#include <bits/stdc++.h>
#define pb push_back
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define f first
#define s second
using namespace std;
using ll = long long;
using ld = double;
using pii = pair <int, int>;

template<class T> struct Point{
	T x, y;
	Point(T x = 0, T y = 0): x(x), y(y) {}
	using P = Point;
	P operator - (P p) const { return P(x - p.x, y - p.y); }
	P operator + (P p) const { return P(x + p.x, y + p.y); }
	P operator * (T d) const { return P(x * d, y * d); }
	P operator / (T d) const { return P(x / d, y / d); }
	T cross(P p) const { return x * p.y - y * p.x; }
	T cross(P a, P b) const { return (a - *this).cross(b - *this); }
	P perp() const { return P(-y, x); }
	bool side() const {
		if(y == 0) return x < 0;
		return y < 0;
	}
	bool operator < (P p) const{
		if(side() == p.side()) return cross(p) > 0;
		return p.side();
	}
	friend ostream& operator << (ostream& os, P p){
		return os << '(' << p.x << ", " << p.y << ')';
	}
};
template<class P> inline pair<int, P> lineInter(P s1, P e1, P s2, P e2){
	auto d = (e1 - s1).cross(e2 - s2);
	if(d == 0) return {-(s1.cross(e1, s2) == 0), P{0, 0}};
	auto p = s2.cross(e1, e2), q = s2.cross(e2, s1);
	return {1, (s1 * p + e1 * q) / d};
}
template<class P> inline vector<P> polygonCut(vector<P> poly, P s, P e){
	vector<P> res;
	for(int i = 0; i < sz(poly); i++){
		P cur = poly[i], prev = i ? poly[i - 1] : poly.back();
		bool side = s.cross(e, cur) < 0;
		if(side != (s.cross(e, prev) < 0))
			res.pb(lineInter(s, e, cur, prev).second);
		if(side) res.pb(cur);
	}
	return res;
}
using P = Point<ll>;
const int N = 3e3;

int n, W;
P a[N];

inline ld get(Point<ld> c, Point<ld> d){
	vector<Point<ld>> ch = {
		Point<ld>(0, 0),
		Point<ld>(W, 0),
		Point<ld>(W, W),
		Point<ld>(0, W)
	};
	ch = polygonCut(ch, c, c - d);
	ld res = 0;
	for(int i = 0; i < sz(ch); i++) res += ch[i].cross(ch[(i + 1) % sz(ch)]);
	return res / 2;
}

inline ld calc(int v, P L, P R){
	Point<ld> c{a[v].x, a[v].y}, l{L.x, L.y}, r{R.x, R.y};
	ld tl = 0, tr = 1;
	for(int i = 0; i < 0; i++){
		ld m1 = tl + (tr - tl) / 3;
		ld m2 = tr - (tr - tl) / 3;
		if(get(c, l * m1 + r * (1 - m1)) < get(c, l * m2 + r * (1 - m2))) tr = m2;
		else tl = m1;
	}
	return get(c, l * tl + r * (1 - tl));
}

main() {
	ios :: sync_with_stdio(false);
	cin.tie(nullptr);
	cin >> W >> n;
	for(int i = 0; i < n; i++) cin >> a[i].x >> a[i].y;
	ld ans = 0;
	for(int i = 0; i < n; i++){
		vector<pair<P, int>> vec = {
			{P{0, 1}, 0},
			{P{0, -1}, 0},
			{P{1, 0}, 0},
			{P{-1, 0}, 0}
		};
		for(int j = 0; j < n; j++){
			if(i == j) continue;
			vec.pb({a[i] - a[j], -1});
			vec.pb({a[j] - a[i], 1});
			vec.pb({(a[i] - a[j]).perp(), 0});
			vec.pb({(a[j] - a[i]).perp(), 0});
		}
		sort(all(vec));
		for(int j = 0; j < sz(vec); j++) vec[j].second *= -1;
		int cur = 0;
		for(int j = 0; j < n; j++) cur += !(a[j] - a[i]).side();
		for(int j = 0; j < sz(vec); j++){
			cur += vec[j].second;
			ans = max(ans, ld(cur) / n - calc(i, vec[j].first, vec[(j + 1) % sz(vec)].first) / W / W);
		}
	}
	cout << fixed << setprecision(9) << ans;
}