#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pair

using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;

double prob[265][265];
int len, val[15], csum;
bool elim()
{
    rep(i, len - 2) if(val[i] == val[i + 1] && val[i] == val[i + 2]) {
        int j = i;
        while(j < len && val[j] == val[i]) j ++;
        for(int k = j; k < len; k ++) val[k - j + i] = val[k];
        len -= j - i;
        csum += (j - i) * (j - i);
        return true;
    }
    return false;
}

double dp[265];
bool vis[265];
vector<int> ord, chv;
void dfs0(int v)
{
    vis[v] = true;
    rep(i, 256) if(!vis[i] && prob[i][v]) dfs0(i);
    ord.push_back(v);
}
void dfs1(int v)
{
    vis[v] = true; chv.push_back(v);
    rep(i, 256) if(!vis[i] && prob[v][i]) dfs1(i);
}

bool inc[265];
double mat[265][265];
const double EPS = 1e-8;
double absv(double x)
{
    return x < 0 ? -x : x;
}
void calc()
{
    int l = chv.size();
    rep(i, 256) inc[i] = false;
    rep(i, l) inc[chv[i]] = true;
    
    rep(i, l) mat[i][l] = dp[chv[i]];
    rep(i, l) rep(j, 256) if(prob[chv[i]][j] && !inc[j]) mat[i][l] += dp[j] * prob[chv[i]][j];
    rep(i, l) rep(j, l) mat[i][j] = (i == j) - prob[chv[i]][chv[j]];
    
    rep(i, l) {
        int ci = -1;
        for(int j = i; j < l; j ++) if(absv(mat[j][i]) > EPS) {
            ci = j; break;
        }
        if(ci == -1) return;
        if(ci != i) for(int j = i; j <= l; j ++) swap(mat[i][j], mat[ci][j]);
        double cp = 1.0 / mat[i][i];
        for(int j = i + 1; j < l; j ++) {
            for(int k = i + 1; k <= l; k ++) mat[j][k] -= mat[j][i] * cp * mat[i][k];
            mat[j][i] = 0;
        }
    }
    
    for(int i = l - 1; i >= 0; i --) {
        dp[chv[i]] = mat[i][l];
        for(int j = i + 1; j < l; j ++) dp[chv[i]] -= mat[i][j] * dp[chv[j]];
        dp[chv[i]] /= mat[i][i];
    }
}

char buf[15];
int main()
{
    rep(i, 256) {
        csum = 0; len = 8;
        rep(j, 8) val[j] = i >> j & 1;
        while(elim()) ;
        dp[i] = csum;
        double cp = 1.0 / (1 << (8 - len));
        int cm = 0;
        rep(j, len) cm |= val[j] << j;
        rep(j, 1 << (8 - len)) prob[i][cm | j << len] = cp;
    }
    
    rep(i, 256) if(!vis[i]) dfs0(i);
    rep(i, 256) vis[i] = false;
    reverse(ord.begin(), ord.end());
    rep(i, 256) if(!vis[ord[i]]) {
        chv.clear();
        dfs1(ord[i]);
        calc();
    }
    
    int T;
    scanf("%d", &T);
    while(T --) {
        scanf("%s", buf);
        int x = 0;
        rep(i, 8) x |= (buf[i] - '0') << i;
        printf("%.10lf\n", dp[x]);
    }
    return 0;
}