#include<bits/stdc++.h>
#define eps 1e-6
#define Ms(a,b) memset(a,b,sizeof a)
#define db(x) cerr<<#x<<"="<<x<<endl;
#define db2(x,y) cerr<<#x<<"="<<x<<" "<<#y<<"="<<y<<endl;
#define db3(x,y,z) cerr<<#x<<"="<<x<<" "<<#y<<"="<<y<<" "<<#z<<"="<<z<<endl;
using namespace std;
int rd(){
    int res=0,c,f=0;
    while(!isdigit(c=getchar()))f=c=='-';
    do res=(res<<1)+(res<<3)+(c^48);
    while(isdigit(c=getchar()));
    return f?-res:res;
}
double a[1<<8][1<<8|5];
int x[10];
bool solve(int &n,double &res){
    int cnt=1;
    for(int i=2;i<=n+1;i++){
        if(i!=n+1&&x[i]==x[i-1])++cnt;
        else{
            if(cnt>=3){
                res+=cnt*cnt;
                for(int j=i-cnt;j<=n-cnt;j++)x[j]=x[j+cnt];
                n-=cnt;
                return 1;
            }
            cnt=1;
        }
    }
    return 0;
}
int main(){
    for(int i=0;i<1<<8;i++){
        for(int j=0;j<8;j++)x[j+1]=i>>j&1;
        int n=8;
        while(solve(n,a[i][1<<8]));
        //double p=pow(1<<(8-n),-1);
        if(n!=8)
            for(int j=0;j<1<<(8-n);j++){
                for(int k=0;k<8-n;k++)x[n+k+1]=j>>k&1;
                int to=0;
                for(int k=8;k>=1;k--)to=to<<1|x[k];
                a[i][to]=-1;
            }
        a[i][i]+=1<<(8-n);
        a[i][1<<8]*=1<<(8-n);
    }
    for(int i=0;i<1<<8;i++){
        for(int j=1<<8;j>=i;j--)a[i][j]/=a[i][i];
        for(int j=0;j<1<<8;j++)if(i!=j){
            if(abs(a[j][i])>eps)
                for(int k=1<<8;k>=i;k--)a[j][k]-=a[j][i]*a[i][k];
        }
    }
    int T=rd();
    while(T--){
        char s[20];
        scanf("%s",s+1);
        int x=0;
        for(int i=8;i>=1;i--)x=x<<1|(s[i]-'0');
        //for(int i=1;i<=8;i++)x=x<<1|(s[i]-'0');
        printf("%.12lf\n",a[x][1<<8]);
    }
    return 0;
}