;flag=true;break; }
    }
    if (!flag) return 0;
    int h1=0,h2=0;
    for (int i=1;i<=tot;i++) if (!bo[i]) h1++,h2=h2*2+num[i];
    return id[h1][h2];
}

inline void gauss()
{
    for (int i=1;i<=tt;i++)
    {
        int id=0;
        for (int j=i;j<=tt;j++) if (abs(a[j][i])>eps) { id=j;break; }
        swap(a[i],a[id]);
        for (int j=i+1;j<=tt;j++) if (abs(a[j][i])>eps)
        {
            double hh=a[j][i]/a[i][i];
            for (int k=i;k<=tt+1;k++) a[j][k]-=a[i][k]*hh;
        }
    }
    for (int i=tt;i;i--)
    {
        double now=a[i][tt+1];
        for (int j=i+1;j<=tt;j++) now+=ans[j]*a[i][j];
        ans[i]=-now/a[i][i];
    }
}

inline void pre_gao()
{
    for (int i=0;i<=8;i++) for (int j=0;j<(1<<i);j++) id[i][j]=++tt,len[tt]=i;
    for (int i=0;i<=8;i++) for (int j=0;j<(1<<i);j++)
    {
        int now=id[i][j],hh=gao(i,j);
        a[now][now]=-1;
        if (!hh)
        {
            if (i==8) continue;
            double hhh=1.0;
            for (int k=1;k<=8-i;k++) hhh/=2;
            for (int k=0;k<(1<<(8-i));k++)
            {
                a[now][id[8][(j<<(8-i))+k]]+=hhh;
            }
        }
        else
        {
            a[now][hh]=1;
            a[now][tt+1]=(i-len[hh])*(i-len[hh]);
        }
    }
    gauss();
}

int main()
{
    t=rd();pre_gao();
    while (t--)
    {
        scanf("%s",s+1);
        int now=0;
        for (int i=1;i<=8;i++) now=now*2+s[i]-'0';
        printf("%.10lf\n",ans[id[8][now]]);
    }
    return 0;
}