#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
const int inf = 0x3f3f3f3f;
const long long llf = 0x3f3f3f3f3f3f3f3f;
const int maxn = (int)1e6 + 7;
const double eps = 1e-10;
const long long mod1 = (int)1e9 + 7;
const long long mod2 = 998244353;
const long long has = 99959;
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
};
int dcmp(double x) {
  if (fabs(x) < eps) return 0;
  return x < 0 ? -1 : 1;
}
Point operator-(Point A, Point B) { return Point(A.x - B.x, A.y - B.y); }
Point operator+(Point A, Point B) { return Point(A.x + B.x, A.y + B.y); }
Point operator*(Point A, double p) { return Point(A.x * p, A.y * p); }
Point operator/(Point A, double p) { return Point(A.x / p, A.y / p); }
bool operator<(const Point &a, const Point &b) {
  return a.x < b.x || (a.x == b.x && a.y < b.y);
}
bool operator==(const Point &a, const Point &b) {
  return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}
double Dot(Point A, Point B) { return A.x * B.x + A.y * B.y; }
double Cross(Point A, Point B) { return A.x * B.y - A.y * B.x; }
double Length(Point A) { return sqrt(Dot(A, A)); }
double Angle(Point A, Point B) {
  return acos(Dot(A, B) / Length(A) / Length(B));
}
double angle(Point v) { return atan2(v.y, v.x); }
double Area(Point A, Point B, Point C) { return Cross(B - A, C - A) / 2; }
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 Normal(Point A) {
  double L = Length(A);
  return Point(-A.y / L, A.x / L);
}
struct Line {
  Point p;
  Point v;
  double ang;
  Line() {}
  Line(Point p, Point v) : p(p), v(v) { ang = atan2(v.y, v.x); }
  bool operator<(const Line &L) const { return ang < L.ang; }
  Point point(double t) { return p + v * t; }
  Line move(double d) { return Line(p + Normal(v) * d, v); }
};
Point GetLineIntersection(const Line &a, const Line &b) {
  Point u = a.p - b.p;
  double t = Cross(b.v, u) / Cross(a.v, b.v);
  return a.p + a.v * t;
}
double DistanceToLine(Point P, Point A, Point B) {
  Point v1 = B - A, v2 = P - A;
  return fabs(Cross(v1, v2)) / Length(v1);
}
double DistanceToSegment(Point P, Point A, Point B) {
  if (A == B) return Length(P - A);
  Point v1 = B - A, v2 = P - A, v3 = P - B;
  if (dcmp(Dot(v1, v2)) < 0)
    return Length(v2);
  else if (dcmp(Dot(v1, v3)) > 0)
    return Length(v3);
  else
    return fabs(Cross(v1, v2)) / Length(v1);
}
Point GetLineProjection(Point P, Point A, Point B) {
  Point v = B - A;
  return A + v * (Dot(v, P - A) / Dot(v, v));
}
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
  double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1),
         c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
  return (dcmp(c1) ^ dcmp(c2)) == -2 && (dcmp(c3) ^ dcmp(c4)) == -2;
}
bool OnSegment(Point p, Point a1, Point a2) {
  return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
}
double PolygonArea(Point *p, int n) {
  double area = 0;
  for (int i = 1; i < n - 1; i++) area += Cross(p[i] - p[0], p[i + 1] - p[0]);
  return fabs(area / 2);
}
int n;
Point a[maxn];
int main() {
  std::ios::sync_with_stdio(false);
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i].x >> a[i].y;
  }
  double mn = 1e12;
  for (int i = 0; i < n; ++i) {
    mn = min(mn,
             DistanceToSegment(a[i], a[((i - 1) % n + n) % n], a[(i + 1) % n]));
  }
  printf("%.12lf\n", mn / 2);
  return 0;
}

### Prompt

Your challenge is to write 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>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
const int inf = 0x3f3f3f3f;
const long long llf = 0x3f3f3f3f3f3f3f3f;
const int maxn = (int)1e6 + 7;
const double eps = 1e-10;
const long long mod1 = (int)1e9 + 7;
const long long mod2 = 998244353;
const long long has = 99959;
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
};
int dcmp(double x) {
  if (fabs(x) < eps) return 0;
  return x < 0 ? -1 : 1;
}
Point operator-(Point A, Point B) { return Point(A.x - B.x, A.y - B.y); }
Point operator+(Point A, Point B) { return Point(A.x + B.x, A.y + B.y); }
Point operator*(Point A, double p) { return Point(A.x * p, A.y * p); }
Point operator/(Point A, double p) { return Point(A.x / p, A.y / p); }
bool operator<(const Point &a, const Point &b) {
  return a.x < b.x || (a.x == b.x && a.y < b.y);
}
bool operator==(const Point &a, const Point &b) {
  return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}
double Dot(Point A, Point B) { return A.x * B.x + A.y * B.y; }
double Cross(Point A, Point B) { return A.x * B.y - A.y * B.x; }
double Length(Point A) { return sqrt(Dot(A, A)); }
double Angle(Point A, Point B) {
  return acos(Dot(A, B) / Length(A) / Length(B));
}
double angle(Point v) { return atan2(v.y, v.x); }
double Area(Point A, Point B, Point C) { return Cross(B - A, C - A) / 2; }
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 Normal(Point A) {
  double L = Length(A);
  return Point(-A.y / L, A.x / L);
}
struct Line {
  Point p;
  Point v;
  double ang;
  Line() {}
  Line(Point p, Point v) : p(p), v(v) { ang = atan2(v.y, v.x); }
  bool operator<(const Line &L) const { return ang < L.ang; }
  Point point(double t) { return p + v * t; }
  Line move(double d) { return Line(p + Normal(v) * d, v); }
};
Point GetLineIntersection(const Line &a, const Line &b) {
  Point u = a.p - b.p;
  double t = Cross(b.v, u) / Cross(a.v, b.v);
  return a.p + a.v * t;
}
double DistanceToLine(Point P, Point A, Point B) {
  Point v1 = B - A, v2 = P - A;
  return fabs(Cross(v1, v2)) / Length(v1);
}
double DistanceToSegment(Point P, Point A, Point B) {
  if (A == B) return Length(P - A);
  Point v1 = B - A, v2 = P - A, v3 = P - B;
  if (dcmp(Dot(v1, v2)) < 0)
    return Length(v2);
  else if (dcmp(Dot(v1, v3)) > 0)
    return Length(v3);
  else
    return fabs(Cross(v1, v2)) / Length(v1);
}
Point GetLineProjection(Point P, Point A, Point B) {
  Point v = B - A;
  return A + v * (Dot(v, P - A) / Dot(v, v));
}
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
  double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1),
         c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
  return (dcmp(c1) ^ dcmp(c2)) == -2 && (dcmp(c3) ^ dcmp(c4)) == -2;
}
bool OnSegment(Point p, Point a1, Point a2) {
  return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
}
double PolygonArea(Point *p, int n) {
  double area = 0;
  for (int i = 1; i < n - 1; i++) area += Cross(p[i] - p[0], p[i + 1] - p[0]);
  return fabs(area / 2);
}
int n;
Point a[maxn];
int main() {
  std::ios::sync_with_stdio(false);
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i].x >> a[i].y;
  }
  double mn = 1e12;
  for (int i = 0; i < n; ++i) {
    mn = min(mn,
             DistanceToSegment(a[i], a[((i - 1) % n + n) % n], a[(i + 1) % n]));
  }
  printf("%.12lf\n", mn / 2);
  return 0;
}

```