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#include <bits/stdc++.h> |
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using namespace std; |
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#define EPS 1e-8 |
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struct Point { |
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double x, y; |
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Point():x(0),y(0){} |
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Point(double x, double y):x(x),y(y){} |
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bool operator < (const Point &o) const { return x < o.x; } |
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bool operator == (const Point &o) const { return fabs(x-o.x)<EPS && fabs(y-o.y)<EPS; } |
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double operator * (const Point o) const { return x*o.x + y*o.y; } |
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Point operator - (const Point o) const { return Point(x-o.x, y-o.y); } |
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Point operator + (const Point o) const { return Point(x+o.x, y+o.y); } |
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Point operator / (double den) const { return Point(x/den, y/den); } |
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}; |
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std::istream& operator>> (std::istream& stream, Point& p) { |
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stream >> p.x >> p.y; |
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return stream; |
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} |
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double dist2(const Point p1, const Point p2) { |
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double xx = p1.x - p2.x, yy = p1.y - p2.y; |
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return xx*xx + yy*yy; |
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} |
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struct Line { |
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double a, b, c; |
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Line():a(0),b(0),c(1){} |
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Line(double x, double y):a(x),b(y),c(1){} |
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Line(double a, double b, double c):a(a),b(b),c(c){} |
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Line(const Point p1, const Point p2) { |
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if (fabs(p1.x - p2.x) < EPS) { |
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b = 0; |
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if (fabs(p1.x) < EPS) a=1, c=0; |
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else a = -1/p1.x, c = 1; |
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} |
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else { |
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a = p2.y - p1.y; |
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b = p1.x - p2.x; |
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c = -p1.y*b - p1.x*a; |
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} |
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} |
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double y(double x0) { return (-a*x0 - c) / b; } |
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double x(double y0) { return (-b*y0 - c) / a; } |
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}; |
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Line bisector(const Point &a, const Point &b) { |
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Line l(a, b); |
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Point m = (a+b) / 2; |
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swap(l.a, l.b); |
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l.b = -l.b; |
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l.c = -l.a*m.x - l.b*m.y; |
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return l; |
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} |
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int intersect(const Line l1, const Line l2, Point &r) { |
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r.x = l1.b*l2.c - l2.b*l1.c; |
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r.y = l2.a*l1.c - l1.a*l2.c; |
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double cc = l1.a*l2.b - l2.a*l1.b; |
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if (fabs(cc) < EPS) |
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return fabs(r.y)<EPS && fabs(r.x)<EPS ? 2 : 0; |
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r.x /= cc; |
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r.y /= cc; |
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return 1; |
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} |
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bool circle3pts(const Point &a, const Point &b, const Point &c, Point &r) { |
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return intersect(bisector(a, b), bisector(a, c), r) == 1; |
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} |
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double minCoverCircle(Point P[], int n) { |
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double cr = 0; |
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Point c = P[0]; |
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for (int i=1; i<n; ++i) |
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if (dist2(P[i], c) > cr+EPS) { |
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c = P[i]; cr = 0; |
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for (int j=0; j<i; ++j) |
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if (dist2(P[j], c) > cr+EPS) { |
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c = (P[i] + P[j]) / 2; |
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cr = dist2(P[i], c); |
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for (int k=0; k<j; ++k) |
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if (dist2(P[k], c) > cr+EPS) { |
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circle3pts(P[i], P[j], P[k], c); |
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cr = dist2(P[i], c); |
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} |
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} |
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} |
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return sqrt(cr); |
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} |
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int main() { |
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ios_base::sync_with_stdio(0);cin.tie(0); |
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int n; |
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double r; |
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Point P[143]; |
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while (cin >> n && n) { |
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for (int i=0; i<n; ++i) |
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cin >> P[i]; |
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cin >> r; |
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cout << (minCoverCircle(P, n) <= r |
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? "The polygon can be packed in the circle.\n" |
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: "There is no way of packing that polygon.\n" |
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); |
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} |
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} |
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