#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define int ll

using ld = long double;
#define double ld

#define all(v) (v).begin(), (v).end()

void dbg_out() { cerr << endl; }
template <typename H, typename... T>
void dbg_out(H h, T... t) { cerr << ' ' << h; dbg_out(t...); }
#define dbg(...) { cerr << #__VA_ARGS__ << ':'; dbg_out(__VA_ARGS__); }

constexpr double EPS = 1e-8;

const int N = 1123456;

double t[N];

struct point {
	double x, y;
	point operator-(point p) const {
		return {x - p.x, y - p.y};
	}
	double size() {
		return sqrt(x * x + y * y);
	}
} pts[N];

struct seg {
	point a, b;
	double size() {
		return (b - a).size();
	}
	point walk(double x) {
		double tt = x / size();
		point diff = b - a;
		return {a.x + tt * diff.x, a.y + tt * diff.y};
	}
};

struct pos {
	int i;
	double x;
	bool operator<(pos o) const {
		return make_pair(i, x) < make_pair(o.i, o.x);
	}
};

pos walk(pos s, double x) {
	if (s.x + x > t[s.i]) return walk({s.i + 1, 0}, x - (t[s.i] - s.x));
	if (s.x + x + EPS > t[s.i]) return {s.i + 1, 0};
	return {s.i, s.x + x};
}

point to_point(pos p) {
	seg s = {pts[p.i], pts[p.i+1]};
	return s.walk(p.x);
}

seg to_seg(pos a, pos b) {
	return {to_point(a), to_point(b)};
}

double dist_pos(pos a, pos b) {
	assert(a.i == b.i);
	return b.x - a.x;
}

double min_dist(seg a, seg b) {
	//b = {b.b, b.a};
	double l = 0, r = a.size();
	for (int i = 0; i < 60; i++) {
		double m1 = l + (r - l) * (1.0 / 3.0);
		double m2 = l + (r - l) * (2.0 / 3.0);
		double dist_m1 = (a.walk(m1) - b.walk(m1)).size();
		double dist_m2 = (a.walk(m2) - b.walk(m2)).size();
		if (dist_m1 > dist_m2) {
			l = m1;
		} else {
			r = m2;
		}
	}
	return (a.walk(r) - b.walk(r)).size();
}

void solve() {
	double s; 
	cin >> s;
	int n; 
	cin >> n;

	for(int i = 0; i < n; i++) {
		int x, y;
		cin >> x >> y;
		pts[i] = {x, y};
	}

	for(int i = 0; i < n - 1; i++) {
		seg ss = {pts[i], pts[i + 1]};
		t[i] = ss.size();
	}

	pos p1 = {0, 0};
	pos p2 = walk(p1, s);
	double resp = s;
	while (p2.i != n) {
		if (p1.i == p2.i) {
			double d = t[p1.i] - p2.x;
			p1 = walk(p1, d);
			p2 = {p2.i + 1, 0};
			continue;
		}
		dbg(p1.i, p2.i);
		pos pp1 = min(p2, {p1.i, t[p1.i]});
		pos pp2 = {p2.i, t[p2.i]};
		double dist = min(dist_pos(p1, pp1), dist_pos(p2, pp2));
		resp = min(resp, min_dist(to_seg(p1, {p1.i, p1.x + dist}), to_seg(p2, {p2.i, p2.x + dist})));
		p1 = walk(p1, dist);
		p2 = walk(p2, dist);
	}
	
	cout << fixed << setprecision(10);
	cout << resp << endl;
}

signed main() {
	ios::sync_with_stdio(false); cin.tie(0);
	solve();
}