#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <ctime>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <set>
#include <map>
#include <iostream>
#include <deque>
#include <complex>
#include <string>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <valarray>
#include <unordered_map>
#include <iterator>
#include <assert.h>
using namespace std;
typedef long long int ll;
typedef unsigned int uint;
typedef unsigned char uchar;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

#define REP(i,x) for(int i=0;i<(int)(x);i++)
#define REPS(i,x) for(int i=1;i<=(int)(x);i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RREPS(i,x) for(int i=((int)(x));i>0;i--)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++)
#define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++)
#define ALL(container) (container).begin(), (container).end()
#define RALL(container) (container).rbegin(), (container).rend()
#define SZ(container) ((int)container.size())
#define mp(a,b) make_pair(a, b)
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os;
}
template<class T> ostream& operator<<(ostream &os, const set<T> &t) {
os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}
template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first-t.first, s.second-t.second);}

namespace geom{
#define X real()
#define Y imag()
#define at(i) ((*this)[i])
#define SELF (*this)
	enum {TRUE = 1, FALSE = 0, BORDER = -1};
	typedef int BOOL;
	typedef long double R;
	const R INF = 1e10;
	R EPS = 1e-10;
	const R PI = 3.1415926535897932384626;
	inline int sig(const R &x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }
	inline BOOL less(const R &x, const R &y) {return sig(x-y) ? x < y : BORDER;}
	typedef complex<R> P;
	inline R norm(const P &p){return p.X*p.X+p.Y*p.Y;}
	inline R inp(const P& a, const P& b){return (conj(a)*b).X;}
	inline R outp(const P& a, const P& b){return (conj(a)*b).Y;}
	inline P unit(const P& p){return p/abs(p);}
	inline P proj(const P &s, const P &t){return t*inp(s, t)/norm(t);}
	inline int ccw(const P &s, const P &t, const P &p, int adv=0){
		int res = sig(outp(t-s, p-s));
		if(res || !adv) return res;
		if(sig(inp(t-s, p-s)) < 0) return -2;	// p-s-t
		if(sig(inp(s-t, p-t)) < 0) return 2;	// s-t-p
		return 0;								// s-p-t
	}
	
	
	struct L : public vector<P>{	// line
		L(const P &p1, const P &p2){this->push_back(p1);this->push_back(p2);}
		L(){}
		P dir()const {return at(1) - at(0);}
		BOOL online(const P &p)const {return !sig(outp(p-at(0), dir()));}
	};
	struct S : public L{	// segment
		S(const P &p1, const P &p2):L(p1, p2){}
		S(){}
		BOOL online(const P &p)const {
			if(!sig(norm(p - at(0))) || !sig(norm(p - at(1)))) return BORDER;
			return !sig(abs(at(0)-p) + abs(at(1) - p) - abs(at(0) - at(1)));
		}
	};
	struct C : public P{
		C(){}
		C(const P& p, const R r):P(p), r(r){}
		R r;
		BOOL inside(const P& p)const { return less(norm(p-SELF), r*r);}
	};
	struct F : public C{
		R s, t;
		F(const C &c, R ss, R tt):C(c), s(ss), t(tt){
			if(PI < s) s -= 2*PI;
			if(PI < t) t -= 2*PI;
		}
		BOOL inside(const P& p)const {
			P v = p - SELF;
			if(!sig(norm(v))) return BORDER;
			R a = arg(v);
			if(t < s){
				if((!less(s, a) && !less(a, t)) || !less(norm(v), r*r)) return FALSE;
				return less(s, a) | less(a, t) | less(norm(v), r*r);
			}else{
				if(!less(s, a) || !less(a, t) || !less(norm(v), r*r)) return FALSE;
				return less(s, a) | less(a, t) | less(norm(v), r*r);
			}
		}
	};
	P crosspoint(const L &l, const L &m);
	struct G : public vector<P>{
		G(size_type size=0):vector(size){}
		S edge(int i)const {return S(at(i), at(i+1 == size() ? 0 : i+1));}
		BOOL contains(const P &p)const {
			R sum = .0;
			REP(i, size()){
				if(S(at(i), at((i+1)%size())).online(p)) return BORDER;	// online
				sum += arg((at(i) - p) / (at((i+1)%size()) - p));
			}
			return !!sig(sum);
		}
		R area()const {
			R sum = 0;
			REP(i, size()) sum += outp(at(i), at((i+1)%size()));
			return abs(sum / 2.);
		}
		P gp()const {
			P r(.0, .0);
			REP(i, size()){
				const S &s = edge(i);
				r += (s[0]+s[1])*outp(s[0], s[1]);
			}
			return r / (6*area());
		}
		G convex_hull(bool online = false) {
			if(size() < 2) return *this;
			sort(ALL(*this));
			G r;
			r.resize((int)size()*2);
			int k=0;
			for(int i=0;i<size();r[k++]=at(i++))
				while(k>1 && ccw(r[k-2], r[k-1], at(i)) < 1-online) k--;
			int t = k;
			for(int i=(int)size()-1;i>=0;r[k++]=at(i--))
				while(k>t && ccw(r[k-2], r[k-1], at(i)) < 1-online) k--;
			r.resize(k-1);
			return r;
		}
		G cut(const L &l)const {
			G g;
			REP(i, size()){
				const S &s = edge(i);
				if(ccw(l[0], l[1], s[0], 0) >= 0) g.push_back(s[0]);
				if(ccw(l[0], l[1], s[0], 0) * ccw(l[0], l[1], s[1], 0) < 0)
					g.push_back(crosspoint(s, l));
			}
			return g;
		}
		G Voronoi(const vector<P> &p, const int t)const {
			G g = *this;
			REP(i, p.size())if(i!=t){
				const P m = (p[t]+p[i])*(R)0.5;
				g = g.cut(L(m, m+(p[i]-p[t])*P(0, 1)));
			}
			return g;
		}
	};

	inline P proj(const P &s, const L &t){return t[0] + proj(s-t[0], t[1]-t[0]);}
	inline P reflect(const P &s, const L &t){return (R)2.*proj(s, t) - s;}
	inline S reflect(const S &s, const L &t){return S(reflect(s[0], t), reflect(s[1], t));}
	BOOL intersect(const S &s, const S &t){
		const int p = ccw(t[0], t[1], s[0], 1) * ccw(t[0], t[1], s[1], 1);
		const int q = ccw(s[0], s[1], t[0], 1) * ccw(s[0], s[1], t[1], 1);
		return (p>0||q>0) ? FALSE : (!p||!q) ? BORDER : TRUE;
	}
	BOOL intersect(const S &s, const L &l){
		if(l.online(s[0]) || l.online(s[1])) return BORDER;
		return (sig(outp(l.dir(), s[0]-l[0])) * sig(outp(l.dir(), s[1]-l[0])) <= 0);
	}
	R dist2(const L &l, const P &p){return norm(outp(l.dir(), p - l[0])) / norm(l.dir());}
	R dist2(const S &s, const P &p){
		if(inp(p-s[0],  s.dir()) < EPS) return norm(p - s[0]);
		if(inp(p-s[1], -s.dir()) < EPS) return norm(p - s[1]);
		return dist2((const L &)s, p);
	}
	R dist2(const S &s, const L &l){
		return intersect(s, l) ? .0 : min(dist2(l, s[0]), dist2(l, s[1]));
	}
	R dist2(const S &s, const S &t){
		return intersect(s, t) ? .0 : min(min(dist2(s, t[0]), dist2(t, s[0])), 
									   	  min(dist2(s, t[1]), dist2(t, s[1])));
	}
	template <class T> R dist2(const G &g, const T& t){ // todo: テ・ツ??ゥツδィテ」ツ?ォテ・ツョツ古・ツ?ィテ」ツ?ォテ・ツ青ォテ」ツ?セテ」ツつ古」ツつ凝・ツ?エテ・ツ青?
		R res = INF;
		REP(i, g.size()) res = min(res, dist2(g.edge(i), t));
		return res;
	}
	template<class S, class T> R dist(const S& s, const T& t){return sqrt(dist2(s, t));}
	inline BOOL intersect(const C &a, const C &b){
		return less((a.r-b.r)*(a.r-b.r), norm(a-b)) + less(norm(a-b), (a.r+b.r)*(a.r+b.r)) - 1;
	}

#undef SELF
#undef at
}

using namespace geom;

int f = 0;
namespace std{
	bool operator<(const P &a, const P &b){return sig(a.X-b.X) ? a.X < b.X : a.Y+EPS < b.Y;}
	bool operator==(const P &a, const P &b){return abs(a-b) < EPS;}
	istream& operator>>(istream &is, P &p){R x,y;is>>x>>y;p=P(x, y);return is;}
	istream& operator>>(istream &is, L &l){l.resize(2);return is >> l[0] >> l[1];}
	istream& operator>>(istream &is, C &c){return is >> (P &)c >> c.r;}
	const R B = 500;
	const R Z = 30;
	ostream& operator<<(ostream &os, const C &c){return os << "circle("<<B+Z*(c.X)<<", "<<1000-B-Z*(c.Y)<<", "<<Z*(c.r)<<")";}
	ostream& operator<<(ostream &os, const P &p){return os << C(p, 2./Z);}
	ostream& operator<<(ostream &os, const S &s){return os << "line("<<B+Z*(s[0].X)<<", "<<1000-B-Z*(s[0].Y)<<", "<<B+Z*(s[1].X)<<", "<<1000-B-Z*(s[1].Y)<<")";}
	ostream& operator<<(ostream &os, const G &g){REP(i, g.size()) cout << g.edge(i) << endl;return os;}

}

int n;

C icpc;
G g;

pair<P, R> getType(const P &p){
	REP(i, n){
		const S s = g.edge(i);
		if(s.online(p) == TRUE) return mp(s.dir(), abs(s[1] - p));
	}
	REP(i, n){
		const P q = g[i];
		if(!sig(abs(q - p))){
			P tar = q + unit(g.edge(i).dir())*P(0, 1)*icpc.r;
			if(!sig(abs(icpc - tar))) return mp(g.edge(i).dir(), abs(g.edge(i).dir()));
			return mp(tar, arg((tar - p)/(icpc - p)));
		}
	}
	assert(false);
}

P getNavigator(){
	vector<pair<R, P>> isc;
	REP(i, n){
		const S s = g.edge(i);
		P q = proj(icpc, s);
		if(s.online(q) == TRUE && !sig(abs(q - icpc) - icpc.r))
			isc.emplace_back(arg(q - icpc), q);
	}
	REP(i, n){
		const P q = g[i];
		if(!sig(abs(q - icpc) - icpc.r)) isc.emplace_back(arg(q - icpc), q);
	}
	sort(ALL(isc));
	pair<R, P> pp(.0, P(0, 0));
	REP(i, isc.size()){
		const auto cur = isc[i];
		const auto nxt = isc[(i+1)%isc.size()];
		R nxtarg = i+1 == isc.size() ? nxt.first + 2*PI : nxt.first;
		pp = max(pp, mp(nxtarg - cur.first, cur.second));
	}
	
	return pp.second;
}

R straight(P dir, R d = INF){
	REP(i, n){
		const S s = g.edge(i);
		if(sig(arg(dir*P(0, 1)/s.dir())) || inp(proj(icpc, s) - icpc, dir) < EPS || s.online(proj(icpc, s)) != TRUE) continue;
		d = min(d, abs(proj(icpc, s) - icpc) - icpc.r);
	}
	REP(i, n){
		const P q = g[i];
		R r = abs(q - proj(q, L(icpc, icpc+dir)));
		if(r + EPS > icpc.r || inp(q - icpc, dir) < EPS) continue;
		d = min(d, abs(proj(q, L(icpc, icpc+dir)) - icpc) - sqrt(icpc.r*icpc.r-r*r));
	}
	return d;
}

R rot(P nav, R r){
	REP(i, n){
		const S s = g.edge(i);
		if(abs(proj(nav, s) - nav) < EPS) continue;
		R t = arg((proj(nav, s) - nav)/(icpc - nav));
		if(t > 0 && t < PI) continue;
		R d = abs(proj(nav, s) - nav);
		if(d > 2*icpc.r - EPS) continue;
		R x = arg(s.dir()) - asin((d-icpc.r) / icpc.r) - arg(icpc-nav);
		if(d-icpc.r < 0) x = arg(s.dir()) - arg(icpc-nav)  + asin((icpc.r-d) / icpc.r);
		if(x < -PI) x += 2*PI;
		if(x > PI)  x -= 2*PI;
		if(x < -EPS) r = max(r, x);
	}
	REP(i, n){
		const P q = g[i];
		R d = abs(q-nav);
		if(d > 2*icpc.r - EPS || d < EPS) continue;
		P med = (nav + q) * (R).5;
		R d2 = sqrt(max((R).0, icpc.r*icpc.r - d*d*(R).25));
		P p1 = med + unit(med - nav)*P(0, 1)*d2;
		P p2 = med + unit(med - nav)*P(0, -1)*d2;

		if(arg((p1 - nav)/(icpc-nav)) < -EPS) r = max(r, arg((p1 - nav)/(icpc-nav)));
		if(arg((p2 - nav)/(icpc-nav)) < -EPS) r = max(r, arg((p2 - nav)/(icpc-nav)));
	}
	return r;
}
int main(){
	ios::sync_with_stdio(false);
	while(cin >> n >> icpc, n){
		g.resize(n);
		REP(i, n) cin >> g[i];
		R d = straight(P(1, 0));
		icpc += P(1, 0)*d;
		R ans = 0;
		G root;
		P prev = getNavigator();
		P start = icpc;
		while(1){
			P nav = getNavigator();
			if(sig(abs(prev-nav))){
				root.push_back(prev);
				root.push_back(icpc);
				ans += icpc.r * icpc.r * arg((nav-icpc)/(prev-icpc)) * .5;
			}
			if(!sig(abs(icpc-start)) && sig(root.area())) break;
			root.push_back(nav);
			prev = nav;
			auto t = getType(nav);
			if(t.second > 0){
				P picpc = icpc;
				prev += unit(t.first) * straight(t.first, t.second);
				icpc += unit(t.first) * straight(t.first, t.second);
				if(S(picpc, icpc).online(start) == TRUE && sig(root.area())) break;
			}else{
				(P &)icpc = nav + (icpc - nav)*polar((R)1., rot(nav, t.second));
				if(sig(abs(icpc-start)) && !sig(abs(start - nav) - icpc.r) && sig(root.area())) break;
			}
		}
		printf("%.10f\n", (double)(ans + root.area()));
	}
	return 0;
}

Measured memory_bytes: 1320