#include <bits/stdc++.h>
using namespace std;
const int MAXN = 50005;
typedef long long lint;
#include<string>
/*
N
// N//
///// ////
//////N/////
/////y//y/////
///:y//yyy////
//`////y/////
///``////y////
///NN////y////
///y N///y////
//`y `/`/y///
``````//y//
````:://
::
--
N``--
`N` -
h -N
-hhNN
hhNNNN
-hhNNNN
hhNNNNNN-
hhhNNNNNN
- -NNNNNN
``NNN-NNNNN
NNNNNN--NNNN
- NN-NNN
--- N--N
- N-
- N
--
--
--
-
-
hhh-hh
hhhNNhhh
hhhhhh
*/
#include<stdio.h>
#include<set>
#include<assert.h>
#include<queue>
#include<algorithm>
#include<vector>
#include<cmath>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef pair<double, int> pdi;
const double EPS = 1e-8;
const double PI = acos(-1);
double sq(double x){ return x*x; }
ll sq(ll x){ return x*x; }
int sign(ll x){ return x < 0? -1 : x > 0? 1 : 0; }
int sign(int x){ return x < 0? -1 : x > 0? 1 : 0; }
double sign(double x){ return abs(x) < EPS? 0 : x < 0? -1 : 1; }
pii operator+(const pii &l, const pii &r){ return pii(l.first + r.first, l.second + r.second); }
pii operator-(const pii &l, const pii &r){ return pii(l.first - r.first, l.second - r.second); }
ll operator^(const pii &l, const pii &r){ return (ll)l.first * r.second - (ll)l.second * r.first; }
ll operator/(const pii &l, const pii &r){ return (ll)l.first * r.second - (ll)l.second * r.first; }
ll operator*(const pii &l, const pii &r){ return (ll)l.first * r.first + (ll)l.second * r.second; }
pii operator*(const pii &l, const int &r){ return pii(l.first * r, l.second * r); }
pii operator-(const pii &l){ return pii(-l.first, -l.second); }
pdd operator+(const pdd &l, const pdd &r){ return pdd(l.first + r.first, l.second + r.second); }
pdd operator-(const pdd &l, const pdd &r){ return pdd(l.first - r.first, l.second - r.second); }
double operator^(const pdd &l, const pdd &r){ return l.first * r.second - l.second * r.first; }
double operator/(const pdd &l, const pdd &r){ return l.first * r.second - l.second * r.first; }
double operator*(const pdd &l, const pdd &r){ return l.first * r.first + l.second * r.second; }
pdd operator*(const pdd &l, const double &r){ return pdd(l.first * r, l.second * r); }
pdd operator-(const pdd &l){ return pdd(-l.first, -l.second); }
double size(pdd x){ return hypot(x.first, x.second); }
double size2(pdd x){ return sq(x.first) + sq(x.second); }
ll size2(pii x){ return sq((ll)x.first) + sq((ll)x.second); }
double polar(pdd x){ return atan2(x.second, x.first); }
pdd unit(double a){ return pdd(cos(a), sin(a)); }
pdd norm(pdd a){ return a * (1.0 / size(a)); }
pdd rotate(pdd v, double a){ return unit(a) * v.first + unit(a + PI / 2) * v.second; }
pdd r90(pdd v){ return pdd(-v.second, v.first); }
void normalize(double &a){
while (a < 0) a += 2 * PI;
while (a >= 2 * PI) a -= 2 * PI;
}
struct circle{
circle(pdd O, double r):O(O), r(r){}
circle(){}
pdd O;
double r;
};
int tangent(circle &A, circle &B, pdd des[4]){
// outer
int top = 0;
double d = size(A.O - B.O), a = polar(B.O - A.O), b = PI + a;
double t = sq(d) - sq(A.r - B.r);
if (t >= 0){
t = sqrt(t);
double p = atan2(B.r - A.r, t);
des[top++] = pdd(a + p + PI / 2, b + p - PI / 2);
des[top++] = pdd(a - p - PI / 2, b - p + PI / 2);
}
// inner
t = sq(d) - sq(A.r + B.r);
if (t >= 0){
t = sqrt(t);
double p = atan2(B.r + A.r, t);
des[top++] = pdd(a + p - PI / 2, b + p - PI / 2);
des[top++] = pdd(a - p + PI / 2, b - p + PI / 2);
}
return top;
}
int intersect(circle &A, circle &B, pdd des[2]){
double d = size(A.O - B.O), t = (sq(A.r) + sq(d) - sq(B.r)) / 2 / A.r / d, u = (sq(B.r) + sq(d) - sq(A.r)) / 2 / B.r / d;
if (abs(d) < EPS) return 0;
if (1 - t*t < 0 || 1 - u*u < 0) return 0;
double a = atan2(sqrt(1 - t*t), t), b = atan2(sqrt(1 - u*u), u), p = polar(B.O - A.O), q = PI + p;
des[0] = pdd(p + a, q - b);
des[1] = pdd(p - a, q + b);
return 2;
}
int intersect(circle A, pdd s, pdd d, pdd des[2]){
double c = size2(A.O - s) - sq(A.r), b = d * (s - A.O), a = size2(d);
if (b*b - a*c < 0) return 0;
des[0].second = (-b - sqrt(b*b - a*c)) / a;
des[1].second = (-b + sqrt(b*b - a*c)) / a;
des[0].first = polar(s + d*des[0].second - A.O);
des[1].first = polar(s + d*des[1].second - A.O);
return 2;
}
int intersect(pdd a, pdd b, pdd u, pdd v, pdd &des){
if (abs(b^v) < EPS) return 0;
des = pdd(((a - u) ^ v) / (v^b), ((a - u) ^ b) / (v^b));
return 1;
}
double dist(const pdd &A, const pdd &p, const pdd &d){
if( size(A-p) <= EPS ) return 0;
else if( size(d) <= EPS ) return size(A-p);
double sina = ((A-p) ^ d) / size(A-p) / size(d);
double cosa = ((A-p) * d) / size(A-p) / size(d);
double r = abs(size(A - p) * sina), e = size(A - p) * cosa;
if (0 < e && e < size(d));
else r = min(size(A - p), size(A - p - d));
return r;
}
int get_circle(pdd a, pdd b, double R, circle des[2]){
pdd m = (a+b) * 0.5, t = (b-a);
double d = (R*R - size2(m-a));
if( d < 0 ) return 0;
d = sqrt(d);
pdd p = norm(pdd(t.second, -t.first));
des[0] = circle(m + p*d, R);
des[1] = circle(m - p*d, R);
return 2;
}
int get_circle(pdd p0, pdd p1, pdd p2, circle &des){
pdd a = (p0+p1) * 0.5, b = r90(p0-p1);
pdd u = (p0+p2) * 0.5, v = r90(p0-p2), R;
if( !intersect(a, b, u, v, R) ) return 0;
des = circle(a+b*R.first, size(a+b*R.first - p0));
return 1;
}
struct v3{
double x, y, z;
v3(){}
v3(double x, double y, double z) :x(x), y(y), z(z){}
v3 operator-()const{ return v3(-x, -y, -z); }
v3 operator-(const v3 &l)const{ return v3(x - l.x, y - l.y, z - l.z); }
v3 operator+(const v3 &l)const{ return v3(x + l.x, y + l.y, z + l.z); }
v3 operator*(const double c)const{ return v3(x*c, y*c, z*c); }
double operator*(const v3 &l)const{ return x*l.x + y*l.y + z*l.z; }
v3 operator^(const v3 &l)const{ return v3(y*l.z - z*l.y, z*l.x - x*l.z, x*l.y - y*l.x); }
double size(){ return sqrt(sq(x) + sq(y) + sq(z)); }
double size2(){ return sq(x) + sq(y) + sq(z); }
v3 norm(){
double p = size();
return v3(x / p, y / p, z / p);
}
void print(){ printf("%lf %lf %lf\n", x, y, z); }
bool operator < (const v3 &l) const {
if (abs(x - l.x) >= EPS) return x < l.x;
if (abs(y - l.y) >= EPS) return y < l.y;
if (abs(z - l.z) >= EPS) return z < l.z;
return false;
}
bool operator == (const v3 &l) const {
return abs(x - l.x) < EPS && abs(y - l.y) < EPS && abs(z - l.z) < EPS;
}
};
struct Quad{
double a;
v3 v;
Quad(double a, v3 v) :a(a), v(v){}
Quad operator * (const double &c)const{ return Quad(a * c, v * c); }
Quad operator~() const { return Quad(-a, -v); }
Quad operator-() const { return Quad(a, -v) * (1 / (sq(a) + sq(v.x) + sq(v.y) + sq(v.z))); }
Quad operator * (const Quad &l)const{ return Quad(a*l.a - v*l.v, l.v*a + v*l.a + (v^l.v)); }
v3 apply(v3 p){
return ((*this) * Quad(0, p) * -(*this)).v;
}
};
double size(v3 a){ return a.size(); }
double size2(v3 a){ return a.size2(); }
v3 norm(v3 a){ return a.norm(); }
v3 unit(double a, double b){ return v3(cos(a)*cos(b),sin(a)*cos(b),sin(b)); }
Quad set_rotate(v3 axis, double a){
return Quad(cos(a / 2), axis.norm() * sin(a / 2));
}
struct sphere{
sphere(v3 O, double r):O(O), r(r){}
v3 O;
double r;
};
//sphere - line
int intersect(sphere A, v3 s, v3 d, double des[2]){
double c = (A.O - s).size2() - sq(A.r), b = d * (s - A.O), a = d.size2();
if (b*b - a*c < 0) return 0;
des[0] = (-b + sqrt(b*b - a*c)) / a;
des[1] = (-b - sqrt(b*b - a*c)) / a;
return 2;
}
// face - face
int intersect(v3 u, v3 v, v3 p, v3 q, v3 &s, v3 &d){ // v.size(), q.size() == 1
if( abs(v*q-1) < EPS ) return 0;
d = v^q;
double t = v*q;
s = v*((u*v - p*q*t) / (1-t*t)) + q*((u*v*t - p*q) * 1.0 / (t*t-1));
return 1;
}
// face - line
int intersect(v3 u, v3 v, v3 p, v3 q, v3 &s){ // v.size(), q.size() == 1
if( abs(q*v) <= EPS ) return 0;
s = p + q * (((p-u)*v) / (q*v));
printf("%.10lf\n", (u-s)*v);
return 1;
}
bool isintersect(pdd &a, pdd &b, pdd &u, pdd &v){
if( (((u-a)^(b-a)) < 0) ^ (((v-a)^(b-a)) < 0) );
else return false;
if( (((a-u)^(v-u)) < 0) ^ (((b-u)^(v-u)) < 0) ) return true;
else return false;
}
double area(circle C, double s, double e)
{
double p = C.O.first, q = C.O.second, r = C.r;
return (p*r*(sin(e) - sin(s)) + q*r*(cos(s)-cos(e)) + r*r*(e-s)) * 0.5;
}
template<typename T>
void convex_hull(vector<T> &L, vector<T> &R){
int mn = 0;
for(int i = 1; i < L.size(); i++){
if( L[mn] < L[i] ) mn = i;
}
swap(L[mn], L[0]);
T t = L[0];
for(int i = 1; i < L.size(); i++) L[i] = L[i] - L[0];
L[0] = T(0, 0);
sort(L.begin()+1, L.end(), [](T l, T r){
if( sign(l^r) != 0 ) return sign(l^r) < 0;
return size(l) < size(r);
});
for(T c : L){
while(R.size() >= 2 && sign((R[R.size()-2] - R.back()) ^ (c - R.back())) <= 0 ) R.pop_back();
R.push_back(c);
}
for(T &c : R) c = c + t;
}
double area(pdd A[4], pdd B[4]){
vector<pdd> L;
for(int i = 0; i < 3; i++) L.push_back(A[i]);
for(int i = 0; i < 3; i++) L.push_back(B[i]);
for(int i = 0; i < 3; i++){
for(int j = 0; j < 3; j++){
pdd R;
if( !intersect(A[i], A[i+1]-A[i], B[j], B[j+1] - B[j], R) ) continue;
if( R.first < -EPS || R.first > 1+EPS || R.second < -EPS || R.second > 1+EPS ) continue;
L.push_back(A[i] + (A[i+1]-A[i]) * R.first);
}
}
vector<pdd> tmp;
swap(tmp, L);
for(pdd c : tmp){
bool ch = 1;
for(int i = 0; ch && i < 3; i++){
if( ((A[i+1]-A[i]) ^ (c-A[i])) > EPS ) ch = 0;
}
for(int i = 0; ch && i < 3; i++){
if( ((B[i+1]-B[i]) ^ (c-B[i])) > EPS ) ch = 0;
}
if( ch ) L.push_back(c);
}
if( L.size() == 0 ) return 0;
sort(L.begin(), L.end());
L.resize(unique(L.begin(), L.end()) - L.begin());
vector<pdd> R; convex_hull(L, R);
double ans = 0;
R.push_back(R[0]);
for(int i = 0; i+1 < R.size(); i++) ans += R[i+1] ^ R[i];
return ans;
}
circle make_circle(vector<pdd> Q){
if( Q.size() == 0 ) return circle(pdd(0, 0), 0);
if( Q.size() == 1 ) return circle(Q[0], 0);
circle res;
for(int i = 0; i < Q.size(); i++){
swap(Q.back(), Q[i]);
res = circle((Q[0]+Q[1]) * 0.5, size(Q[0]-Q[1])/2);
bool ch = 1; for(pdd c : Q) if( size2(c-res.O) > sq(res.r) + EPS ) ch = 0;
if( ch ) return res;
swap(Q.back(), Q[i]);
}
get_circle(Q[0], Q[1], Q[2], res);
return res;
}
circle smallest_circle(vector<pdd> &P, vector<pdd> &Q, int N)
{
circle c = make_circle(Q);
if( N == 0 || Q.size() >= 3 ) return c;
for(int i = 0; i < N; i++){
if( size2(c.O - P[i]) > sq(c.r) ){
Q.push_back(P[i]);
c = smallest_circle(P, Q, i);
Q.pop_back();
}
}
return c;
}
void convex_hull(vector<v3> &L, vector<v3> &R, vector<v3> &O, vector<v3> &D, vector<v3> &X)
{
int N = L.size();
static bool chk[1005][1005];
static bool in[1005];
for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) chk[i][j] = 0, in[i] = 0;
int q1 = 0, q2 = 1;
queue<pii> Q;
vector<pair<pii, int>> F;
for(int i = 1; i < N; i++) if( L[i].z < L[q1].z ) q1 = i, q2 = 0;
for(int i = 0; i < N; i++){
if( i == q1 ) continue;
if( (norm(L[i] - L[q1]) * v3(0, 0, 1)) < (norm(L[q2]-L[q1]) * v3(0, 0, 1)) ) q2 = i;
}
Q.push(pii(q1, q2)); chk[q1][q2] = 1;
while(Q.size()){
pii f = Q.front(); Q.pop();
int a = f.first, b = f.second, c = -1;
in[a] = in[b] = 1;
for(int i = 0; i < N; i++){
if( i == a || i == b ) continue;
if( c == -1 || ((L[i]-L[a])^(L[c]-L[a]))*(L[b]-L[a]) < 0 ) c = i;
}
if( !chk[c][b] ) Q.push(pii(c, b)), chk[c][b] = 1;
if( !chk[a][c] ) Q.push(pii(a, c)), chk[a][c] = 1;
if( a > b ) swap(a, b);
if( b > c ) swap(b, c);
if( a > b ) swap(a, b);
F.emplace_back(pii(a, b), c);
}
sort(F.begin(), F.end());
F.resize(unique(F.begin(), F.end()) - F.begin());
for(auto f : F){
int a = f.first.first, b = f.first.second, c = f.second;
O.push_back(L[a]); X.push_back(norm(L[a] - L[b]));
D.push_back(norm((L[a]-L[b])^(L[c]-L[b])));
}
for(int i = 0; i < N; i++) if( in[i] ) R.push_back(L[i]);
}
// C : conter_clockwise(C[0] == C[N])
// return highest point in C <- P(clockwise) or -1 in convex
// recommend : strongly convex, C.size() >= 3, C[i] != P
// up^down == 0 : on line
int convex_tangent(vector<pii> &C, pii P, int up = 1){
auto sign = [&](ll c){ return c > 0 ? up : c == 0 ? 0 : -up; };
auto local = [&](pii P, pii a, pii b, pii c) {
return sign((a - P) ^ (b - P)) <= 0 && sign((b - P) ^ (c - P)) >= 0;
};
assert(C.size() >= 2);
int N = C.size()-1, s = 0, e = N, m;
if( local(P, C[1], C[0], C[N-1]) ) return 0;
// for(int i = 1; i < N; i++) if( local(P, C[i-1], C[i], C[i+1])) return i;
while(s+1 < e){
m = (s+e) / 2;
if( local(P, C[m-1], C[m], C[m+1]) ) return m;
if( sign((C[s]-P) ^ (C[s+1]-P)) < 0 ){ // up
if( sign((C[m]-P) ^ (C[m+1]-P)) > 0 ) e = m;
else if( sign((C[m]-P) ^ (C[s]-P)) > 0 ) s = m;
else e = m;
}
else{ // down
if( sign((C[m]-P) ^ (C[m+1]-P)) < 0 ) s = m;
else if( sign((C[m]-P) ^ (C[s]-P)) < 0 ) s = m;
else e = m;
}
}
if( s && local(P, C[s-1], C[s], C[s+1]) ) return s;
if( e != N && local(P, C[e-1], C[e], C[e+1]) ) return e;
return -1;
}
// lo = 1 : lower_convex
int cmp_flag = 0, cmp_lo = 0;
struct Convex{
struct line{
line(pii x){
if( !cmp_flag ) s = x;
else d = x;
}
line(pii s, pii d):s(s), d(d){}
pii s, d;
bool operator<(const line &l)const{
if( !cmp_flag ) return s < l.s;
return cmp_lo ? d/l.d > 0 : d/l.d < 0;
}
};
int lo;
set<line> C;
void add(pii p){
cmp_flag = 0;
auto pos = [&](ll x){ return lo ? x >= 0 : x <= 0; };
auto neg = [&](ll x){ return lo ? x <= 0 : x >= 0; };
auto e = C.upper_bound(line(p)), d = e;
if( e != C.end() && d != C.begin() ){ d--;
if( pos((e->s - d->s)/(p - d->s)) ) return;
}
if( lo && e == C.end() && C.size() && C.rbegin()->s.first == p.first ) return;
if( !lo && e == C.begin() && C.size() && e->s.first == p.first ) return;
while(1){
d = C.upper_bound(line(p)), e = d;
if( d == C.end() || ++e == C.end()) break;
if( neg((d->s - p)/(e->s - p)) ) C.erase(d);
else break;
}
while(1){
d = C.upper_bound(line(p)), e = d;
if( d == C.begin() || --e == C.begin()) break;
d = e; --e; if( pos((d->s - p)/(e->s - p)) ) C.erase(d);
else break;
}
if( lo && C.size() && C.rbegin()->s.first == p.first) C.erase(--C.end());
if( !lo && C.size() && C.begin()->s.first == p.first) C.erase(C.begin());
d = C.upper_bound(line(p));
if( d != C.begin() ){
e = prev(d);
line t = line(e->s, p - e->s);
C.erase(e); C.insert(t);
}
if( d == C.end() ) C.insert(line(p, pii(0, lo? 1 : -1)));
else C.insert(line(p, d->s - p));
}
// x * -m.second + y * m.first minimize
ll get_mn(pii m){
cmp_flag = 1; cmp_lo = lo;
auto d = C.lower_bound(m);
return (ll)d->s.first * -m.second + (ll)d->s.second * m.first;
}
};
namespace halfplane_intersection{
const int INF = 1e9;
struct line{
line(pdd u, pdd v):u(u), v(v){}
pdd u, v;
};
double C(line A, line B){
return B.v / A.v == 0 ? 1e18 : ((A.u - B.u)/B.v) / (double)(B.v/A.v);
}
bool V(line A, line B, double cur){
double l = (cur - A.u.first) / A.v.first * A.v.second + A.u.second;
double r = (cur - B.u.first) / B.v.first * B.v.second + B.u.second;
return l >= r;
}
pdd W(line A, line B){
return (pdd)A.v * C(A, B) + (pdd)A.u;
}
void chain(vector<line> &X, double l,double r, int up){
vector<line> R;
sort(X.begin(), X.end(), [&](line l, line r){ return l.v/r.v*up < 0; });
R.emplace_back(pdd(l, 0), pdd(0, up));
X.emplace_back(pdd(r, 0), pdd(0, -up));
for(line c : X){
while(R.size() >= 2 && C(R[R.size()-2], R.back()) >= C(R[R.size()-2], c)) R.pop_back();
R.push_back(c);
} swap(R, X);
X.pop_back(); X.erase(X.begin());
}
int reduce(vector<line> &X, vector<line> &Y, double &cur, int left){
while(X.size() && Y.size()){
if( V(X.back(), Y.back(), cur) ) break;
if( X.back().v/Y.back().v*left >= 0 ) return 0;
cur = W(X.back(), Y.back()).first;
int ch = 0;
while(X.size() >= 2 && !V(X[X.size()-2], X.back(), cur)) X.pop_back(), ch = 1;
while(Y.size() >= 2 && V(Y[Y.size()-2], Y.back(), cur)) Y.pop_back(), ch = 1;
if( !ch ) break;
}
return 1;
}
// U + kV, CCW(Ex. ->: up, <-: down)
// 0 : empty, 1 : convex
// R -> 0: empty, 1: ccw order closed points
// added -1e9 ~ 1e9 x -1e9 ~ 1e9 bounding box
int run(vector<pdd> &U, vector<pdd> &V, vector<pdd> &R, double l = -INF, double r = INF,
double u = -INF, double d = INF){
U.emplace_back(0, u); V.emplace_back(1, 0);
U.emplace_back(0, d); V.emplace_back(-1, 0);
vector<line> X, Y; // X : up convex, Y : down convex
int N = V.size();
for(int i = 0; i < N; i++){
if( V[i].first == 0 ){
if( V[i].second > 0 ) r = min(r, U[i].first);
else l = max(l, U[i].first);
}
else if( V[i].first < 0 ) X.emplace_back(U[i], -V[i]);
else Y.emplace_back(U[i], V[i]);
}
chain(X, l, r, 1);
chain(Y, l, r, -1);
double left = l, right = r;
auto rv = [](vector<line> &t){ reverse(t.begin(), t.end()); };
if( !reduce(X, Y, right, -1) ){
return 0;
}
rv(X), rv(Y); reduce(X, Y, left, 1); rv(Y);
vector<line> L;
if( left == l ) L.emplace_back(pdd(l, 0), pdd(0, 1));
for(line c : Y) L.push_back(c);
if( right == r ) L.emplace_back(pdd(r, 0), pdd(0, -1));
for(line c : X) L.push_back(c);
for(int i = 0; i+1 < L.size(); i++) R.push_back(W(L[i], L[i+1]));
R.push_back(W(L.back(), L[0]));
R.resize(unique(R.begin(), R.end()) - R.begin());
return 1;
}
};
double area(pdd A, pdd B, double R) {
auto helper = [](pdd A, pdd B, double R){ return R*R*atan2(A^B, A*B) / 2; };
auto is_valid = [](double x) { return 0 <= x && x <= 1; };
double ans = 0, rv = 1;
pdd C, D, res[2];
if( size2(A) > size2(B) ) swap(A, B), rv = -1;
if (size2(B) <= R*R) ans = (A^B) / 2;
else if (size2(A) <= R*R) {
if (!intersect(circle(pdd(0, 0), R), A, B-A, res)) ans = (A^B) / 2;
else C = A + (B-A) * (is_valid(res[1].second)? res[1].second : res[0].second), ans = (A^C) / 2 + helper(C, B, R);
}
else {
if (!intersect(circle(pdd(0, 0), R), A, B-A, res) ||
res[0].second < 0 && res[1].second < 0 || res[0].second > 1 && res[1].second > 1) ans = helper(A, B, R);
else C = A + (B-A) * res[0].second, D = A + (B-A) * res[1].second, ans = helper(A, C, R) + (C^D) / 2 + helper(D, B, R);
}
return ans * rv;
}
#include<stdio.h>
#include<math.h>
#define PI 3.14159
typedef pair<double, double> pi;
struct point{
double x, y;
}w[100100], Deq[50100];
double S;
int n;
bool ccw(point p, point q, point r){
return (q.x - p.x)*(r.y - p.y) - (q.y - p.y)*(r.x - p.x) > 0;
}
point inter(point a, point b, point c, point d){
double t = (-(a.y - b.y)*(d.x - b.x) + (a.x - b.x)*(d.y - b.y)) / ((a.y - b.y)*(c.x - d.x) - (a.x - b.x)*(c.y - d.y));
point R;
R.x = t*c.x + (1 - t)*d.x;
R.y = t*c.y + (1 - t)*d.y;
return R;
}
double dis(point a, point b){
return (b.x - a.x)*(b.x - a.x) + (b.y - a.y)*(b.y - a.y);
}
const double eps = 1e-6;
pi sub(vector<pi> &v, int x, int y){
x %= v.size(), y %= v.size();
return pi(v[y].first - v[x].first, v[y].second - v[x].second);
}
double dist(pi a, pi b){
return hypot(b.second - a.second, b.first - a.first);
}
double ccw(pi a, pi b, pi c){
double dx1 = b.first - a.first;
double dy1 = b.second - a.second;
double dx2 = c.first - a.first;
double dy2 = c.second - a.second;
return dx1 * dy2 - dy1 * dx2;
}
bool IsPossible(double R){
int i, h = 1, t = 0, ck = 0, pv;
double dx, dy, L;
vector<pi> U, V;
for (i = 0; i < n; i++){
dx = -(w[i + 1].y - w[i].y);
dy = w[i + 1].x - w[i].x;
L = sqrt(dx*dx + dy*dy);
dx = dx*R / L, dy = dy*R / L;
pi x = pi(w[i].x + dx, w[i].y + dy);
pi y = pi(w[i+1].x - w[i].x, w[i+1].y - w[i].y);
U.push_back(x);
V.push_back(y);
}
reverse(U.begin(), U.end());
reverse(V.begin(), V.end());
vector<pi> w;
if(!halfplane_intersection::run(U, V, w, -1e9, 1e9, -1e9, 1e9)) return false;
double ret = 0;
int p = 0;
for(int i=0; i<w.size(); i++){
while(ccw(pi(0, 0), sub(w, p+1, p), sub(w, i, i+1)) > -eps){
ret = max(ret, dist(w[i], w[p]));
p = (p+1)%w.size();
ret = max(ret, dist(w[i], w[p]));
}
ret = max(ret, dist(w[i], w[p]));
}
return ret >= 2 * R;
}
int main()
{
int i;
double B, E, R;
scanf("%d", &n);
for (i = 0; i < n; i++)
scanf("%lf%lf", &w[i].x, &w[i].y);
w[n] = w[0];
for (i = 0; i < n; i++)
S += w[i].x*w[i + 1].y - w[i].y*w[i + 1].x;
if (S < 0)S = -S;
S /= 2;
B = 0, E = sqrt(S / (2 * PI));
while (E-B > 0.0001){
R = (B + E)*0.5;
if (IsPossible(R))B = R;
else E = R;
}
printf("%.3lf\n", R);
}
Compilation message
2circles.cpp: In function 'double area(pdd*, pdd*)':
2circles.cpp:346:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 0; i+1 < R.size(); i++) ans += R[i+1] ^ R[i];
^
2circles.cpp: In function 'circle make_circle(std::vector<std::pair<double, double> >)':
2circles.cpp:354:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 0; i < Q.size(); i++){
^
2circles.cpp: In function 'int halfplane_intersection::run(std::vector<std::pair<double, double> >&, std::vector<std::pair<double, double> >&, std::vector<std::pair<double, double> >&, double, double, double, double)':
2circles.cpp:595:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 0; i+1 < L.size(); i++) R.push_back(W(L[i], L[i+1]));
^
2circles.cpp: In function 'double area(pdd, pdd, double)':
2circles.cpp:616:23: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
res[0].second < 0 && res[1].second < 0 || res[0].second > 1 && res[1].second > 1) ans = helper(A, B, R);
^
2circles.cpp:616:65: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
res[0].second < 0 && res[1].second < 0 || res[0].second > 1 && res[1].second > 1) ans = helper(A, B, R);
^
2circles.cpp: In function 'bool IsPossible(double)':
2circles.cpp:687:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i=0; i<w.size(); i++){
^
2circles.cpp:668:9: warning: unused variable 'h' [-Wunused-variable]
int i, h = 1, t = 0, ck = 0, pv;
^
2circles.cpp:668:16: warning: unused variable 't' [-Wunused-variable]
int i, h = 1, t = 0, ck = 0, pv;
^
2circles.cpp:668:23: warning: unused variable 'ck' [-Wunused-variable]
int i, h = 1, t = 0, ck = 0, pv;
^
2circles.cpp:668:31: warning: unused variable 'pv' [-Wunused-variable]
int i, h = 1, t = 0, ck = 0, pv;
^
2circles.cpp: In instantiation of 'void convex_hull(std::vector<_RealType>&, std::vector<_RealType>&) [with T = std::pair<double, double>]':
2circles.cpp:342:33: required from here
2circles.cpp:294:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 1; i < L.size(); i++){
^
2circles.cpp:299:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 1; i < L.size(); i++) L[i] = L[i] - L[0];
^
2circles.cpp: In function 'int main()':
2circles.cpp:702:17: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%d", &n);
^
2circles.cpp:704:36: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%lf%lf", &w[i].x, &w[i].y);
^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
5636 KB |
Output is correct |
| 2 |
Incorrect |
0 ms |
5636 KB |
Output isn't correct |
| 3 |
Correct |
0 ms |
5636 KB |
Output is correct |
| 4 |
Correct |
0 ms |
5636 KB |
Output is correct |
| 5 |
Correct |
19 ms |
6120 KB |
Output is correct |
| 6 |
Correct |
116 ms |
7648 KB |
Output is correct |
| 7 |
Correct |
109 ms |
7588 KB |
Output is correct |
| 8 |
Correct |
166 ms |
8104 KB |
Output is correct |
| 9 |
Correct |
316 ms |
10080 KB |
Output is correct |
| 10 |
Correct |
413 ms |
13920 KB |
Output is correct |
