#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
struct Point {
double x, y;
Point(double x = 0, double y = 0) : x(x), y(y) {}
Point operator+(const Point& p) const { return Point(x + p.x, y + p.y); }
Point operator-(const Point& p) const { return Point(x - p.x, y - p.y); }
Point operator*(double t) const { return Point(x * t, y * t); }
double cross(const Point& p) const { return x * p.y - y * p.x; }
double len() const { return sqrt(x * x + y * y); }
Point normalize() const { double l = len(); return Point(x / l, y / l); }
Point perpLeft() const { return Point(-y, x); }
};
double dist(const Point& a, const Point& b) { return (a - b).len(); }
int n;
vector<Point> poly;
double originalArea;
double polygonArea(const vector<Point>& p) {
double area = 0;
int m = p.size();
for (int i = 0; i < m; i++)
area += p[i].cross(p[(i + 1) % m]);
return area / 2.0;
}
bool lineIntersect(Point p1, Point d1, Point p2, Point d2, Point& res) {
double denom = d1.cross(d2);
if (abs(denom) < EPS) return false;
double t = (p2 - p1).cross(d2) / denom;
res = p1 + d1 * t;
return true;
}
vector<Point> shrinkPolygon(double R) {
int m = poly.size();
if (m < 3) return {};
vector<Point> shiftedP(m), shiftedD(m);
for (int i = 0; i < m; i++) {
Point a = poly[i];
Point b = poly[(i + 1) % m];
Point d = b - a;
Point normal = d.perpLeft().normalize();
shiftedP[i] = a + normal * R;
shiftedD[i] = d;
}
vector<Point> result;
for (int i = 0; i < m; i++) {
int j = (i + 1) % m;
Point inter;
if (lineIntersect(shiftedP[i], shiftedD[i], shiftedP[j], shiftedD[j], inter)) {
result.push_back(inter);
}
}
if (result.size() < 3) return {};
double area = polygonArea(result);
if (area <= EPS || area >= originalArea - EPS) {
return {};
}
return result;
}
// Rotating calipers - O(n) convex polygon diameter
double polygonDiameter(const vector<Point>& p) {
int m = p.size();
if (m < 2) return 0;
if (m == 2) return dist(p[0], p[1]);
// Find antipodal pairs using rotating calipers
int j = 1;
double maxDist = 0;
for (int i = 0; i < m; i++) {
Point edge = p[(i + 1) % m] - p[i];
// Advance j while triangle area increases
while (abs(edge.cross(p[(j + 1) % m] - p[i])) > abs(edge.cross(p[j] - p[i])) + EPS) {
j = (j + 1) % m;
}
maxDist = max(maxDist, dist(p[i], p[j]));
maxDist = max(maxDist, dist(p[(i + 1) % m], p[j]));
}
return maxDist;
}
bool canFit(double R) {
vector<Point> shrunk = shrinkPolygon(R);
if (shrunk.size() < 2) return false;
return polygonDiameter(shrunk) >= 2.0 * R - EPS;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n;
poly.resize(n);
for (int i = 0; i < n; i++)
cin >> poly[i].x >> poly[i].y;
originalArea = polygonArea(poly);
double lo = 0, hi = 2e7;
for (int iter = 0; iter < 100; iter++) {
double mid = (lo + hi) / 2.0;
if (canFit(mid)) lo = mid;
else hi = mid;
}
cout << fixed << setprecision(3) << lo << endl;
return 0;
}
