#include<bits/stdc++.h>
using std::cin;
using std::cout;
typedef long long ll;
using db = long double;
const int N = 300;
db a[N][N | 1], b[N][N | 1];
db ans[N | 1];
inline void init() {
    for(int i = 0;i < 1 << 8;++i) {
        int l = 0, r = 0, L = 8, score = 0, state = i;
again:
        for(;l < L;++l) {
            r = l;
            for(;r < L && (state >> r & 1) == (state >> l & 1);) ++ r;
            if(r - l >= 3) {
                score += (r - l) * (r - l);
                state = (state & (1 << l) - 1) | state >> r << l;
                L -= r - l;
                l = 0;
                goto again;
            }
        }
        if(L < 8) {
            for(int p = 0;p < 256;p += 1 << L) {
                a[i][state | p] = 1. / (1 << 8 - L);
            }
            a[i][256] = score;
        }
        a[i][i] -= 1;
    }
    memcpy(b, a, sizeof(a));
}
inline void gs() {
    const db eps = 1e-13;
    for(int i = 0;i < 256;++i) {
        if(fabs(a[i][i]) < eps) {
            for(int j = i + 1;j < 256;++j) {
                if(fabs(a[j][i]) > eps) {
                    std::swap(a[i], a[j]);
                    break;
                }
            }
        }
        for(int j = i + 1;j < 256;++j) {
            const db sub = a[j][i] / a[i][i];
            for(int k = i;k <= 256;++k) {
                a[j][k] -= a[i][k] * sub;
            }
        }
    }
    for(int i = 255;i >= 0;--i) {
        db su = a[i][256];
        for(int j = i + 1;j < 256;++j) su += ans[j] * a[i][j];
        if(fabs(a[i][i]) < eps) exit(1);
        ans[i] = -su / a[i][i];
    }
}
int main() {
    std::ios::sync_with_stdio(false), cin.tie(0);
    init();
    gs();
    int test;
    cin >> test;
    for(int i = 0, o = 0;i < test;++i) {
        o = 0;
        for(int j = 0;j < 8;++j) {
            char c; cin >> c;
            o |= (c & 1) << j;
        }
        cout << std::setprecision(10) << ans[o] << '\n';
    }
}