#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define _for(i,a,b) for(register int (i)=(a);(i)<=(b);(i)++)
#define For(i,a,b) for(register int (i)=(a);(i)>=(b);(i)--)
#define INF 0x7fffffff
#define il inline
#define rg register
const int N=515;
double a[N][N];
int pr[N],top[N];
#define eps 1e-13
#define id(x,i) (((x)&(1<<(i)))>>(i))
#define ins(x,i,p) x+=((p)<<(i))-(id(x,i)<<(i));
int qwq(){
    _for(t,0,255){
        int x=t;
        int sum[2];
        sum[0]=sum[1]=0;
        int tmp=0;
        a[t][256]=0;
        top[t]=7;
        _for(i,0,top[t]){
            ++sum[id(x,i)];
            sum[id(x,i)^1]=0;
            if(sum[id(x,i)]==3){
                int m=top[t];
                tmp=i;
                while(id(x,tmp)==id(x,i) and tmp<=m) ++tmp;
                tmp--;
                for(int k=1;k<=m-tmp;++k) ins(x,i-3+k,id(x,tmp+k));
                for(int k=i-tmp+m-2;k<=m;++k) ins(x,k,0);
                pr[t]=x, top[t]=i-tmp+m-3, a[t][256]-=(m-top[t])*(m-top[t]), i=-1, sum[0]=sum[1]=0;
            }
        }
    }
    _for(i,0,255){
        int sum=0;
        a[i][i]=-1;
        if(top[i]!=7){
            a[i][i]=0;
            _for(j,0,255){
                int bo=1;
                _for(k,0,top[i]) if(id(pr[i],k)!=id(j,k)) bo&=0;
                if(bo){
                    sum++;
                    a[i][j]+=1.00;
                }
            }
            a[i][i]-=sum, a[i][256]=a[i][256]*sum;
        }
    }
}
const int n=256;
void qaq(){
    int r=0;
    int t;
    _for(c,0,n-1){
        t=r;
        _for(i,r,n-1) if (fabs(a[i][c])>fabs(a[t][c])) t=i;
        if(fabs(a[t][c])<eps) continue;
        _for(i,c,n) swap(a[t][i], a[r][i]);
        For(i,n,c) a[r][i]/=a[r][c];
        _for(i,r+1,n-1) if(fabs(a[i][c])>eps) For(m,n,c) a[i][m]-= a[r][m]*a[i][c];
        r++;
    }
    For(i,n-1,0) _for(m,i+1,n-1) a[i][n]-= a[i][m]*a[m][n];
}
int main(){
    qwq(), qaq();
    rg int q; scanf("%d",&q);
    _for(i,1,q){
        int x=0;
        _for(j,0,7){
            char c=getchar();
            while(c!='0' and c!='1') c=getchar();
            ins(x,j,c-'0');
        }
        printf("%.12lf\n",a[x][256]);        
    }
    return 0;
}