int n, m;
vector <Point> a, b;

double distanceToSegment(Point a, Point b, Point c)
{
    Point vab = b - a;
    Point vac = c - a;
    if (vab % vac <= 0)
        return c.distancetoPoint(a);
    Point vba = a - b;
    Point vbc = c - b;
    if (vba % vbc <= 0)
        return c.distancetoPoint(b);
    Line l = Line(a, b);
    return abs(l.distanceFromPoint(c));
}

ll sqrdst(Point a, Point b)
{
    return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}

/*
    CASE 1           CASE 2           CASE 3
    .A......         ......A.         \.......
 val/-\-----      val-----/-\         .\...../
    ...\.../         \.../...         ..\.../.
    ....\./.         .\./....         ...\./..
    .....V..         ..V.....         ....V...
    d[0] < d[1]      d[0] > d[1]      d[0] > d[1] && d[lst] > d[lst - 1]
*/


int search(int x, int CASE, double val)
{
    if (CASE == 1)
    {
        int id = 0;
        double ans = a[x].sqrdst(b[0]);
        int l = 0, r = m - 1;
        while (r - l > 1)
        {
            int MID = l + r >> 1;
            double nval = a[x].sqrdst(b[MID]);
            if (nval >= val)
                l = MID;
            else
            {
                double nxtval = a[x].sqrdst(b[MID + 1]);
                if (nval >= nxtval)
                    l = MID;
                else
                    r = MID;
            }
        }
        for (int i = l; i <= r; ++i)
            if (ans > a[x].sqrdst(b[i]))
                ans = a[x].sqrdst(b[i]), id = i;
        return id;
    }
    if (CASE == 2)
    {
        int id = 0;
        double ans = a[x].sqrdst(b[0]);
        int l = 0, r = m - 1;
        while (r - l > 1)
        {
            int MID = l + r >> 1;
            double nval = a[x].sqrdst(b[MID]);
            if (nval >= val)
                r = MID;
            else
            {
                double nxtval = a[x].sqrdst(b[MID + 1]);
                if (nval >= nxtval)
                    l = MID;
                else
                    r = MID;
            }
        }
        for (int i = l; i <= r; ++i)
            if (ans > a[x].sqrdst(b[i]))
                ans = a[x].sqrdst(b[i]), id = i;
        return id;
    }
    if (CASE == 3)
    {
        int l = 0, r = m - 1;
        while (r - l > 3)
        {
            int m1 = l + (r - l) / 3;
            int m2 = r - (r - l) / 3;
            if (a[x].sqrdst(b[m1]) < a[x].sqrdst(b[m2]))
                r = m2;
            else
                l = m2;
        }
        int id = l;
        double ans = a[x].sqrdst(b[l]);
        for (int i = l + 1; i <= r; ++i)
            if (ans > a[x].sqrdst(b[i]))
                ans = a[x].sqrdst(b[i]), id = i;
        return id;
    }
}

double get()
{
    double ans = LINF;
    if ((ll)n * (ll)m >= 1e6)
    {
        forn(i, n)
        {
            double d0 = a[i].sqrdst(b[0]);
            double d1 = a[i].sqrdst(b[1]);
            double dm = a[i].sqrdst(b.back());
            double dm1 = a[i].sqrdst(b[m - 2]);
            bool cs1 = d0 <= d1;
            bool cs2 = d0 >= d1;
            bool cs3 = d0 >= d1 && dm1 <= dm;
            int id;
            if (cs3)
                id = search(i, 3, 228);
            else
                if (cs1)
                    id = search(i, 1, d0);
                else
                    id = search(i, 2, dm);
            int id1 = (id + m - 1) % m;
            if (a[i].sqrdst(b[id1]) > a[i].sqrdst(b[(id + 1) % m]))
                id1 = (id + 1) % m;
            ans = min(ans, distanceToSegment(b[id], b[id1], a[i]));
        }
    }
    else
    {
        forn(i, n)
        {
            forn(j, m)
                ans = min(ans, distanceToSegment(b[j], b[(j + 1) % m], a[i]));
        }
    }
    return ans;
}

int solve()
{
    scanf("%d", &n);
    a.resize(n);
    forn(i, n)
        scanf("%lf %lf", &a[i].x, &a[i].y);
    scanf("%d", &m);
    b.resize(m);
    forn(i, m)
        scanf("%lf %lf", &b[i].x, &b[i].y);
    double ans = get();
    swap(a, b);
    swap(n, m);
    ans = min(ans, get());
    cout.precision(15);
    cout << fixed << ans;
    return 0;
}