#include <bits/stdc++.h>
using namespace std;
const double pi = 4 * atan(1);
const double eps = 1e-9;
inline int dcmp(double x) {
  if (fabs(x) < eps)
    return 0;
  else
    return x < 0 ? -1 : 1;
}
inline double getDistance(double x, double y) { return sqrt(x * x + y * y); }
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  void read() { scanf("%lf%lf", &x, &y); }
  void write() { printf("%lf %lf", x, y); }
  bool operator==(const Point& u) const {
    return dcmp(x - u.x) == 0 && dcmp(y - u.y) == 0;
  }
  bool operator!=(const Point& u) const { return !(*this == u); }
  bool operator<(const Point& u) const {
    return x < u.x || (x == u.x && y < u.y);
  }
  bool operator>(const Point& u) const { return u < *this; }
  bool operator<=(const Point& u) const { return *this < u || *this == u; }
  bool operator>=(const Point& u) const { return *this > u || *this == u; }
  Point operator+(const Point& u) { return Point(x + u.x, y + u.y); }
  Point operator-(const Point& u) { return Point(x - u.x, y - u.y); }
  Point operator*(const double u) { return Point(x * u, y * u); }
  Point operator/(const double u) { return Point(x / u, y / u); }
  double operator*(const Point& u) { return x * u.y - y * u.x; }
};
struct Line {
  double a, b, c;
  Line(double a = 0, double b = 0, double c = 0) : a(a), b(b), c(c) {}
};
struct Circle {
  Point o;
  double r;
  Circle(Point o, double r = 0) : o(o), r(r) {}
  Point point(double rad) {
    return Point(o.x + cos(rad) * r, o.y + sin(rad) * r);
  }
};
namespace Punctual {
double getDistance(Point a, Point b) {
  double x = a.x - b.x, y = a.y - b.y;
  return sqrt(x * x + y * y);
}
};  // namespace Punctual
namespace Vectorial {
double getDot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
double getCross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
double getLength(Point a) { return sqrt(getDot(a, a)); }
double getAngle(Point u) { return atan2(u.y, u.x); }
double getAngle(Point a, Point b) {
  return acos(getDot(a, b) / getLength(a) / getLength(b));
}
Point rotate(Point a, double rad) {
  return Point(a.x * cos(rad) - a.y * sin(rad),
               a.x * sin(rad) + a.y * cos(rad));
}
Point getNormal(Point a) {
  double l = getLength(a);
  return Point(-a.y / l, a.x / l);
}
};  // namespace Vectorial
namespace Linear {
using namespace Vectorial;
Line getLine(double x1, double y1, double x2, double y2) {
  return Line(y2 - y1, x1 - x2, y1 * (x2 - x1) - x1 * (y2 - y1));
}
Line getLine(double a, double b, Point u) {
  return Line(a, -b, u.y * b - u.x * a);
}
bool getIntersection(Line p, Line q, Point& o) {
  if (fabs(p.a * q.b - q.a * p.b) < eps) return false;
  o.x = (q.c * p.b - p.c * q.b) / (p.a * q.b - q.a * p.b);
  o.y = (q.c * p.a - p.c * q.a) / (p.b * q.a - q.b * p.a);
  return true;
}
bool getIntersection(Point p, Point v, Point q, Point w, Point& o) {
  if (dcmp(getCross(v, w)) == 0) return false;
  Point u = p - q;
  double k = getCross(w, u) / getCross(v, w);
  o = p + v * k;
  return true;
}
double getDistanceToLine(Point p, Point a, Point b) {
  return fabs(getCross(b - a, p - a) / getLength(b - a));
}
double getDistanceToSegment(Point p, Point a, Point b) {
  if (a == b) return getLength(p - a);
  Point v1 = b - a, v2 = p - a, v3 = p - b;
  if (dcmp(getDot(v1, v2)) < 0)
    return getLength(v2);
  else if (dcmp(getDot(v1, v3)) > 0)
    return getLength(v3);
  else
    return fabs(getCross(v1, v2) / getLength(v1));
}
Point getPointToLine(Point p, Point a, Point b) {
  Point v = b - a;
  return a + v * (getDot(v, p - a) / getDot(v, v));
}
bool haveIntersection(Point a1, Point a2, Point b1, Point b2) {
  double c1 = getCross(a2 - a1, b1 - a1), c2 = getCross(a2 - a1, b2 - a1),
         c3 = getCross(b2 - b1, a1 - b1), c4 = getCross(b2 - b1, a2 - b1);
  return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
bool onSegment(Point p, Point a, Point b) {
  return dcmp(getCross(a - p, b - p)) == 0 && dcmp(getDot(a - p, b - p)) < 0;
}
}  // namespace Linear
using namespace Linear;
double x[2000], y[2000];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%lf%lf", &x[i], &y[i]);
  }
  x[0] = x[n];
  y[0] = y[n];
  x[n + 1] = x[1];
  y[n + 1] = y[1];
  double d = 1e12, xx;
  for (int i = 1; i <= n; i++) {
    xx = getDistanceToLine(Point(x[i], y[i]), Point(x[i - 1], y[i - 1]),
                           Point(x[i + 1], y[i + 1]));
    xx /= 2;
    if (xx < d) d = xx;
  }
  printf("%.10f\n", d);
}

### Prompt

Generate a CPP solution to the following problem:

You are given a convex polygon P with n distinct vertices p1, p2, ..., pn. Vertex pi has coordinates (xi, yi) in the 2D plane. These vertices are listed in clockwise order.

You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.

Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.

Input

The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.

The next n lines contain the coordinates of the vertices. Line i contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).

Output

Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if <image>.

Examples

Input

4
0 0
0 1
1 1
1 0


Output

0.3535533906


Input

6
5 0
10 0
12 -4
10 -8
5 -8
3 -4


Output

1.0000000000

Note

Here is a picture of the first sample

<image>

Here is an example of making the polygon non-convex.

<image>

This is not an optimal solution, since the maximum distance we moved one point is  ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most  ≈ 0.3535533906.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double pi = 4 * atan(1);
const double eps = 1e-9;
inline int dcmp(double x) {
  if (fabs(x) < eps)
    return 0;
  else
    return x < 0 ? -1 : 1;
}
inline double getDistance(double x, double y) { return sqrt(x * x + y * y); }
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  void read() { scanf("%lf%lf", &x, &y); }
  void write() { printf("%lf %lf", x, y); }
  bool operator==(const Point& u) const {
    return dcmp(x - u.x) == 0 && dcmp(y - u.y) == 0;
  }
  bool operator!=(const Point& u) const { return !(*this == u); }
  bool operator<(const Point& u) const {
    return x < u.x || (x == u.x && y < u.y);
  }
  bool operator>(const Point& u) const { return u < *this; }
  bool operator<=(const Point& u) const { return *this < u || *this == u; }
  bool operator>=(const Point& u) const { return *this > u || *this == u; }
  Point operator+(const Point& u) { return Point(x + u.x, y + u.y); }
  Point operator-(const Point& u) { return Point(x - u.x, y - u.y); }
  Point operator*(const double u) { return Point(x * u, y * u); }
  Point operator/(const double u) { return Point(x / u, y / u); }
  double operator*(const Point& u) { return x * u.y - y * u.x; }
};
struct Line {
  double a, b, c;
  Line(double a = 0, double b = 0, double c = 0) : a(a), b(b), c(c) {}
};
struct Circle {
  Point o;
  double r;
  Circle(Point o, double r = 0) : o(o), r(r) {}
  Point point(double rad) {
    return Point(o.x + cos(rad) * r, o.y + sin(rad) * r);
  }
};
namespace Punctual {
double getDistance(Point a, Point b) {
  double x = a.x - b.x, y = a.y - b.y;
  return sqrt(x * x + y * y);
}
};  // namespace Punctual
namespace Vectorial {
double getDot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
double getCross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
double getLength(Point a) { return sqrt(getDot(a, a)); }
double getAngle(Point u) { return atan2(u.y, u.x); }
double getAngle(Point a, Point b) {
  return acos(getDot(a, b) / getLength(a) / getLength(b));
}
Point rotate(Point a, double rad) {
  return Point(a.x * cos(rad) - a.y * sin(rad),
               a.x * sin(rad) + a.y * cos(rad));
}
Point getNormal(Point a) {
  double l = getLength(a);
  return Point(-a.y / l, a.x / l);
}
};  // namespace Vectorial
namespace Linear {
using namespace Vectorial;
Line getLine(double x1, double y1, double x2, double y2) {
  return Line(y2 - y1, x1 - x2, y1 * (x2 - x1) - x1 * (y2 - y1));
}
Line getLine(double a, double b, Point u) {
  return Line(a, -b, u.y * b - u.x * a);
}
bool getIntersection(Line p, Line q, Point& o) {
  if (fabs(p.a * q.b - q.a * p.b) < eps) return false;
  o.x = (q.c * p.b - p.c * q.b) / (p.a * q.b - q.a * p.b);
  o.y = (q.c * p.a - p.c * q.a) / (p.b * q.a - q.b * p.a);
  return true;
}
bool getIntersection(Point p, Point v, Point q, Point w, Point& o) {
  if (dcmp(getCross(v, w)) == 0) return false;
  Point u = p - q;
  double k = getCross(w, u) / getCross(v, w);
  o = p + v * k;
  return true;
}
double getDistanceToLine(Point p, Point a, Point b) {
  return fabs(getCross(b - a, p - a) / getLength(b - a));
}
double getDistanceToSegment(Point p, Point a, Point b) {
  if (a == b) return getLength(p - a);
  Point v1 = b - a, v2 = p - a, v3 = p - b;
  if (dcmp(getDot(v1, v2)) < 0)
    return getLength(v2);
  else if (dcmp(getDot(v1, v3)) > 0)
    return getLength(v3);
  else
    return fabs(getCross(v1, v2) / getLength(v1));
}
Point getPointToLine(Point p, Point a, Point b) {
  Point v = b - a;
  return a + v * (getDot(v, p - a) / getDot(v, v));
}
bool haveIntersection(Point a1, Point a2, Point b1, Point b2) {
  double c1 = getCross(a2 - a1, b1 - a1), c2 = getCross(a2 - a1, b2 - a1),
         c3 = getCross(b2 - b1, a1 - b1), c4 = getCross(b2 - b1, a2 - b1);
  return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
bool onSegment(Point p, Point a, Point b) {
  return dcmp(getCross(a - p, b - p)) == 0 && dcmp(getDot(a - p, b - p)) < 0;
}
}  // namespace Linear
using namespace Linear;
double x[2000], y[2000];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%lf%lf", &x[i], &y[i]);
  }
  x[0] = x[n];
  y[0] = y[n];
  x[n + 1] = x[1];
  y[n + 1] = y[1];
  double d = 1e12, xx;
  for (int i = 1; i <= n; i++) {
    xx = getDistanceToLine(Point(x[i], y[i]), Point(x[i - 1], y[i - 1]),
                           Point(x[i + 1], y[i + 1]));
    xx /= 2;
    if (xx < d) d = xx;
  }
  printf("%.10f\n", d);
}

```