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/*
>>~~ UVa Online Judge ACM Problem Solution ~~<<
ID: 10005
Name: Packing polygons
Problem: https://onlinejudge.org/external/100/10005.pdf
Language: C++
Author: Arash Shakery
Email: [email protected]
*/
#include <bits/stdc++.h>
using namespace std;
#define EPS 1e-8
struct Point {
double x, y;
Point():x(0),y(0){}
Point(double x, double y):x(x),y(y){}
bool operator < (const Point &o) const { return x < o.x; }
bool operator == (const Point &o) const { return fabs(x-o.x)<EPS && fabs(y-o.y)<EPS; }
double operator * (const Point o) const { return x*o.x + y*o.y; }
Point operator - (const Point o) const { return Point(x-o.x, y-o.y); }
Point operator + (const Point o) const { return Point(x+o.x, y+o.y); }
Point operator / (double den) const { return Point(x/den, y/den); }
};
std::istream& operator>> (std::istream& stream, Point& p) {
stream >> p.x >> p.y;
return stream;
}
double dist2(const Point p1, const Point p2) {
double xx = p1.x - p2.x, yy = p1.y - p2.y;
return xx*xx + yy*yy;
}
struct Line {
double a, b, c;
Line():a(0),b(0),c(1){}
Line(double x, double y):a(x),b(y),c(1){}
Line(double a, double b, double c):a(a),b(b),c(c){}
Line(const Point p1, const Point p2) {
if (fabs(p1.x - p2.x) < EPS) {
b = 0;
if (fabs(p1.x) < EPS) a=1, c=0;
else a = -1/p1.x, c = 1;
}
else {
a = p2.y - p1.y;
b = p1.x - p2.x;
c = -p1.y*b - p1.x*a;
}
}
double y(double x0) { return (-a*x0 - c) / b; }
double x(double y0) { return (-b*y0 - c) / a; }
};
Line bisector(const Point &a, const Point &b) {
Line l(a, b);
Point m = (a+b) / 2;
swap(l.a, l.b);
l.b = -l.b;
l.c = -l.a*m.x - l.b*m.y;
return l;
}
int intersect(const Line l1, const Line l2, Point &r) {
r.x = l1.b*l2.c - l2.b*l1.c;
r.y = l2.a*l1.c - l1.a*l2.c;
double cc = l1.a*l2.b - l2.a*l1.b;
if (fabs(cc) < EPS)
return fabs(r.y)<EPS && fabs(r.x)<EPS ? 2 : 0;
r.x /= cc;
r.y /= cc;
return 1;
}
bool circle3pts(const Point &a, const Point &b, const Point &c, Point &r) {
return intersect(bisector(a, b), bisector(a, c), r) == 1;
}
// --------------------------------------------------------------------------------------------
double minCoverCircle(Point P[], int n) {
double cr = 0;
Point c = P[0];
for (int i=1; i<n; ++i)
if (dist2(P[i], c) > cr+EPS) {
c = P[i]; cr = 0;
for (int j=0; j<i; ++j)
if (dist2(P[j], c) > cr+EPS) {
c = (P[i] + P[j]) / 2;
cr = dist2(P[i], c);
for (int k=0; k<j; ++k)
if (dist2(P[k], c) > cr+EPS) {
circle3pts(P[i], P[j], P[k], c);
cr = dist2(P[i], c);
}
}
}
return sqrt(cr);
}
int main() {
ios_base::sync_with_stdio(0);cin.tie(0);
int n;
double r;
Point P[143];
while (cin >> n && n) {
for (int i=0; i<n; ++i)
cin >> P[i];
cin >> r;
cout << (minCoverCircle(P, n) <= r
? "The polygon can be packed in the circle.\n"
: "There is no way of packing that polygon.\n"
);
}
}
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