#include <bits/stdc++.h>
using namespace std;
const int N = 1e4 + 5, M = 11;
vector<int> vec[N];
inline void init()
{
    for (int i = 2; i < N; i++)
    {
        int x = i;
        for (int j = 2; j * j <= x; j++)
        {
            while (x % j == 0)
                vec[i].push_back(j), x /= j;
        }
        if (x > 1) vec[i].push_back(x);
    }
}
char s[N];
int n;
int x[M][1 << M], y[M][1 << M];
int f[M][N], g[M][N];
int now[M];
double p[M];
inline void update(int t, int x, int y, int v)
{
    f[t][1] -= v;
    f[t][x + 1] += v;
    f[t][y + 1] += v;
    f[t][x + y + 2] -= v;
}
inline int get(int l, int r)
{
    int tmp = 0;
    for (int i = l; i <= r; i++) tmp = (tmp << 1) + (s[i] - 'A');
    return tmp;
}
int main()
{
    init();
    int T;
    scanf("%d", &T);
    while (T--)
    {
        scanf("%s", s + 1);
        n = strlen(s + 1);
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= 10; j++)
            {
                if (i <= j) continue;
                int S = get(i - j, i - 1), p = x[j][S], q = y[j][S];
                int c = s[i] - 'A';
                update(j, p, q, -1);
                update(j, p + 1 - c, q + c, 1);
                x[j][S] += 1 - c;
                y[j][S] += c;
            }
        for (int j = 1; j <= 10; j++)
        {
            for (int i = 2; i <= n + 1; i++) f[j][i] += f[j][i - 1];
            f[j][2] += min(n, j);
            for (int i = 2; i <= n + 1; i++)
                for (int k = 0; k < vec[i].size(); k++) g[j][vec[i][k]] += f[j][i];
        }
        for (int i = 2; i <= n + 1; i++)
        {
            int mn = 1e9;
            for (int j = 1; j <= 10; j++) mn = min(mn, g[j][i]);
            for (int j = 1; j <= 10; j++) g[j][i] -= mn;
        }
        for (int j = 1; j <= 10; j++)
        {
            p[j] = 0.1;
            now[j] = 2;
            while (g[j][now[j]] == 0 && now[j] <= n) now[j]++;
        }
        for (;;)
        {
            bool flag = true;
            for (int j = 1; j <= 10; j++) if (now[j] <= n) flag = false;
            if (flag) break;
            double mx = -1;
            int id;
            for (int j = 1; j <= 10; j++) if (now[j] <= n && p[j] > mx)
                mx = p[j], id = j;
            p[id] /= (double) now[id];
            double sum = 0;
            for (int j = 1; j <= 10; j++) sum += p[j];
            for (int j = 1; j <= 10; j++) p[j] /= sum;
            g[id][now[id]]--;
            while (g[id][now[id]] == 0 && now[id] <= n) now[id]++;
        }
        double ans = 0;
        for (int j = 1; j <= 10; j++)
        {
            double tmp = 0;
            if (n <= j) tmp = 1.0 / 2.0;
            else
            {
                int S = get(n - j + 1, n), p = x[j][S], q = y[j][S];
                tmp = (double) (p + 1) / (double) (p + q + 2);
            }
            ans += p[j] * tmp;
        }
        printf("%.15lf\n", ans);
        memset(x, 0, sizeof(x));
        memset(y, 0, sizeof(y));
        for (int j = 1; j <= 10; j++)
            for (int i = 0; i <= n + 1; i++) f[j][i] = g[j][i] = 0;
        memset(now, 0, sizeof(now));
        memset(p, 0, sizeof(p));
    }
    return 0;
}