#include <bits/stdc++.h>

using namespace std;

#define int long long
// #define double long double
#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define FORR(i, a, b) for(int i = (a); i > (b); --i)
#define REP(i, n) for(int i = 0; i < (n); ++i)
#define REPR(i, n) for(int i = n; i >= 0; i--)
#define FOREACH(x, a) for(auto &(x) : (a))
#define VECCIN(x)                                                              \
    for(auto &youso_ : (x)) cin >> youso_
#define bitcnt(x) __builtin_popcount(x)
#define lbit(x) __builtin_ffsll(x)
#define rbit(x) __builtin_clzll(x)
#define fi first
#define se second
#define All(a) (a).begin(), (a).end()
#define rAll(a) (a).rbegin(), (a).rend()
#define cinfast() cin.tie(0), ios::sync_with_stdio(false)
#define PERM(c)                                                                \
    sort(All(c));                                                              \
    for(bool cp = true; cp; cp = next_permutation(All(c)))
#define MKORDER(n)                                                             \
    vector<int> od(n);                                                         \
    iota(All(od), 0LL);

template <typename T = long long> inline T IN() {
    T x;
    cin >> x;
    return (x);
}
inline void CIN() {}
template <class Head, class... Tail>
inline void CIN(Head &&head, Tail &&... tail) {
    cin >> head;
    CIN(move(tail)...);
}
#define CCIN(...)                                                              \
    char __VA_ARGS__;                                                          \
    CIN(__VA_ARGS__)
#define DCIN(...)                                                              \
    double __VA_ARGS__;                                                        \
    CIN(__VA_ARGS__)
#define LCIN(...)                                                              \
    long long __VA_ARGS__;                                                     \
    CIN(__VA_ARGS__)
#define SCIN(...)                                                              \
    string __VA_ARGS__;                                                        \
    CIN(__VA_ARGS__)
#define Printv(v)                                                              \
    {                                                                          \
        FOREACH(x, v) { cout << x << " "; }                                    \
        cout << "\n";                                                          \
    }
template <typename T = string> inline void eputs(T s) {
    cout << s << "\n";
    exit(0);
}
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val) {
    std::fill((T *)array, (T *)(array + N), val);
}

// generic lambdas
template <typename F>
#if defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
[[nodiscard]]
#elif defined(__GNUC__) && (__GNUC__ > 3 || __GNUC__ == 3 && __GNUC_MINOR__ >= 4)
__attribute__((warn_unused_result))
#endif // defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
    static inline constexpr decltype(auto)
    fix(F &&f) noexcept {
    return [f = std::forward<F>(f)](auto &&... args) {
        return f(f, std::forward<decltype(args)>(args)...);
    };
}

template <typename T> using PQG = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using PQ = priority_queue<T>;

typedef long long ll;
typedef vector<ll> VL;
typedef vector<VL> VVL;
typedef pair<ll, ll> PL;
typedef vector<PL> VPL;
typedef vector<bool> VB;
typedef vector<double> VD;
typedef vector<string> VS;

const int INF = 1e9;
const int MOD = 1e9 + 7;
// const int MOD = 998244353;
const ll LINF = 1e18;
const double PI = atan(1.0) * 4.0;
const ll dw[] = {1, 1, 0, -1, -1, -1, 0, 1};
const ll dh[] = {0, 1, 1, 1, 0, -1, -1, -1};
#define PI 3.141592653589793238

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

// COUNTER CLOCKWISE
static const int CCW_COUNTER_CLOCKWISE = 1;
static const int CCW_CLOCKWISE = -1;
static const int CCW_ONLINE_BACK = 2;
static const int CCW_ONLINE_FRONT = -2;
static const int CCW_ON_SEGMENT = 0;

// Intercsect Circle & Circle
static const int ICC_SEPERATE = 4;
static const int ICC_CIRCUMSCRIBE = 3;
static const int ICC_INTERSECT = 2;
static const int ICC_INSCRIBE = 1;
static const int ICC_CONTAIN = 0;

struct Point {
    double x, y;
    Point() {}
    Point(double x, double y) : x(x), y(y) {}
    Point operator+(Point p) { return Point(x + p.x, y + p.y); }
    Point operator-(Point p) { return Point(x - p.x, y - p.y); }
    Point operator*(double k) { return Point(x * k, y * k); }
    Point operator/(double k) { return Point(x / k, y / k); }
    double norm() { return x * x + y * y; }
    double abs() { return sqrt(norm()); }

    bool operator<(const Point &p) const {
        return x != p.x ? x < p.x : y < p.y;
        // grid-point only
        // return !equals(x,p.x)?x<p.x:!equals(y,p.y)?y<p.y:0;
    }

    bool operator==(const Point &p) const {
        return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
    }
};

struct EndPoint {
    Point p;
    int seg, st;
    EndPoint() {}
    EndPoint(Point p, int seg, int st) : p(p), seg(seg), st(st) {}
    bool operator<(const EndPoint &ep) const {
        if(p.y == ep.p.y) return st < ep.st;
        return p.y < ep.p.y;
    }
};

istream &operator>>(istream &is, Point &p) {
    is >> p.x >> p.y;
    return is;
}

ostream &operator<<(ostream &os, Point p) {
    os << fixed << setprecision(12) << p.x << " " << p.y;
    return os;
}

bool sort_x(Point a, Point b) { return a.x != b.x ? a.x < b.x : a.y < b.y; }

bool sort_y(Point a, Point b) { return a.y != b.y ? a.y < b.y : a.x < b.x; }

typedef Point Vector;
typedef vector<Point> Polygon;

istream &operator>>(istream &is, Polygon &p) {
    for(int i = 0; i < (int)p.size(); i++) is >> p[i];
    return is;
}

struct Segment {
    Point p1, p2;
    Segment() {}
    Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};
typedef Segment Line;

istream &operator>>(istream &is, Segment &s) {
    is >> s.p1 >> s.p2;
    return is;
}

struct Circle {
    Point c;
    double r;
    Circle() {}
    Circle(Point c, double r) : c(c), r(r) {}
};

istream &operator>>(istream &is, Circle &c) {
    is >> c.c >> c.r;
    return is;
}

double norm(Vector a) { return a.x * a.x + a.y * a.y; }
double abs(Vector a) { return sqrt(norm(a)); }
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

Point orth(Point p) { return Point(-p.y, p.x); }

bool isOrthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
    return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
    return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
    return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(Segment s1, Segment s2) {
    return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

Point project(Segment s, Point p) {
    Vector base = s.p2 - s.p1;
    double r = dot(p - s.p1, base) / norm(base);
    return s.p1 + base * r;
}

Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }

double arg(Vector p) { return atan2(p.y, p.x); }

Vector polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

int ccw(Point p0, Point p1, Point p2);
bool intersectSS(Point p1, Point p2, Point p3, Point p4);
bool intersectSS(Segment s1, Segment s2);
bool intersectPS(Polygon p, Segment l);
int intersectCC(Circle c1, Circle c2);
bool intersectSC(Segment s, Circle c);
double getDistanceLP(Line l, Point p);
double getDistanceSP(Segment s, Point p);
double getDistanceSS(Segment s1, Segment s2);
Point getCrossPointSS(Segment s1, Segment s2);
Point getCrossPointLL(Line l1, Line l2);
Polygon getCrossPointCL(Circle c, Line l);
Polygon getCrossPointCC(Circle c1, Circle c2);
int contains(Polygon g, Point p);
Polygon andrewScan(Polygon s);
Polygon convex_hull(Polygon ps);
double diameter(Polygon s);
bool isConvex(Polygon p);
double area(Polygon s);
Polygon convexCut(Polygon p, Line l);
Line bisector(Point p1, Point p2);
Vector translate(Vector v, double theta);
vector<Line> corner(Line l1, Line l2);
vector<vector<int>> segmentArrangement(vector<Segment> &ss, Polygon &ps);

int ccw(Point p0, Point p1, Point p2) {
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if(cross(a, b) > EPS) return CCW_COUNTER_CLOCKWISE;
    if(cross(a, b) < -EPS) return CCW_CLOCKWISE;
    if(dot(a, b) < -EPS) return CCW_ONLINE_BACK;
    if(a.norm() < b.norm()) return CCW_ONLINE_FRONT;
    return CCW_ON_SEGMENT;
}

bool intersectSS(Point p1, Point p2, Point p3, Point p4) {
    return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}

bool intersectSS(Segment s1, Segment s2) {
    return intersectSS(s1.p1, s1.p2, s2.p1, s2.p2);
}

bool intersectPS(Polygon p, Segment l) {
    int n = p.size();
    for(int i = 0; i < n; i++)
        if(intersectSS(Segment(p[i], p[(i + 1) % n]), l)) return 1;
    return 0;
}

int intersectCC(Circle c1, Circle c2) {
    if(c1.r < c2.r) swap(c1, c2);
    double d = abs(c1.c - c2.c);
    double r = c1.r + c2.r;
    if(equals(d, r)) return ICC_CIRCUMSCRIBE;
    if(d > r) return ICC_SEPERATE;
    if(equals(d + c2.r, c1.r)) return ICC_INSCRIBE;
    if(d + c2.r < c1.r) return ICC_CONTAIN;
    return ICC_INTERSECT;
}

bool intersectSC(Segment s, Circle c) { return getDistanceSP(s, c.c) <= c.r; }

int intersectCS(Circle c, Segment s) {
    if(norm(project(s, c.c) - c.c) - c.r * c.r > EPS) return 0;
    double d1 = abs(c.c - s.p1), d2 = abs(c.c - s.p2);
    if(d1 < c.r + EPS && d2 < c.r + EPS) return 0;
    if((d1 < c.r - EPS && d2 > c.r + EPS) || (d1 > c.r + EPS && d2 < c.r - EPS))
        return 1;
    Point h = project(s, c.c);
    if(dot(s.p1 - h, s.p2 - h) < 0) return 2;
    return 0;
}

double getDistanceLP(Line l, Point p) {
    return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
    if(dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
    if(dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
    return getDistanceLP(s, p);
}

double getDistanceSS(Segment s1, Segment s2) {
    if(intersectSS(s1, s2)) return 0.0;
    return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPointSS(Segment s1, Segment s2) {
    for(int k = 0; k < 2; k++) {
        if(getDistanceSP(s1, s2.p1) < EPS) return s2.p1;
        if(getDistanceSP(s1, s2.p2) < EPS) return s2.p2;
        swap(s1, s2);
    }
    Vector base = s2.p2 - s2.p1;
    double d1 = abs(cross(base, s1.p1 - s2.p1));
    double d2 = abs(cross(base, s1.p2 - s2.p1));
    double t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}

Point getCrossPointLL(Line l1, Line l2) {
    double a = cross(l1.p2 - l1.p1, l2.p2 - l2.p1);
    double b = cross(l1.p2 - l1.p1, l1.p2 - l2.p1);
    if(abs(a) < EPS && abs(b) < EPS) return l2.p1;
    return l2.p1 + (l2.p2 - l2.p1) * (b / a);
}

Polygon getCrossPointCL(Circle c, Line l) {
    Polygon ps;
    Point pr = project(l, c.c);
    Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
    if(equals(getDistanceLP(l, c.c), c.r)) {
        ps.emplace_back(pr);
        return ps;
    }
    double base = sqrt(c.r * c.r - norm(pr - c.c));
    ps.emplace_back(pr + e * base);
    ps.emplace_back(pr - e * base);
    return ps;
}

Polygon getCrossPointCS(Circle c, Segment s) {
    Line l(s);
    Polygon res = getCrossPointCL(c, l);
    if(intersectCS(c, s) == 2) return res;
    if(res.size() > 1u) {
        if(dot(l.p1 - res[0], l.p2 - res[0]) > 0) swap(res[0], res[1]);
        res.pop_back();
    }
    return res;
}

Polygon getCrossPointCC(Circle c1, Circle c2) {
    Polygon p(2);
    double d = abs(c1.c - c2.c);
    double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
    double t = arg(c2.c - c1.c);
    p[0] = c1.c + polar(c1.r, t + a);
    p[1] = c1.c + polar(c1.r, t - a);
    return p;
}

// IN:2 ON:1 OUT:0
int contains(Polygon g, Point p) {
    int n = g.size();
    bool x = false;
    for(int i = 0; i < n; i++) {
        Point a = g[i] - p, b = g[(i + 1) % n] - p;
        if(fabs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;
        if(a.y > b.y) swap(a, b);
        if(a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
    }
    return (x ? 2 : 0);
}

Polygon andrewScan(Polygon s) {
    Polygon u, l;
    if(s.size() < 3) return s;
    sort(s.begin(), s.end());
    u.push_back(s[0]);
    u.push_back(s[1]);
    l.push_back(s[s.size() - 1]);
    l.push_back(s[s.size() - 2]);
    for(int i = 2; i < (int)s.size(); i++) {
        for(int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CCW_CLOCKWISE; n--) {
            u.pop_back();
        }
        u.push_back(s[i]);
    }
    for(int i = s.size() - 3; i >= 0; i--) {
        for(int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CCW_CLOCKWISE; n--) {
            l.pop_back();
        }
        l.push_back(s[i]);
    }
    reverse(l.begin(), l.end());
    for(int i = u.size() - 2; i >= 1; i--) l.push_back(u[i]);
    return l;
}

Polygon convex_hull(Polygon ps) {
    int n = ps.size();
    sort(ps.begin(), ps.end(), sort_y);
    int k = 0;
    Polygon qs(n * 2);
    for(int i = 0; i < n; i++) {
        while(k > 1 && cross(qs[k - 1] - qs[k - 2], ps[i] - qs[k - 1]) < 0) k--;
        qs[k++] = ps[i];
    }
    for(int i = n - 2, t = k; i >= 0; i--) {
        while(k > t && cross(qs[k - 1] - qs[k - 2], ps[i] - qs[k - 1]) < 0) k--;
        qs[k++] = ps[i];
    }
    qs.resize(k - 1);
    return qs;
}

double diameter(Polygon s) {
    Polygon p = s;
    int n = p.size();
    if(n == 2) return abs(p[0] - p[1]);
    int i = 0, j = 0;
    for(int k = 0; k < n; k++) {
        if(p[i] < p[k]) i = k;
        if(!(p[j] < p[k])) j = k;
    }
    double res = 0;
    int si = i, sj = j;
    while(i != sj || j != si) {
        res = max(res, abs(p[i] - p[j]));
        if(cross(p[(i + 1) % n] - p[i], p[(j + 1) % n] - p[j]) < 0.0) {
            i = (i + 1) % n;
        } else {
            j = (j + 1) % n;
        }
    }
    return res;
}

bool isConvex(Polygon p) {
    bool f = 1;
    int n = p.size();
    for(int i = 0; i < n; i++) {
        int t = ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]);
        f &= t != CCW_CLOCKWISE;
    }
    return f;
}

double area(Polygon s) {
    double res = 0;
    for(int i = 0; i < (int)s.size(); i++) {
        res += cross(s[i], s[(i + 1) % s.size()]) / 2.0;
    }
    return res;
}

double area(Circle c1, Circle c2) {
    double d = abs(c1.c - c2.c);
    if(c1.r + c2.r <= d + EPS) return 0;
    if(d <= abs(c1.r - c2.r)) {
        double r = min(c1.r, c2.r);
        return PI * r * r;
    }
    double rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
    double th = acos(rc / c1.r);
    double ph = acos((d - rc) / c2.r);
    return c1.r * c1.r * th + c2.r * c2.r * ph - d * c1.r * sin(th);
}

Polygon convexCut(Polygon p, Line l) {
    Polygon q;
    for(int i = 0; i < (int)p.size(); i++) {
        Point a = p[i], b = p[(i + 1) % p.size()];
        if(ccw(l.p1, l.p2, a) != -1) q.push_back(a);
        if(ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0)
            q.push_back(getCrossPointLL(Line(a, b), l));
    }
    return q;
}

Line bisector(Point p1, Point p2) {
    Circle c1 = Circle(p1, abs(p1 - p2)), c2 = Circle(p2, abs(p1 - p2));
    Polygon p = getCrossPointCC(c1, c2);
    if(cross(p2 - p1, p[0] - p1) > 0) swap(p[0], p[1]);
    return Line(p[0], p[1]);
}

Vector translate(Vector v, double theta) {
    Vector res;
    res.x = cos(theta) * v.x - sin(theta) * v.y;
    res.y = sin(theta) * v.x + cos(theta) * v.y;
    return res;
}

vector<Line> corner(Line l1, Line l2) {
    vector<Line> res;
    if(isParallel(l1, l2)) {
        double d = getDistanceLP(l1, l2.p1) / 2.0;
        Vector v1 = l1.p2 - l1.p1;
        v1 = v1 / v1.abs() * d;
        Point p = l2.p1 + translate(v1, 90.0 * (PI / 180.0));
        double d1 = getDistanceLP(l1, p);
        double d2 = getDistanceLP(l2, p);
        if(abs(d1 - d2) > d) {
            p = l2.p1 + translate(v1, -90.0 * (PI / 180.0));
        }
        res.push_back(Line(p, p + v1));
    } else {
        Point p = getCrossPointLL(l1, l2);
        Vector v1 = l1.p2 - l1.p1, v2 = l2.p2 - l2.p1;
        v1 = v1 / v1.abs();
        v2 = v2 / v2.abs();
        res.push_back(Line(p, p + (v1 + v2)));
        res.push_back(Line(p, p + translate(v1 + v2, 90.0 * (PI / 180.0))));
    }
    return res;
}

Polygon tangent(Circle c1, Point p2) {
    Circle c2 = Circle(p2, sqrt(norm(c1.c - p2) - c1.r * c1.r));
    Polygon p = getCrossPointCC(c1, c2);
    sort(p.begin(), p.end());
    return p;
}

vector<Line> tangent(Circle c1, Circle c2) {
    vector<Line> ls;
    if(c1.r < c2.r) swap(c1, c2);
    double g = norm(c1.c - c2.c);
    if(equals(g, 0)) return ls;
    Point u = (c2.c - c1.c) / sqrt(g);
    Point v = orth(u);
    for(int s = 1; s >= -1; s -= 2) {
        double h = (c1.r + s * c2.r) / sqrt(g);
        if(equals(1 - h * h, 0)) {
            ls.emplace_back(c1.c + u * c1.r, c1.c + (u + v) * c1.r);
        } else if(1 - h * h > 0) {
            Point uu = u * h, vv = v * sqrt(1 - h * h);
            ls.emplace_back(c1.c + (uu + vv) * c1.r, c2.c - (uu + vv) * c2.r * s);
            ls.emplace_back(c1.c + (uu - vv) * c1.r, c2.c - (uu - vv) * c2.r * s);
        }
    }

    return ls;
}

double closest_pair(Polygon &a, int l = 0, int r = -1) {
    if(r < 0) {
        r = a.size();
        sort(a.begin(), a.end(), sort_x);
    }
    if(r - l <= 1) return abs(a[0] - a[1]);
    int m = (l + r) >> 1;
    double x = a[m].x;
    double d = min(closest_pair(a, l, m), closest_pair(a, m, r));
    inplace_merge(a.begin() + l, a.begin() + m, a.begin() + r, sort_y);

    Polygon b;
    for(int i = l; i < r; i++) {
        if(fabs(a[i].x - x) >= d) continue;
        for(int j = 0; j < (int)b.size(); j++) {
            double dy = a[i].y - next(b.rbegin(), j)->y;
            if(dy >= d) break;
            d = min(d, abs(a[i] - *next(b.rbegin(), j)));
        }
        b.emplace_back(a[i]);
    }
    return d;
}

vector<vector<int>> segmentArrangement(vector<Segment> &ss, Polygon &ps) {
    int n = ss.size();
    for(int i = 0; i < n; i++) {
        ps.emplace_back(ss[i].p1);
        ps.emplace_back(ss[i].p2);
        for(int j = i + 1; j < n; j++)
            if(intersectSS(ss[i], ss[j]))
                ps.emplace_back(getCrossPointSS(ss[i], ss[j]));
    }
    sort(ps.begin(), ps.end());
    ps.erase(unique(ps.begin(), ps.end()), ps.end());

    vector<vector<int>> G(ps.size());
    for(int i = 0; i < n; i++) {
        vector<pair<double, int>> ls;
        for(int j = 0; j < (int)ps.size(); j++)
            if(getDistanceSP(ss[i], ps[j]) < EPS)
                ls.emplace_back(make_pair(norm(ss[i].p1 - ps[j]), j));

        sort(ls.begin(), ls.end());
        for(int j = 0; j + 1 < (int)ls.size(); j++) {
            int a = ls[j].second, b = ls[j + 1].second;
            G[a].emplace_back(b);
            G[b].emplace_back(a);
        }
    }
    for(auto &v : G) {
        sort(v.begin(), v.end());
        v.erase(unique(v.begin(), v.end()), v.end());
    }
    return G;
}

int manhattanIntersection(vector<Segment> ss, const int INF) {
    const int BTM = 0;
    const int LFT = 1;
    const int RGH = 2;
    const int TOP = 3;

    int n = ss.size();
    vector<EndPoint> ep;
    for(int i = 0; i < n; i++) {
        if(ss[i].p1.y == ss[i].p2.y) {
            if(ss[i].p1.x > ss[i].p2.x) swap(ss[i].p1, ss[i].p2);
            ep.emplace_back(ss[i].p1, i, LFT);
            ep.emplace_back(ss[i].p2, i, RGH);
        } else {
            if(ss[i].p1.y > ss[i].p2.y) swap(ss[i].p1, ss[i].p2);
            ep.emplace_back(ss[i].p1, i, BTM);
            ep.emplace_back(ss[i].p2, i, TOP);
        }
    }
    sort(ep.begin(), ep.end());

    set<int> bt;
    bt.insert(INF);

    int cnt = 0;
    for(int i = 0; i < n * 2; i++) {
        if(ep[i].st == TOP) {
            bt.erase(ep[i].p.x);
        } else if(ep[i].st == BTM) {
            bt.emplace(ep[i].p.x);
        } else if(ep[i].st == LFT) {
            auto b = bt.lower_bound(ss[ep[i].seg].p1.x);
            auto e = bt.upper_bound(ss[ep[i].seg].p2.x);
            cnt += distance(b, e);
        }
    }

    return cnt;
}

double area(Polygon ps, Circle c) {
    if(ps.size() < 3u) return 0;
    function<double(Circle, Point, Point)> dfs = [&](Circle c, Point a, Point b) {
        Vector va = c.c - a, vb = c.c - b;
        double f = cross(va, vb), res = 0;
        if(equals(f, 0.0)) return res;
        if(max(abs(va), abs(vb)) < c.r + EPS) return f;
        Vector d(dot(va, vb), cross(va, vb));
        if(getDistanceSP(Segment(a, b), c.c) > c.r - EPS)
            return c.r * c.r * atan2(d.y, d.x);
        auto u = getCrossPointCS(c, Segment(a, b));
        if(u.empty()) return res;
        if(u.size() > 1u && dot(u[1] - u[0], a - u[0]) > 0) swap(u[0], u[1]);
        u.emplace(u.begin(), a);
        u.emplace_back(b);
        for(int i = 1; i < (int)u.size(); i++) res += dfs(c, u[i - 1], u[i]);
        return res;
    };
    double res = 0;
    for(int i = 0; i < (int)ps.size(); i++)
        res += dfs(c, ps[i], ps[(i + 1) % ps.size()]);
    return res / 2;
}

ll N;
struct edge {
    ll to;
    double cost;
    bool operator<(const edge &another) const { return cost < another.cost; };
    bool operator>(const edge &another) const { return cost > another.cost; };
};
vector<vector<edge>> g;
VD d;

void dijkstra(ll s) {
    priority_queue<edge, vector<edge>, greater<edge>> pq;
    d.assign(N, (double)LINF);
    d[s] = 0;
    pq.push({s, 0});

    while(!pq.empty()) {
        edge now = pq.top();
        pq.pop();
        ll v = now.to;
        if(d[v] < now.cost) continue;

        REP(i, g[v].size()) {
            edge e = g[v][i];
            if(d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                pq.push({e.to, d[e.to]});
            }
        }
    }
}

signed main() {
    vector<Circle> cs;
    DCIN(xs, ys, xt, yt);
    Point s(xs, ys), t(xt, yt);
    cs.emplace_back(s, 0);
    cs.emplace_back(t, 0);
    cin >> N;
    REP(i, N) {
        DCIN(x, y, r);
        cs.emplace_back(Point(x, y), r);
    }
    N += 2;
    g.resize(N);
    REP(i, N) REP(j, i) {
        g[i].push_back({j, max(0.0, abs(cs[i].c - cs[j].c) - cs[i].r - cs[j].r)});
        g[j].push_back({i, max(0.0, abs(cs[i].c - cs[j].c) - cs[i].r - cs[j].r)});
    }
    dijkstra(0);
    cout << fixed << setprecision(12) << d[1] << "\n";
}

Measured memory_bytes: 22532