#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
// /*
// //////////**DEFINES - START**//////////
#define ret return
#define fi first
#define se second
#define mp make_pair
#define all(x) x.begin(), x.end()
#define be(x) x.begin()
#define en(x) x.end()
#define sz(x) ll(x.size())
#define for0(i, n) for (ll i = 0; i < (n); ++i)
#define for1(i, n) for (ll i = 1; i < (n); ++i)
#define rfor0(i, n) for (ll i = (n) - 1; i >= 0; --i)
#define rfor1(i, n) for (ll i = (n) - 1; i >= 1; --i)
#define rep(i, a, n) for (ll i = a; i < ll(n); ++i)
#define rrep(i, a, n) for (ll i = a - 1; i >= ll(n); --i)
#define popcount __builtin_popcount
#define popcountll __builtin_popcountll
#define fastIO() ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define con continue
#define pb push_back
#define pob pop_back
#define deb(x) cout << (#x) << " is " << (x) << endl
#define ins insert
#define len(s) (s).length()
#define gi greater<int>()
#define gll greater<ll >()
#define gstr greater<string>()
#define gpll greater<pair<ll , ll >>()
#define rast(x1, y1, x2, y2) sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))
#define rev reverse
#define ub upper_bound
#define lb lower_bound
#define bs binary_search
#define rs resize
#define last(a) a.back()
#define co count
#define ba(a) a.back()
#define um unordered_map
#define rsun(a) a.resize(unique(a.begin(), a.end())-a.begin())
#define endl '\n'
#ifdef OG_Matveychick1
bool local = true;
#else
bool local = false;
#endif
// \\\\\\\\\\**DEFINES - END**\\\\\\\\\\
// */
// /*
// //////////**TYPEDEFS - START**//////////
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<char> vc;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
typedef vector<string> vs;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<ull> vull;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<pll> vpll;
typedef pair<double, double> pdd;
typedef double ld;
typedef double D;
typedef vector<ld> vld;
typedef vector<pair<ld, ld>>
vpld;
typedef string str;
typedef set<ll> sll;
typedef set<int> si;
typedef set<str> ss;
typedef set<pii> spii;
typedef multiset<int> msi;
typedef multiset<ll> msll;
typedef multiset<str> mss;
typedef multiset<pii> mspii;
typedef multiset<pll> mspll;
typedef map<str, str> mps;
typedef map<int, int> mpi;
typedef map<ll, ll> mpll;
typedef map<int, vi> mpvi;
typedef map<int, vll> mpvll;
typedef map<char, int> mpci;
typedef multimap<ll, ll> mmpll;
typedef multimap<str, str> mmps;
typedef multimap<int, int> mmpi;
typedef vector<vector<int>> vvi;
typedef vector<vector<ll>> vvll;
typedef vector<vector<long double>> vvld;
typedef vector<vvi> vvvi;
typedef vector<vector<char>> vvc;
typedef vector<vs> vvs;
typedef vector<D> vD;
typedef set<pair<ll, ll>>
spll;
typedef pair<ull, ull> pull;
typedef vector<pull> vpull;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef set<char> sc;
typedef queue<int> qi;
typedef queue<ll> qll;
typedef queue<bool> qb;
typedef vector<sll> vsll;
typedef queue<pair<ll, ll>>
qpll;
typedef vector<vector<pair<int, int>>>
vvpii;
typedef vector<vector<pair<ll, ll>>>
vvpll;
typedef vector<spll> vspll;
typedef multiset<char> msc;
typedef queue<str> qs;
typedef vector<set<int>> vsi;
typedef priority_queue<ll> pqll;
typedef vector<vsll> vvsll;
typedef pair<ld, ld> pld;
typedef vector<vvll> vvvll;
typedef set<ld> sld;
typedef vector<vpld> vvpld;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update>
ordered_set;
typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update>
ordered_multiset;
// \\\\\\\\\\**TYPEDEFS - END**\\\\\\\\\\
// */
// /*
// //////////**CONSTANTS - START**//////////
const ld pi = acosl(-1);
const ll mod1 = 1e9 + 7;
const ll mod2 = 998244353;
const ll MAXLL = 9223372036854775807;
//const ll MAXINT = 2147483647;
const ld eps = 1e-6;
// \\\\\\\\\\**CONSTANTS - END**\\\\\\\\\\
// */
// /*
// //////////**TEMPLATES - START**//////////
template<typename T>
istream &operator>>(istream &in, vector<T> &a) {
for (T &i: a) in >> i;
return in;
}
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &a) {
in >> a.fi >> a.se;
return in;
}
template<typename T1, typename T2>
ostream &operator<<(ostream &out, pair<T1, T2> a) {
out << a.fi << " " << a.se;
return out;
}
template<typename T1, typename T2>
istream &operator>>(istream &in, vector<pair<T1, T2>>
&a) {
for (
pair<T1, T2> &i
: a)
in >> i.fi >> i.
se;
return
in;
}
template<typename T>
ostream &operator<<(ostream &out, const vector<T> &a) {
for (auto i: a) {
out << i << " ";
}
return out;
}
template<typename T1, typename T2>
ostream &operator<<(ostream &out, vector<pair<T1, T2>>
&a) {
for (
pair<T1, T2> i
: a)
out << i.fi << " " << i.se <<
endl;
return
out;
}
template<typename T1>
ostream &operator<<(ostream &out, vector<vector<T1>> &a) {
for (vector<T1> i: a) {
for (T1 j: i) out << j << " ";
out << endl;
}
return out;
}
template<typename T1, typename T2>
inline T1 min(T1 a, T2 b) {
b = (T1) b;
return a > b ? b : a;
}
template<typename T1, typename T2>
inline T1 max(T1 a, T2 b) {
b = (T1) b;
return a > b ? a : b;
}
template<typename T1, typename T2>
inline void amin(T1 &a, T2 b) {
a = min(a, b);
}
template<typename T1, typename T2>
inline void amax(T1 &a, T2 b) {
a = max(a, b);
}
// \\\\\\\\\\**TEMPLATES - END**\\\\\\\\\\
// */
// This bear is a good alternative to duck!!!
/*
???? ??????
???????????????????
???????????????? ???
??? ??????????? ???
??? ???????????? ??
??????????????????
??????????????? ?
?????????????????
??????? ??? ??
???? ??????????
???? ?? ???
???????????? ?????
????????????????????
???????? ?? ???????
??????? ?????
*/
ld getTime() {
return (ld) clock() / (ld) CLOCKS_PER_SEC;
}
mt19937_64 rn(chrono::steady_clock::now().time_since_epoch().count());
//mt19937_64 rn(4);
ll rnd(ll l, ll r) {
ll a = rn() % (r - l + 1) + l;
return a;
}
void solve();
ll T = 1;
signed main(int argc, char **argv) {
// setlocale(LC_ALL, "RUS");
fastIO()
cout.precision(12);
cout << fixed;
if (local && argc == 1) {
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
}
// cin >> T;
while (T--) {
solve();
}
if (local && argc == 1) {
cout << endl << fixed << "time = " << getTime();
}
return 0;
}
/*
___ __ __ ______ __ _____ __ __ __ __
/ | _____/ /___ ______ _/ / / ____/___ ____/ /__ / ___// /_____ ______/ /______ / / / /__ ________
/ /| |/ ___/ __/ / / / __ `/ / / / / __ \/ __ / _ \ \__ \/ __/ __ `/ ___/ __/ ___/ / /_/ / _ \/ ___/ _ \
/ ___ / /__/ /_/ /_/ / /_/ / / / /___/ /_/ / /_/ / __/ ___/ / /_/ /_/ / / / /_(__ ) / __ / __/ / / __/
/_/ |_\___/\__/\__,_/\__,_/_/ \____/\____/\__,_/\___/ /____/\__/\__,_/_/ \__/____/ /_/ /_/\___/_/ \___/
*/
using num = ld;
struct vec {
num x, y;
vec(num x, num y) : x(x), y(y) {}
vec() : x(0), y(0) {}
bool operator==(vec a) {
ret abs(a.x - x) < eps && abs(a.y - y) < eps;
}
void operator+=(vec a) {
x += a.x;
y += a.y;
}
vec operator+(vec a) {
ret {x + a.x, y + a.y};
}
void operator-=(vec a) {
x -= a.x;
y -= a.y;
}
vec operator-(vec a) {
ret {x - a.x, y - a.y};
}
void operator*=(vec a) {
x *= a.x;
y *= a.y;
}
vec operator*(num a) {
ret {x * a, y * a};
}
num operator*(vec a) {
ret x * a.x + y * a.y;
}
void operator*=(num a) {
x *= a;
y *= a;
}
void operator/=(num a) {
x /= a;
y /= a;
}
num operator%(vec a) {
ret x * a.y - y * a.x;
}
num len2() {
ret x * x + y * y;
}
friend istream &operator>>(istream &in, vec &a) {
in >> a.x >> a.y;
ret in;
}
friend ostream &operator<<(ostream &out, vec a) {
out << a.x << " " << a.y << " ";
ret out;
}
num napr(vec a) {
if ((*this) % a > 0)ret 1;
else if ((*this) % a < 0)ret -1;
else
ret 0;
}
ld angle(vec a) {
ret atan2l(a % *this, a * *this);
}
ld polar_angle() {
ret atan2l(y, x);
}
bool point_in_ray(vec a) //точка
{
ret (abs(*this % a - 0) < eps && *this * a >= -eps);
}
bool point_in_square_ray(vec a) //точка
{
ret (*this * a >= 0);
}
bool point_in_line(vec a) //точка
{
ret (*this % a == 0);
}
bool point_in_segment(vec a) //точка
{
ret (abs(*this % a - 0) < eps && *this * a >= -eps && vec(0 - x, 0 - y) * vec(a.x - x, a.y - y) >= -eps);
}
bool point_in_square_segment(vec a) //точка
{
ret (*this * a >= 0 && vec(0 - x, 0 - y) * vec(a.x - x, a.y - y) >= 0);
}
bool point_in_angle(vec a, vec b) //две крайние точки угла
{
ret (a.napr(b) * a.napr(*this) >= 0 && b.napr(a) * b.napr(*this) >= 0);
}
ld dist_from_point_to_line(vec a) //точка
{
ret *this % a / sqrt(len2());
}
ld dist_from_point_to_ray(vec a) //точка
{
ret (point_in_square_ray(a) ? *this % a / sqrtl(len2()) : min(sqrtl(vec(a).len2()),
sqrtl(vec(a - *this).len2())));
}
ld dist_from_point_to_segment(vec a) //точка
{
ret (point_in_square_segment(a) ? *this % a / sqrtl(len2()) : min(sqrtl(vec(a).len2()),
sqrtl(vec(a - *this).len2())));
}
void turn() {
swap(x, y);
x = -x;
}
void turn(ld a) {
*this = vec(x * cosl(a) - y * sinl(a), x * sinl(a) + y * cosl(a));
}
};
bool segment_in_segment(vec a1, vec a2, vec b1, vec b2) {
vec a(a2.x - a1.x, a2.y - a1.y), b(a1.x - a2.x, a1.y - a2.y), al(b1.x - a1.x, b1.y - a1.y), ar(b2.x - a1.x,
b2.y - a1.y), bl(
b1.x - a2.x, b1.y - a2.y), br(b2.x - a2.x, b2.y - a2.y);
vec c(b2.x - b1.x, b2.y - b1.y), d(b1.x - b2.x, b1.y - b2.y), cl(a1.x - b1.x, a1.y - b1.y), cr(a2.x - b1.x,
a2.y - b1.y), dl(
a1.x - b2.x, a1.y - b2.y), dr(a2.x - b2.x, a2.y - b2.y);
if ((a % al) * (a % ar) <= 0 && (b % bl) * (b % br) <= 0 && (c % cl) * (c % cr) <= 0 &&
(d % dl) * (d % dr) <= 0) {
if (a % al == 0 && a % ar == 0 && (max(a1.x, a2.x) < min(b1.x, b2.x) || max(b1.x, b2.x) < min(a1.x, a2.x) ||
max(a1.y, a2.y) < min(b1.y, b2.y) ||
max(b1.y, b2.y) < min(a1.y, a2.y))) {
ret 0;
}
ret 1;
} else {
ret 0;
}
}
ld dist_from_segment_to_segment(vec a1, vec a2, vec b1, vec b2) {
ret (segment_in_segment(a1, a2, b1, b2) ? 0.0 : min(abs(vec(a2 - a1).dist_from_point_to_segment(vec(b1 - a1))),
min(abs(vec(a2 - a1).dist_from_point_to_segment(
vec(b2 - a1))),
min(abs(vec(b2 - b1).dist_from_point_to_segment(
a1 - b1)),
abs(vec(b2 - b1).dist_from_point_to_segment(
a2 - b1))))));
}
struct line {
num a, b, c;
line() {}
line(vec x, vec y) {
a = y.y - x.y;
b = x.x - y.x;
c = -a * x.x - b * x.y;
}
line(num aa, num bb, vec cc) {
a = aa;
b = bb;
c = -a * cc.x - b * cc.y;
}
line(num a, num b, num c) : a(a), b(b), c(c) {}
friend ostream &operator<<(ostream &out, line &_a) {
out << _a.a << " " << _a.b << " " << _a.c;
ret out;
}
friend istream &operator>>(istream &in, line &_a) {
in >> _a.a >> _a.b >> _a.c;
ret in;
}
bool point_in_line(vec aa) {
ret (a * aa.x + b * aa.y + c == 0);
}
num napr(vec aa) {
if (a * aa.x + b * aa.y + c < 0)ret -1;
else if (a * aa.x + b * aa.y + c > 0) ret 1;
else
ret 0;
}
ld dist_from_point_to_line(vec aa) //точка
{
ret (a * aa.x + b * aa.y + c) / sqrtl(vec(a, b).len2());
}
vec point_of_intersection_of_lines(line aa) {
if (a != 0)
ret vec((-b * (aa.c * a - c * aa.a) / (b * aa.a - aa.b * a) - c) / a,
(aa.c * a - c * aa.a) / (b * aa.a - aa.b * a));
else
ret vec((-aa.b * (c * aa.a - aa.c * a) / (aa.b * a - b * aa.a) - aa.c) / aa.a,
(c * aa.a - aa.c * a) / (aa.b * a - b * aa.a));
}
bool lines_is_parallel(line aa) {
if (a == 0) {
if (aa.a != 0) ret 0;
ret 1;
} else {
if (b == 0) {
if (aa.b != 0) ret 0;
ret 1;
}
ret abs(aa.a / a - aa.b / b) < eps;
}
}
ld dist_of_parallel_lines(line aa) {
vec z(a, b);
ld d = (-c) / sqrtl(z.len2());
z *= d / sqrtl(z.len2());
ret aa.dist_from_point_to_line(z);
}
};
struct circle {
num r;
vec t;
circle() {}
circle(num x, num y, num r) : t(vec(x, y)), r(r) {}
bool point_in_circle(vec a) {
ret sqrtl(vec(a - vec(t.x, t.y)).len2()) <= r;
}
friend istream &operator>>(istream &in, circle &a) {
cin >> a.t.x >> a.t.y >> a.r;
ret in;
}
bool intersection_of_segnent(vec a, vec b) {
ret vec(b - a).dist_from_point_to_segment(vec(t - a)) < r;
}
pair<vec, vec> tangents_from_point(vec a) {
pair<vec, vec> re;
num d = rast(t.x, t.y, a.x, a.y);
ld u = asin(r / d);
re = {t - a, t - a};
re.fi.turn(u);
re.se.turn(-u);
re.fi /= sqrtl(re.fi.len2());
re.se /= sqrtl(re.se.len2());
num d1 = sqrtl(d * d - r * r);
re.fi *= d1;
re.se *= d1;
re.fi += a;
re.se += a;
ret re;
}
ld ln() {
ret pi * 2 * r;
}
};
line bisector_of_three_points(vec x, vec y, vec z) {
y -= x;
z -= x;
vec X = vec(y - z) * (sqrtl(z.len2()) / (sqrtl(z.len2()) + sqrtl(y.len2())));
X += z;
X += x;
ret line(x, X);
}
ll area_of_triangle(vec a, vec b, vec c) {
ret vec(b - a) % vec(c - a);
}
ll area_of_polygon(vector<vec> &a) {
ll sum = 0;
rep(i, 2, sz(a)) {
sum += area_of_triangle(a[0], a[i - 1], a[i]);
}
ret sum;
}
bool point_in_polygon(ll n, vec p, vector<vec> &a) {
a.pb(a[0]);
for0(i, n) {
if (a[i] == p) {
a.pob();
ret 1;
}
}
for1(i, n + 1) {
if (vec(a[i - 1] - a[i]).point_in_segment(p - a[i])) {
a.pob();
ret 1;
}
}
ld sum = 0;
for1(i, n + 1) {
sum += vec(a[i] - p).angle(a[i - 1] - p);
}
a.pob();
ret (abs(abs(sum) - pi * 2) < eps ? 1 : 0);
}
bool point_in_triangle(vec a, vec b, vec c, vec t) {
ret abs(area_of_triangle(a, b, c)) ==
abs(area_of_triangle(a, c, t)) + abs(area_of_triangle(c, b, t)) + abs(area_of_triangle(a, b, t));
}
bool point_in_convex_polygon(ll n, vec p, vector<vec> &a) {
ll l = 0, r = n;
p -= a[0];
if (p.x < 0) ret 0;
while (l + 1 < r) {
ll m = (l + r) / 2;
(a[m].polar_angle() <= p.polar_angle() ? l : r) = m;
}
if (l == n - 1 || l == 0) ret 0;
ret point_in_triangle(vec(0, 0), a[l], a[l + 1], p);
}
bool convex_polygon(vector<vec> a) {
a.pb(a[0]);
a.pb(a[1]);
ll n = sz(a);
bool mi = 0, ma = 0;
rep(i, 2, n) {
if (vec(a[i - 1] - a[i - 2]) % vec(a[i] - a[i - 2]) > 0)ma = 1;
if (vec(a[i - 1] - a[i - 2]) % vec(a[i] - a[i - 2]) < 0)mi = 1;
}
ret !(mi && ma);
}
vector<vec> convex_hull(ll n, vector<vec> &a) {
vec st(10000000000000, 10000000000000);
for0(i, n) {
if (a[i].x < st.x || (a[i].x == st.x && a[i].y < st.y)) {
st = a[i];
}
}
for0(i, n) {
a[i] -= st;
}
sort(all(a), [&](vec &a, vec &b) { ret (a % b == 0 ? a.len2() < b.len2() : a % b > 0); });
vector<vec> ans;
for0(i, n) {
while (sz(ans) > 1 && vec(ans[sz(ans) - 1] - ans[sz(ans) - 2]) % vec(a[i] - ans[sz(ans) - 1]) <= 0) {
ans.pob();
}
ans.pb(a[i]);
}
for (auto &x: ans) x += st;
ret ans;
}
ld area_of_union_of_triangle(vector<vector<vec>> &_a) {
struct segment {
vec s, f;
ll id;
segment(vec &a, vec &b, ll &id) : s(a), f(b), id(id) {}
};
struct item {
ld y1, y2;
ll id;
item() {}
item(ld y1, ld y2, ll id) : y1(y1), y2(y2), id(id) {}
};
ll n = 3 * sz(_a);
vector<segment> a;
for0(i, n / 3) {
for0(j, 3) {
a.pb({_a[i][j], _a[i][(j + 1) % 3], i});
}
}
vector<ld> b;
for0(i, n)
rep(j, i + 1, n)
if (!(line(a[i].s, a[i].f).lines_is_parallel(line(a[j].s, a[j].f)) &&
dist_from_segment_to_segment(a[i].s, a[i].f, a[j].s, a[j].f) < eps) &&
dist_from_segment_to_segment(a[i].s, a[i].f, a[j].s, a[j].f) < eps)
b.pb(line(a[i].s, a[i].f).point_of_intersection_of_lines(line(a[j].s, a[j].f)).x);
sort(all(b));
b.erase(unique(all(b), [&](ld &a, ld &b) { ret abs(a - b) < eps; }), en(b));
ld re = 0;
vll used(n / 3, -1);
vector<item> c(n);
for0(i, sz(b) - 1) {
ld x1 = b[i], x2 = b[i + 1];
ll csz = 0;
for0(j, n) {
if (abs(a[j].f.x - a[j].s.x) > eps && min(a[j].s.x, a[j].f.x) <= x1 + eps &&
max(a[j].f.x, a[j].s.x) >= x2 - eps) {
c[csz++] = item(line(vec(x1, 0), vec(x1, 1)).point_of_intersection_of_lines(line(a[j].s, a[j].f)).y,
line(vec(x2, 0), vec(x2, 1)).point_of_intersection_of_lines(line(a[j].s, a[j].f)).y,
a[j].id);
}
}
if (csz % 2) exit(0);
sort(be(c), be(c) + csz,
[&](item &a, item &b) { ret a.y1 < b.y1 - eps || abs(a.y1 - b.y1) < eps && a.y2 < b.y2 - eps; });
ld pl = 0;
ll cnt = 0;
item l, r;
for0(j, csz) {
if (used[c[j].id] == i) {
cnt--;
if (!cnt) {
r = c[j];
pl += r.y1 - l.y1 + r.y2 - l.y2;
}
} else {
cnt++;
if (cnt == 1) {
l = c[j];
}
}
used[c[j].id] = i;
}
re += pl * (x2 - x1) / 2.0;
}
ret re;
}
struct pt {
ld x, y;
ll c, i;
pt() {}
pt(ld x, ld y, ll c) : x(x), y(y), c(c) {}
};
const ll N = 250;
ll n, s, used[N][N], was[N][N], dp[N][N][2][2][2][2], c[N];
pt p[N];
pair<vec, vec> a[N];
bool check(ll i, ll j) {
line l1 = line(vec(p[i].x, p[i].y), vec(p[j].x, p[j].y));
line l;
vec t;
l = line(vec(s, s), vec(s, -s));
t = l.point_of_intersection_of_lines(l1);
if ((vec(p[i].x, p[i].y) - vec(p[j].x, p[j].y)).point_in_segment(t - vec(p[j].x, p[j].y))) {
t.x = abs(t.x), t.y = abs(t.y);
t.x += eps;
t.y += eps;
if (min(t.x, t.y) < s) ret 0;
}
l = line(vec(s, s), vec(-s, s));
t = l.point_of_intersection_of_lines(l1);
if ((vec(p[i].x, p[i].y) - vec(p[j].x, p[j].y)).point_in_segment(t - vec(p[j].x, p[j].y))) {
t.x = abs(t.x), t.y = abs(t.y);
t.x += eps;
t.y += eps;
if (min(t.x, t.y) < s) ret 0;
}
l = line(vec(-s, -s), vec(s, -s));
t = l.point_of_intersection_of_lines(l1);
if ((vec(p[i].x, p[i].y) - vec(p[j].x, p[j].y)).point_in_segment(t - vec(p[j].x, p[j].y))) {
t.x = abs(t.x), t.y = abs(t.y);
t.x += eps;
t.y += eps;
if (min(t.x, t.y) < s) ret 0;
}
l = line(vec(-s, -s), vec(-s, s));
t = l.point_of_intersection_of_lines(l1);
if ((vec(p[i].x, p[i].y) - vec(p[j].x, p[j].y)).point_in_segment(t - vec(p[j].x, p[j].y))) {
t.x = abs(t.x), t.y = abs(t.y);
t.x += eps;
t.y += eps;
if (min(t.x, t.y) < s) ret 0;
}
ret 1;
}
bool check1(ll i, ll j) {
if (i == 2 && j == 9) {
bool fl = 0;
}
for0(k, n) {
if (vec(a[k].fi - a[k].se).point_in_segment(vec(p[i].x, p[i].y) - a[k].se) &&
vec(a[k].fi - a[k].se).point_in_segment(vec(p[j].x, p[j].y) - a[k].se))
ret 0;
}
ret 1;
}
void solve() {
cin >> n >> s;
ll it = 0, id = 0;
p[it++] = pt(s, s, id++);
p[it++] = pt(-s, s, id++);
p[it++] = pt(s, -s, id++);
p[it++] = pt(-s, -s, id++);
for0(i, n) {
ll x1, y1, x2, y2;
cin >> x1 >> y1 >> x2 >> y2;
a[i] = {vec(x1, y1), vec(x2, y2)};
p[it++] = pt(x1, y1, id);
p[it++] = pt(x2, y2, id++);
// line l1 = line(vec(x1, y1), vec(x2, y2));
// line l;
// vec t;
//
// l = line(vec(s, s), vec(s, -s));
// t = l.point_of_intersection_of_lines(l1);
// p[it++] = pt(t.x, t.y, id++);
//
// l = line(vec(s, s), vec(-s, s));
// t = l.point_of_intersection_of_lines(l1);
// p[it++] = pt(t.x, t.y, id++);
//
// l = line(vec(-s, -s), vec(s, -s));
// t = l.point_of_intersection_of_lines(l1);
// p[it++] = pt(t.x, t.y, id++);
//
// l = line(vec(-s, -s), vec(-s, s));
// t = l.point_of_intersection_of_lines(l1);
// p[it++] = pt(t.x, t.y, id++);
}
ll sit = it;
for0(i, sit) {
for0(j, n) {
line l1(a[j].fi, a[j].se);
line l2(vec(p[i].x, p[i].y), vec(p[i].x + l1.a, p[i].y + l1.b));
vec t = l1.point_of_intersection_of_lines(l2);
vector<vec> cp{vec(s, s), vec(-s, s), vec(-s, -s), vec(s, -s)};
if (!point_in_polygon(4, t, cp)) p[it++] = pt(t.x, t.y, id++);
}
}
sort(p, p + it, [&](pt a, pt b) {
vec va(a.x, a.y), vb(b.x, b.y);
ret va.polar_angle() < vb.polar_angle();
});
for0(i, it) p[i].i = i;
for0(i, it) {
for0(j, it) {
used[i][j] = !check(i, j);
was[i][j] = check1(i, j);
}
}
for0(i, it) {
ll tp = -1;
if (p[i].x <= 0) {
if (p[i].y <= 0) tp = 0;
else if (p[i].y >= 0) tp = 1;
} else if (p[i].x >= s - eps) {
if (p[i].y <= 0) tp = 2;
else if (p[i].y >= 0) tp = 3;
}
c[i] = tp;
}
ld ans = 1e18;
for0(i, it) {
for0(j, it) {
for0(f1, 2) {
for0(f2, 2) {
for0(f3, 2) {
for0(f4, 2) {
dp[i][j][f1][f2][f3][f4] = 1e18;
}
}
}
}
}
dp[i][i][(c[i] == 0)][(c[i] == 1)][(c[i] == 2)][(c[i] == 3)] = 0;
rep(j, i, it) {
rep(k, j + 1, it) {
if (used[j][k]) con;
for0(f1, 2) {
for0(f2, 2) {
for0(f3, 2) {
for0(f4, 2) {
amin(dp[i][k][f1 | (c[k] == 0)][f2 | (c[k] == 1)]
[f3 | (c[k] == 2)][f4 | (c[k] == 3)], dp[i][j]
[f1][f2][f3][f4] + (was[j][k] ?
rast(p[j].x, p[j].y,
p[k].x, p[k].y)
: 0));
}
}
}
}
}
}
rep(j, i, it) {
for1(f1, 2) {
for1(f2, 2) {
for1(f3, 2) {
for1(f4, 2) {
if (used[j][i]) con;
amin(ans, dp[i][j][f1][f2][f3][f4] + (was[j][i] ?
rast(p[j].x, p[j].y,
p[i].x, p[i].y)
: 0));
}
}
}
}
}
}
cout << ans;
}
