#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>

using namespace std;
using namespace chrono;

#define endl '\n'
#define debug(x) cerr << #x << ": " << x << endl
// #define int long long

// #pragma comment(linker, "/STACK:200000000")

// #pragma GCC optimize("Ofast,unroll-loops")
// #pragma GCC target("avx2,tune=native")

const long long mod = 1e9 + 7;
// const long long mod = 998244353;
// const long long mod = 786433;
const long double eps = 1e-9;
const long double pi = acosl(-1.0);
mt19937_64 engine;
mt19937 engine32;

inline long long sqr(long long x)
{
    return x * x;
}

inline double fsqr(double x)
{
    return x * x;
}

long long binpow(long long x, long long y)
{
    if (y == 0)
        return 1;
    if (y == 1)
        return x;

    long long f = binpow(x, y / 2);
    if (y % 2 == 0)
        return (f * f) % mod;
    else
        return (((f * f) % mod) * x) % mod;
}

long long gcd(long long x, long long y)
{
    if (x == 0)
        return y;
    else
        return gcd(y % x, x);
}

long long lcm(long long x, long long y)
{
    return x / gcd(x, y) * y;
}

struct Vector
{
    long double x, y;

    Vector operator+(Vector v1) const
    {
        return {x + v1.x, y + v1.y};
    }

    Vector operator-(Vector v1) const
    {
        return {x - v1.x, y - v1.y};
    }

    Vector operator*(long double l) const
    {
        return {x * l, y * l};
    }

    Vector operator/(long double l) const
    {
        return {x / l, y / l};
    }

    bool operator==(Vector v1)
    {
        if (abs(x - v1.x) <= eps && abs(y - v1.y) <= eps)
        {
            return true;
        }
        else
        {
            return false;
        }
    }

    bool operator!=(Vector v1)
    {
        if (abs(x - v1.x) > eps || abs(y - v1.y) > eps)
        {
            return true;
        }
        else
        {
            return false;
        }
    }

    long double len()
    {
        return sqrt(x * x + y * y);
    }

    void norm()
    {
        long double l = len();

        x /= len();
        y /= len();
    }

    void set(long double f)
    {
        norm();

        x *= f;
        y *= f;
    }
};

struct Line
{
    long double a, b, c;
};

#define Point Vector

long double dot(Vector v1, Vector v2)
{
    return v1.x * v2.x + v1.y * v2.y;
}

long double cross(Vector v1, Vector v2)
{
    return v1.x * v2.y - v1.y * v2.x;
}

Vector make_vector(Point p1, Point p2)
{
    return {p2.x - p1.x, p2.y - p1.y};
}

Line make_line(Point p1, Point p2)
{
    long double a = p1.y - p2.y;
    long double b = p2.x - p1.x;
    long double c = -b * p1.y - a * p1.x;
    Vector v = {a, b};
    long double dist = v.len();
    return {a / dist, b / dist, c / dist};
}

Point intersec(Line l1, Line l2)
{
    if (l1.a * l2.b - l2.a * l1.b == 0 || l1.a * l2.b - l2.a * l1.b == 0)
    {
        return {(long double)LLONG_MAX, (long double)LLONG_MAX};
    }
    else
    {
        return {-(l1.c * l2.b - l2.c * l1.b) / (l1.a * l2.b - l2.a * l1.b),
                -(l2.c * l1.a - l1.c * l2.a) / (l1.a * l2.b - l2.a * l1.b)};
    }
}

class Sector
{
  public:
    int x, y, r;
    double s, a;

    bool inside(double x, double y)
    {
        if (fabs(x - this->x) < eps && fabs(y - this->y) < eps)
            return true;
        double l = s;
        double r = s + a;
        double angle = atan2(y - this->y, x - this->x);
        if (angle < l)
            angle += 2 * pi;
        if (angle < l)
            angle += 2 * pi;

        double rad = sqrt(fsqr(this->x - x) + fsqr(this->y - y));
        return rad - eps < this->r && angle + eps >= l && angle - eps <= r;
    }
};

bool onSegment(Point p, Point p1, Point p2)
{
    return ((p.x >= p1.x && p.x <= p2.x) || (p.x <= p1.x && p.x >= p2.x)) &&
           ((p.y >= p1.y && p.y <= p2.y) || (p.y <= p1.y && p.y >= p2.y));
}

inline vector<pair<double, double>> getPts(double x, Sector sec)
{
    if (fabs(x - sec.x) >= 100)
        return {};

    vector<double> ys;
    double r2 = sec.r * sec.r;
    double dx2 = (sec.x - x) * (sec.x - x);
    double sqrt_val = sqrt(r2 - dx2);

    double p1 = sec.y + sqrt_val;
    if (sec.inside(x, p1))
        ys.push_back(p1);

    double p2 = sec.y - sqrt_val;
    if (sec.inside(x, p2))
        ys.push_back(p2);

    if (fabs(x - sec.x) < eps) {
        if (ys.size() == 1) {
            ys.push_back(sec.y);
        }
        sort(ys.begin(), ys.end());
        vector<pair<double, double>> ret;
        for (size_t i = 0; i < ys.size(); i += 2) {
            ret.push_back({ys[i], ys[i + 1]});
        }
        return ret;
    }

    Point r1 = {sec.r * cos(sec.s) + sec.x, sec.r * sin(sec.s) + sec.y};
    Point r2 = {sec.r * cos(sec.s + sec.a) + sec.x, sec.r * sin(sec.s + sec.a) + sec.y};
    Point mid = {sec.x, sec.y};
    Line l1 = make_line(mid, r1);
    Line l2 = make_line(mid, r2);
    Line l3 = make_line({x, 0}, {x, 1});
    Point intersec1 = intersec(l1, l3);
    Point intersec2 = intersec(l2, l3);

    if (onSegment(intersec1, mid, r1))
        ys.push_back(intersec1.y);
    if (onSegment(intersec2, mid, r2))
        ys.push_back(intersec2.y);

    sort(ys.begin(), ys.end());
    vector<pair<double, double>> ret;
    for (size_t i = 0; i < ys.size(); i += 2) {
        ret.push_back({ys[i], ys[i + 1]});
    }
    return ret;
}

inline bool joint(pair<double, double> s1, pair<double, double> s2)
{
    return !(s1.first > s2.second || s1.second < s2.first);
}

inline pair<double, double> merge(pair<double, double> s1, pair<double, double> s2)
{
    return {min(s1.first, s2.first), max(s1.second, s2.second)};
}

void insert(set<pair<double, double>> &s, pair<double, double> p)
{
    auto it = s.lower_bound(p);
    if (it != s.begin() && joint(*prev(it), p))
    {
        --it;
    }

    while (it != s.end() && joint(*it, p))
    {
        p = merge(p, *it);
        it = s.erase(it);
    }

    s.insert(p);
}

class Event
{
  public:
    int qnum;
    double x;
    int num;
    bool open;
    Event(int qnum, double x, int num, bool open)
    {
        this->qnum = qnum;
        this->x = x;
        this->num = num;
        this->open = open;
    }
    bool operator<(Event &other) const
    {
        return x < other.x;
    }
};

class Q
{
  public:
    int n;
    vector<Sector> v;
    double ans;

    Q(int on, vector<Sector> ov, double oans) : n(on), v(ov), ans(oans)
    {
    }
};

void task()
{
    vector<Q> qs;
    int n;
    vector<Event> events;
    while (cin >> n)
    {
        qs.push_back(Q(n, vector<Sector>(), 0));
        vector<Sector> v(n);
        for (int i = 0; i < n; ++i)
        {
            cin >> v[i].x >> v[i].y >> v[i].r >> v[i].s >> v[i].a;
            events.push_back(Event((int)qs.size() - 1, (double)v[i].x - v[i].r, (int)i, true));
            events.push_back(Event((int)qs.size() - 1, (double)v[i].x + v[i].r, (int)i, false));
        }
        qs.back().v = v;
    }

    sort(events.begin(), events.end());
    int cur = 0;

    vector<unordered_set<int>> opened(qs.size());
    int balance = 0;

    double step = 4e-4;
    for (double i = events[0].x; i < events.back().x; i += step)
    {
        while (cur != events.size() && events[cur].x <= i)
        {
            if (events[cur].open)
            {
                if (opened[events[cur].qnum].empty())
                    ++balance;
                opened[events[cur].qnum].insert(events[cur].num);
            }
            else
            {
                opened[events[cur].qnum].erase(events[cur].num);
                if (opened[events[cur].qnum].empty())
                    --balance;
            }
            ++cur;
        }

        if (balance == 0)
        {
            if (cur == events.size())
                break;
            i = events[cur].x;
            i -= step;
            continue;
        }

        for (int j = 0; j < qs.size(); ++j)
        {
            if (opened[j].empty())
                continue;
            set<pair<double, double>> segs;
            for (auto sect : opened[j])
            {
                vector<pair<double, double>> ns = getPts(i, qs[j].v[sect]);
                for (auto it : ns)
                {
                    insert(segs, it);
                }
            }

            double calc = 0;
            for (auto it : segs)
            {
                calc += (it.second - it.first) * step;
            }
            qs[j].ans += calc;
        }
    }

    for (int i = 0; i < qs.size(); ++i)
    {
        cout << qs[i].ans << endl;
    }
}

signed main()
{
    // freopen("in.txt", "r", stdin);
    // freopen("out.txt", "w", stdout);
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    // engine.seed(1);
    engine.seed(58);
    // engine.seed(time(0));
    engine32.seed(58);
    cout << fixed << setprecision(15);

    bool multitest = 0;
    int t = 1;
    if (multitest)
        cin >> t;
    while (t--)
        task();

    return 0;
}

answer.code: In function ‘std::vector<std::pair<double, double> > getPts(double, Sector)’:
answer.code:236:11: error: conflicting declaration ‘Vector r2’
  236 |     Point r2 = {sec.r * cos(sec.s + sec.a) + sec.x, sec.r * sin(sec.s + sec.a) + sec.y};
      |           ^~
answer.code:211:12: note: previous declaration as ‘double r2’
  211 |     double r2 = sec.r * sec.r;
      |            ^~
answer.code:237:22: warning: narrowing conversion of ‘sec.Sector::x’ from ‘int’ to ‘long double’ [-Wnarrowing]
  237 |     Point mid = {sec.x, sec.y};
      |                  ~~~~^
answer.code:237:29: warning: narrowing conversion of ‘sec.Sector::y’ from ‘int’ to ‘long double’ [-Wnarrowing]
  237 |     Point mid = {sec.x, sec.y};
      |                         ~~~~^
answer.code:239:30: error: could not convert ‘r2’ from ‘double’ to ‘Vector’
  239 |     Line l2 = make_line(mid, r2);
      |                              ^~
      |                              |
      |                              double
answer.code:246:35: error: could not convert ‘r2’ from ‘double’ to ‘Vector’
  246 |     if (onSegment(intersec2, mid, r2))
      |                                   ^~
      |                                   |
      |                                   double