#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loos")
#endif

#include <bits/stdc++.h>

using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
template<class t>using vc=vector<t>;
template<class t>using vvc=vc<vc<t>>;
template<class t, class u>bool chmin(t &a, u b){
	if(a > b){ a = b; return true;}
	else return false;
}
template<class t, class u>bool chmax(t &a, u b){
	if(a < b){ a = b; return true;}
	else return false;
}
using vi=vc<int>;
#define a first
#define b second
#define mp make_pair
using pi=pair<int,int>;

using ld=long double;
const ld eps=1e-9;
using pt=complex<ld>;
#define x real()
#define y imag()

ld dot(pt a,pt b){return a.x*b.x+a.y*b.y;}
int sgn(ld a){return a<-eps?-1:a>eps?1:0;}
int sgn(ld a,ld b){return sgn(a-b);}
ld crs(pt a,pt b){return a.x*b.y-a.y*b.x;}
ld crs(pt a,pt b,pt c){return crs(b-a,c-a);}
int ccw(pt a,pt b){return sgn(crs(a,b));}
int ccw(pt a,pt b,pt c){return ccw(b-a,c-a);}
int bet(pt a,pt b,pt c){
	pt d=b-a;
	ld e=dot(d,c-a);
	if(sgn(e)<=0)return sgn(e)-1;
	return sgn(e-norm(d))+1;
}

using ln=pair<pt,pt>;
pt dir(ln a){return a.b-a.a;}
pt eval(ln a,ld b){return a.a+dir(a)*b;}

pt cll(ln a,ln b){
	return eval(a,crs(b.a,b.b,a.a)/crs(dir(a),dir(b)));
}

template<class t> int lwb(const vc<t>&vs,t v){
	return lower_bound(all(vs),v)-vs.bg;
}

bool ptcmp(pt a,pt b){
	int s=sgn(a.x,b.x);
	if(s)return s<0;
	else return sgn(a.y,b.y)<0;
}

void slv(){
	ld side;cin>>side;
	int n;cin>>n;
	vc<pt> ps(n);
	
	vc<pt> rect{pt(0,0),pt(side,0),pt(side,side),pt(0,side)};
	vc<pt> work;
	auto getarea=[&](pt a,pt b){
		work.clear();
		rep(i,4){
			int j=(i+1)%4;
			if(ccw(a,b,rect[i])>=0){
				work.pb(rect[i]);
				if(ccw(a,b,rect[j])<0)
					work.pb(cll(ln(a,b),ln(rect[i],rect[j])));
			}else{
				if(ccw(a,b,rect[j])>=0)
					work.pb(cll(ln(a,b),ln(rect[i],rect[j])));
			}
		}
		ld sum=0;
		rep(i,si(work)){
			sum+=crs(work[i],work[(i+1)%si(work)]);
			//cerr<<i<<" "<<work[i].x<<" "<<work[i].y<<" "<<sum<<endl;
		}
		
		//cerr<<"{"<<a.x<<","<<a.y<<"},{"<<b.x<<","<<b.y<<"} "<<sum/2<<endl;
		
		return sum/2/(side*side);
	};
	
	rep(i,n){
		ld a,b;cin>>a>>b;
		ps[i]=pt(a,b);
	}
	sort(all(ps),ptcmp);
	
	ld ans=0;
	rep(i,n){
		pt a,b;
		if(ps[i].y*2<side){
			if(ps[i].x*2<side){
				a=pt(ps[i].x*2,0);
				b=pt(0,ps[i].y*2);
			}else{
				a=pt(side,ps[i].y*2);
				b=pt(ps[i].x*2-side,0);
			}
		}else{
			if(ps[i].x*2<side){
				a=pt(0,ps[i].y*2-side);
				b=pt(ps[i].x*2,side);
			}else{
				a=pt(ps[i].x*2-side,side);
				b=pt(side,ps[i].y*2-side);
			}
		}
		int cnt=0;
		rep(j,n)if(ccw(a,b,ps[j])>=0)cnt++;
		
		chmax(ans,ld(cnt)/n-getarea(a,b));
	}
	
	//cerr<<ans<<endl;
	
	vc<pi> qs;
	rep(i,n)rng(j,i+1,n){
		qs.eb(i,j);
	}
	auto Qcmp=[&](pi a,pi b){
		pt adir=ps[a.b]-ps[a.a];
		pt bdir=ps[b.b]-ps[b.a];
		int c=ccw(adir,bdir);
		if(c)return c>0;
		ld d=dot(ps[a.a],adir);
		ld e=dot(ps[b.a],adir);
		c=sgn(d,e);
		if(c)return c<0;
		d=dot(ps[a.b],adir);
		e=dot(ps[b.b],bdir);
		return sgn(d,e)<0;
	};
	
	vi idx(n);iota(all(idx),0);
	vi pos=idx;
	
	sort(all(qs),Qcmp);
	for(auto q:qs){
		pt a=ps[q.a];
		pt b=ps[q.b];
		int i=pos[q.a];
		int j=pos[q.b];
		
		assert(i+1==j);
		//cerr<<i<<" "<<j<<endl;
		//cerr<<"{"<<a.x<<","<<a.y<<"},{"<<b.x<<","<<b.y<<"}"<<" "<<i<<" "<<j<<endl;
		
		chmax(ans,ld(n-min(i,j))/n-getarea(a,b));
		chmax(ans,ld(max(i,j)+1)/n-getarea(b,a));
		
		swap(idx[i],idx[j]);
		swap(pos[idx[i]],pos[idx[j]]);
	}
	
	cout<<ans<<endl;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	slv();
}