//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#define N 300
#define inf 2147483647
#define LL long long
#define DB double
using namespace std;
int T,A[10],pw[10];char s[10];double f[N],a[N][N];
struct FastIO{
    static const int S=1048576;
    char buf[S],*L,*R;int stk[20],Top;~FastIO(){clear();}
    inline char nc(){return L==R&&(R=(L=buf)+fread(buf,1,S,stdin),L==R)?EOF:*L++;}inline void clear(){fwrite(buf,1,Top,stdout);Top=0;}
    inline void pc(char ch){Top==S&&(clear(),0);buf[Top++]=ch;}inline void endl(){pc('\n');}
    FastIO& operator >> (char&ch){while(ch=nc(),ch==' '||ch=='\n');return *this;}
    template<typename T>FastIO& operator >> (T&ret){
        ret=0;int f=1;char ch=nc();while(ch<'0'||ch>'9'){if(ch=='-')f=-f;ch=nc();}
        while(ch>='0'&&ch<='9'){ret=ret*10+ch-'0';ch=nc();}ret*=f;return *this;
    }
    FastIO& operator >> (char* s){int Len=0;char ch=nc();while(ch!='\n'){*(s+Len)=ch;Len++;ch=nc();}}
    template<typename T>FastIO& operator << (T x){
        if(x<0){pc('-');x=-x;}do{stk[++stk[0]]=x%10;x/=10;}while(x);
        while(stk[0]) pc('0'+stk[stk[0]--]);return *this;
    }
    FastIO& operator << (char ch){pc(ch);return *this;}
    FastIO& operator << (string str){int Len=str.size()-1;for(stk[0]=0;Len>=0;Len--) stk[++stk[0]]=str[Len];while(stk[0]) pc(stk[stk[0]--]);return *this;}
}fin,fout;
int main(){
//    freopen("data.in","r",stdin);
//    freopen("jxc.out","w",stdout);
    pw[0]=1;for(register int i=1;i<=8;i++) pw[i]=pw[i-1]<<1;int S=pw[8];for(register int i=0;i<S;i++){
        for(register int j=7;~j;j--) if((1<<j)&i) A[j]=1;else A[j]=0;int len=0,pos;
        for(register int j=7;~j;j--) {int k=j;while(k>=0&&A[j]==A[k]) k--;k++;if(j-k+1>=3){pos=k,len=j-k+1;break;}j=k;}
        if(!len){a[i][i]=1.0;continue;}int x=0;for(register int j=7;~j;j--) if(j<pos||j>=pos+len) x<<=1,x+=A[j];int now=7-len,L=len,v=len*len;while(now>=0){
            len=0;for(register int j=now;~j;j--) if((1<<j)&x) A[j]=1;else A[j]=0;
            for(register int j=now;~j;j--){int k=j;while(k>=0&&A[j]==A[k]) k--;k++;if(j-k+1>=3){pos=k,len=j-k+1;break;}j=k;}
            if(!len) break;x=0;for(register int j=now;~j;j--) if(j<pos||j>=pos+len) x<<=1,x+=A[j];v+=len*len,now-=len,L+=len;
        }
//        for(register int j=7;~j;j--) if((1<<j)&i) cout<<1;else cout<<0;cout<<' ';cout<<pos<<' '<<len<<' ';
//        for(register int j=7;~j;j--) if((1<<j)&x) cout<<1;else cout<<0;cout<<'\n';
        a[i][S]=v,a[i][i]=1.0;for(register int j=0;j<pw[L];j++) if(((x<<L)|j)==i) a[i][i]-=1.0/pw[L];else a[i][(x<<L)|j]=-1.0/pw[L];
    }
    for(register int i=0;i<S;++i){
        int Max=i;for(register int j=i+1;j<S;++j) if(fabs(a[j][i])>fabs(a[Max][i])) Max=j;
        for(register int j=0;j<=S;++j) swap(a[i][j],a[Max][j]);for(register int j=0;j<S;++j) if(i^j)
        {double tmp=a[j][i]/a[i][i];for(register int k=i+1;k<=S;++k) a[j][k]-=a[i][k]*tmp;}
    }
    for(register int i=0;i<S;++i) f[i]=a[i][S]/a[i][i];cin>>T;while(T--){scanf("%s",s+1);int res=0;for(register int i=1;i<=8;i++) res<<=1,res+=s[i]-'0';printf("%0.12lf\n",f[res]);} return 0;
}