#include<bits/stdc++.h>
typedef long long ll;
ll gi(){
    ll x=0,f=1;
    char ch=getchar();
    while(!isdigit(ch))f^=ch=='-',ch=getchar();
    while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
    return f?x:-x;
}
std::mt19937 rnd(time(NULL));
#define rand rnd
#define pr std::pair<int,int>
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
template<class T>void cxk(T&a,T b){a=a>b?a:b;}
template<class T>void cnk(T&a,T b){a=a<b?a:b;}
#ifdef mod
int pow(int x,int y){
    int ret=1;
    while(y){
        if(y&1)ret=1ll*ret*x%mod;
        x=1ll*x*x%mod;y>>=1;
    }
    return ret;
}
template<class Ta,class Tb>void inc(Ta&a,Tb b){a=a+b>=mod?a+b-mod:a+b;}
template<class Ta,class Tb>void dec(Ta&a,Tb b){a=a>=b?a-b:a+mod-b;}
#endif
char str[10];
bool solve(int&S,double&score){
    static char s[11];
    int i,st,lst,len;
    for(i=0,st=0,lst=-1,len=0;i<9;++i){
        s[i]=S>>i&1;
        if(!st){
            if(s[i])st=1;
        }else if(s[i]==lst){
            ++len;
        }else{
            if(len>=3){
                score+=len*len;
                S=((S<<len)&((1<<i)-1))|(S&~((1<<i)-1));
                return 1;
            }
            lst=s[i],len=1;
        }
    }
    if(len>=3){
        score+=len*len;
        S=(S<<len&((1<<9)-1))|(S&~((1<<9)-1));
        return 1;
    }
    return 0;
}
int to[1<<9];double score[1<<9];
double A[1<<8|11][1<<8|11];
void output(int x,int s=0){
    int lim=s?8:9;
    for(int i=0;i<lim;++i){
        if(x>>i&1){
            if(!s)s=1;
            else putchar('1');
        }else if(s)putchar('0');
    }
}
int main(){
#ifdef LOCAL
    freopen("in.in","r",stdin);
    //freopen("out.out","w",stdout);
#endif
    for(int i=1;i<1<<9;++i){
        to[i]=i;while(solve(to[i],score[i]));
    }
    int N=1<<8;
    for(int i=0;i<N;++i){
        A[i][i]=1;A[i][N]=score[i<<1|1];
        int t=to[i<<1|1],c=t&-t;
        if(c>1)for(int j=0;j<c;++j){
            A[i][((t/c)>>1)|(j*N/c)]-=1./c;
            //output(i,1);putchar(' ');output(((t/c)>>1)|(j*c),1);putchar('\n');
        }
    }
    for(int i=0;i<N;++i){
        if(fabs(A[i][i])<1e-8)
            for(int j=i+1;j<N;++j)
                if(fabs(A[j][i])>1e-8){std::swap(A[i],A[j]);break;}
        for(int j=i+1;j<N;++j)
            for(int k=N;k>i;--k)
                A[j][k]-=A[i][k]*(A[j][i]/A[i][i]);
    }
    for(int i=N-1;~i;--i){
        for(int j=i+1;j<N;++j)A[i][N]-=A[i][j]*A[j][N];
        A[i][N]/=A[i][i];
    }
    int T=gi();
    while(T--){
        scanf("%s",str);
        int S=0;for(int i=0;i<8;++i)S|=str[i]-'0'<<i;
        printf("%.10lf\n",A[S][N]);
    }
    return 0;
}