#include <iostream>#include <cstdio>#include <cmath>#include <cstring>#include <algorithm>#include <vector>using namespace std;#define N 55#define EPS 1e-7const double PI = acos(-1.0);int sgn(double a){ return (a > EPS) - (a < -EPS);}struct Po{ double x, y; Po(double a = 0, double b = 0) { x = a; y = b; } Po operator +(const Po & a) const { return Po(x + a.x, y + a.y); } Po operator -(const Po & a) const { return Po(x - a.x, y - a.y); } Po vect(double a) const // return a vector of length a { a /= sqrt(x * x + y * y); return Po(x * a, y * a); } Po left() const // rotate 90 degrees { return Po(-y, x); }};struct Seg{ Po s,e; Seg(){} Seg(Po a,Po b){s=a;e=b;}};struct Line{ double a,b,c; Line(double x=1,double y=-1,double z=0){a=x;b=y;c=z;} Line(Po p1,Po p2) { int sig=1; a=p2.y-p1.y; if(a<0) {a=-a;sig=-1;} b=sig*(p1.x-p2.x); c=sig*(p1.y*p2.x-p1.x*p2.y); }};double xm(Po a,Po b,Po c) { return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y);}double dm(Po a,Po b,Po c) { return (b.x-a.x)*(c.x-a.x)+(b.y-a.y)*(c.y-a.y);}double dis(Po a,Po b){ return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}bool posy(Po &a){ if(a.y>0||(a.y==0&&a.x>0)) return 1; return 0;}bool Linecross(Line l1,Line l2,Po &p){ double d=l1.a*l2.b-l2.a*l1.b; if(fabs(d)<EPS) return false; p.x=(l2.c*l1.b-l1.c*l2.b)/d; p.y=(l2.a*l1.c-l1.a*l2.c)/d; return true;}int cli(Po cp,double r, Po l1,Po l2,Po& p1,Po& p2){ Po p=cp+(l2-l1).left(),rp; p.x+=l1.y-l2.y; p.y+=l2.x-l1.x; Linecross(Line(p,cp),Line(l1,l2),rp); double d=dis(rp,cp); if(sgn(d-r)>0) return 0; double t; if(sgn(d-r)==0) t=0; else t=sqrt(r*r-d*d); p1=rp-(rp-cp).left().vect(t); p2=rp+(rp-cp).left().vect(t); return 2;}bool inrec(Po a,Po b,Po p){ if(sgn(p.x-a.x)>0&&sgn(b.x-p.x)>0&&sgn(p.y-a.y)>0&&sgn(b.y-p.y)>0) return true; return false;}double midang(double a,double b){ if(b<a) b+=2*PI; double md=(a+b)/2; if(md>PI) md-=2*PI; return md;}struct FK{ double a; int dt; FK(double b=0,int d=0) { a=b; dt=d; }};int fkcmp(FK a,FK b){ if(sgn(b.a-a.a)>0) return 1; if(sgn(b.a-a.a)==0) return a.dt>b.dt; return 0;}int main(){ double r; int n; while(scanf("%lf%d",&r,&n)==2) { double x1[N],x2[N],y1[N],y2[N]; for(int i=0;i<n;i++) { scanf("%lf%lf%lf%lf",&x1[i],&y1[i],&x2[i],&y2[i]); } int ok=0; for(int i=0;i<n;i++) { if(x1[i]-EPS<=-r&&x2[i]>=r-EPS&&y1[i]-EPS<=-r&&y2[i]>=r-EPS) { printf("%.3lfn",2*r*PI); ok=1; break; } } if(ok) continue; vector<FK> vec; for(int i=0;i<n;i++) { vector<double> tmp; Po p1,p2; if(cli(Po(0,0),r,Po(x1[i],y1[i]),Po(x2[i],y1[i]),p1,p2)==2) { if(dm(p1,Po(x1[i],y1[i]),Po(x2[i],y1[i]))<EPS) tmp.push_back(atan2(p1.y,p1.x)); if(dm(p2,Po(x1[i],y1[i]),Po(x2[i],y1[i]))<EPS) tmp.push_back(atan2(p2.y,p2.x)); } if(cli(Po(0,0),r,Po(x1[i],y2[i]),Po(x2[i],y2[i]),p1,p2)==2) { if(dm(p1,Po(x1[i],y2[i]),Po(x2[i],y2[i]))<EPS) tmp.push_back(atan2(p1.y,p1.x)); if(dm(p2,Po(x1[i],y2[i]),Po(x2[i],y2[i]))<EPS) tmp.push_back(atan2(p2.y,p2.x)); } if(cli(Po(0,0),r,Po(x1[i],y1[i]),Po(x1[i],y2[i]),p1,p2)==2) { if(dm(p1,Po(x1[i],y1[i]),Po(x1[i],y2[i]))<EPS) tmp.push_back(atan2(p1.y,p1.x)); if(dm(p2,Po(x1[i],y1[i]),Po(x1[i],y2[i]))<EPS) tmp.push_back(atan2(p2.y,p2.x)); } if(cli(Po(0,0),r,Po(x2[i],y1[i]),Po(x2[i],y2[i]),p1,p2)==2) { if(dm(p1,Po(x2[i],y1[i]),Po(x2[i],y2[i]))<EPS) tmp.push_back(atan2(p1.y,p1.x)); if(dm(p2,Po(x2[i],y1[i]),Po(x2[i],y2[i]))<EPS) tmp.push_back(atan2(p2.y,p2.x)); } int sz=tmp.size(); sort(tmp.begin(),tmp.end()); for(int j=0;j<sz;j++) { double ma=midang(tmp[j],tmp[(j+1)%sz]); Po pp(r*cos(ma),r*sin(ma)); if(inrec(Po(x1[i],y1[i]),Po(x2[i],y2[i]),pp)) { vec.push_back(FK(tmp[j],1)); vec.push_back(FK(tmp[(j+1)%sz],-1)); if(tmp[(j+1)%sz]<tmp[j]) { vec.push_back(FK(PI,-1)); vec.push_back(FK(-PI,1)); } } } } sort(vec.begin(),vec.end(),fkcmp); double ans=0; int cnt=0; for(int i=0;i<vec.size();i++) { if(cnt) ans+=vec[i].a-vec[i-1].a; cnt+=vec[i].dt; } printf("%.3lfn",ans*r); } return 0;}
