#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-9;
const double pi = acos(-1);
bool Equal(double x, double y) { return fabs(x - y) < eps; }
bool Greater(double x, double y) { return x - eps > y; }
bool Lesser(double x, double y) { return x + eps < y; }
struct point {
  double x, y;
  point() { x = y = 0.0; }
  point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  bool operator<(point p) const {
    if (fabs(x - p.x) > eps)
      return x < p.x;
    else
      return y < p.y;
  }
};
double dist(point A, point B) {
  return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
}
point pointRotate(point P, double rad) {
  return point(P.x * cos(rad) - P.y * sin(rad),
               P.x * sin(rad) + P.y * cos(rad));
}
point pointRotatePoint(point P, point Q, double rad) {
  point A = pointRotate(point(P.x - Q.x, P.y - Q.y), rad);
  A.x = A.x + Q.x;
  A.y = A.y + Q.y;
  return A;
}
struct line {
  double a, b, c;
};
line pointsToLine(point A, point B) {
  line L;
  if (Equal(A.x, B.x)) {
    L.a = 1;
    L.b = 0.0;
    L.c = -A.x;
  } else {
    L.a = -(A.y - B.y) / (A.x - B.x);
    L.b = 1;
    L.c = -(L.a * A.x) - A.y;
  }
  return L;
}
bool areParallel(line L1, line L2) {
  return Equal(L1.a, L2.a) && Equal(L1.b, L2.b);
}
bool onSegment(point P, point A, point B) {
  return P.x >= min(A.x, B.x) && P.x <= max(A.x, B.x) && P.y >= min(A.y, B.y) &&
         P.y <= max(A.y, B.y);
}
bool doIntersect(point A, point B, point C, point D, point &P) {
  line L1 = pointsToLine(A, B);
  line L2 = pointsToLine(C, D);
  if (areParallel(L1, L2)) return false;
  P.x = (L2.b * L1.c - L1.b * L2.c) / (L2.a * L1.b - L1.a * L2.b);
  if (fabs(L1.b) > eps)
    P.y = -(L1.a * P.x + L1.c);
  else
    P.y = -(L2.a * P.x + L2.c);
  return true;
}
struct vec {
  double x, y;
  vec() { x = y = 0.0; }
  vec(double _x, double _y) {
    x = _x;
    y = _y;
  }
};
vec toVector(point A, point B) { return vec(B.x - A.x, B.y - A.y); }
vec scale(vec v, double s) { return vec(v.x * s, v.y * s); }
point translate(point P, vec v) { return point(P.x + v.x, P.y + v.y); }
double dotProduct(vec A, vec B) { return A.x * B.x + A.y * B.y; }
double crossProduct(vec A, vec B) { return A.x * B.y - A.y * B.x; }
double norm_sq(vec v) { return v.x * v.x + v.y * v.y; }
double distToLineOrSeg(point P, point A, point B, point &C, bool _segment) {
  vec AP = toVector(A, P), AB = toVector(A, B);
  double u = dotProduct(AP, AB) / norm_sq(AB);
  if (_segment) {
    if (u < 0.0)
      C = A;
    else if (u > 1.0)
      C = B;
    else
      C = translate(A, scale(AB, u));
  } else
    C = translate(A, scale(AB, u));
  return dist(C, P);
}
point mirrorPoint(point P, point A, point B) {
  point C, R;
  distToLineOrSeg(P, A, B, C, false);
  R = translate(P, scale(toVector(P, C), 2.0));
  return R;
}
double angle(point A, point O, point B) {
  vec OA = toVector(O, A), OB = toVector(O, B);
  return acos(dotProduct(OA, OB) / (sqrt(norm_sq(OA) * norm_sq(OB))));
}
double angleWRTx(vec v) {
  double rad = atan2(v.y, v.x);
  if (rad < 0.0) rad = 2.0 * pi + rad;
  return rad;
}
bool collinear(point P, point Q, point R) {
  return fabs(crossProduct(toVector(P, Q), toVector(P, R))) < eps;
}
bool ccw(point P, point Q, point R) {
  if (collinear(P, Q, R))
    return crossProduct(toVector(P, Q), toVector(P, R)) >= 0;
  return crossProduct(toVector(P, Q), toVector(P, R)) > 0;
}
double angleFromLength(double A, double B, double C) {
  return acos((A * A + B * B - C * C) / (2.0 * A * B));
}
double areaFromLength(double A, double B, double C) {
  double s = (A + B + C) / 2.0;
  return sqrt(s * (s - A) * (s - B) * (s - C));
}
double rCircumCircle(double ab, double bc, double ca) {
  return ab * bc * ca / (4.0 * areaFromLength(ab, bc, ca));
}
double rCircumCircle(point A, point B, point C) {
  return rCircumCircle(dist(A, B), dist(B, C), dist(C, A));
}
double rInCircle(double ab, double bc, double ca) {
  return areaFromLength(ab, bc, ca) / (0.5 * (ab + bc + ca));
}
double rInCircle(point A, point B, point C) {
  return rInCircle(dist(A, B), dist(B, C), dist(C, A));
}
int inCircle(point p1, point p2, point p3, point &ctr, double &r) {
  r = rInCircle(p1, p2, p3);
  if (fabs(r) < eps) return 0;
  double ration = dist(p1, p2) / dist(p1, p3);
  point p = translate(p2, scale(toVector(p2, p3), ration / (1 + ration)));
  ration = dist(p2, p1) / dist(p2, p3);
  p = translate(p1, scale(toVector(p1, p3), ration / (1 + ration)));
  doIntersect(p1, p, p2, p, ctr);
  return 1;
}
double overlapCircleArea(point c1, double r1, point c2, double r2) {
  double d, rad1, rad2, area1, area2, chord;
  if (r1 > r2) {
    swap(c1, c2);
    swap(r1, r2);
  }
  d = dist(c1, c2);
  if (d >= r1 + r2) return 0;
  if (d <= r2 - r1) return pi * r1 * r1;
  rad1 = angleFromLength(r1, d, r2), rad2 = angleFromLength(r2, d, r1);
  chord = 2.0 * r1 * sin(rad1);
  area1 = (r1 * r1 * rad1) -
          ((2 * rad1 > pi) ? -1 : 1) * areaFromLength(r1, r1, chord);
  area2 = (r2 * r2 * rad2) - areaFromLength(r2, r2, chord);
  return area1 + area2;
}
bool inPolygon(point poly[], int n, point p) {
  int i, j, k;
  double totAngle = 0;
  for (i = 0; i < n; ++i)
    if (poly[i].x == p.x && poly[i].y == p.y) return true;
  for (i = 1; i < n; ++i)
    if (collinear(p, poly[i - 1], poly[i]) &&
        onSegment(p, poly[i - 1], poly[i]))
      return true;
  for (i = 1; i < n; ++i) {
    if (ccw(poly[i - 1], p, poly[i]))
      totAngle -= angle(poly[i - 1], p, poly[i]);
    else
      totAngle += angle(poly[i - 1], p, poly[i]);
  }
  return fabs(totAngle - 2.0 * pi) < eps;
}
double cross(point p1, point p2, point p3) {
  return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
}
vector<point> ConvexHull(int n, point ara[]) {
  int i, j, k;
  vector<point> cnvx(2 * n);
  sort(ara, ara + n);
  for (i = 0, k = 0; i < n; ++i) {
    while (k >= 2 && cross(cnvx[k - 2], cnvx[k - 1], ara[i]) <= 0) k--;
    cnvx[k++] = ara[i];
  }
  for (i = n - 2, j = k + 1; i >= 0; --i) {
    while (k >= j && cross(cnvx[k - 2], cnvx[k - 1], ara[i]) <= 0) k--;
    cnvx[k++] = ara[i];
  }
  cnvx.resize(k - 1);
  return cnvx;
}
int main() {
  int n;
  cin >> n;
  point p[n + 5];
  for (int i = 0; i < n; i++) cin >> p[i].x >> p[i].y;
  p[n] = p[0];
  p[n + 1] = p[1];
  p[n + 2] = p[2];
  p[n + 3] = p[3];
  double mx = 1e11;
  for (int i = 2; i <= n + 2; i++) {
    point a = p[i - 2];
    point b = p[i - 1];
    point c = p[i];
    point d;
    double res = distToLineOrSeg(b, a, c, d, true);
    mx = min(mx, res);
  }
  cout << fixed << setprecision(7) << mx / 2.0 << endl;
  return 0;
}

### Prompt

Create a solution in Cpp for 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 eps = 1e-9;
const double pi = acos(-1);
bool Equal(double x, double y) { return fabs(x - y) < eps; }
bool Greater(double x, double y) { return x - eps > y; }
bool Lesser(double x, double y) { return x + eps < y; }
struct point {
  double x, y;
  point() { x = y = 0.0; }
  point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  bool operator<(point p) const {
    if (fabs(x - p.x) > eps)
      return x < p.x;
    else
      return y < p.y;
  }
};
double dist(point A, point B) {
  return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
}
point pointRotate(point P, double rad) {
  return point(P.x * cos(rad) - P.y * sin(rad),
               P.x * sin(rad) + P.y * cos(rad));
}
point pointRotatePoint(point P, point Q, double rad) {
  point A = pointRotate(point(P.x - Q.x, P.y - Q.y), rad);
  A.x = A.x + Q.x;
  A.y = A.y + Q.y;
  return A;
}
struct line {
  double a, b, c;
};
line pointsToLine(point A, point B) {
  line L;
  if (Equal(A.x, B.x)) {
    L.a = 1;
    L.b = 0.0;
    L.c = -A.x;
  } else {
    L.a = -(A.y - B.y) / (A.x - B.x);
    L.b = 1;
    L.c = -(L.a * A.x) - A.y;
  }
  return L;
}
bool areParallel(line L1, line L2) {
  return Equal(L1.a, L2.a) && Equal(L1.b, L2.b);
}
bool onSegment(point P, point A, point B) {
  return P.x >= min(A.x, B.x) && P.x <= max(A.x, B.x) && P.y >= min(A.y, B.y) &&
         P.y <= max(A.y, B.y);
}
bool doIntersect(point A, point B, point C, point D, point &P) {
  line L1 = pointsToLine(A, B);
  line L2 = pointsToLine(C, D);
  if (areParallel(L1, L2)) return false;
  P.x = (L2.b * L1.c - L1.b * L2.c) / (L2.a * L1.b - L1.a * L2.b);
  if (fabs(L1.b) > eps)
    P.y = -(L1.a * P.x + L1.c);
  else
    P.y = -(L2.a * P.x + L2.c);
  return true;
}
struct vec {
  double x, y;
  vec() { x = y = 0.0; }
  vec(double _x, double _y) {
    x = _x;
    y = _y;
  }
};
vec toVector(point A, point B) { return vec(B.x - A.x, B.y - A.y); }
vec scale(vec v, double s) { return vec(v.x * s, v.y * s); }
point translate(point P, vec v) { return point(P.x + v.x, P.y + v.y); }
double dotProduct(vec A, vec B) { return A.x * B.x + A.y * B.y; }
double crossProduct(vec A, vec B) { return A.x * B.y - A.y * B.x; }
double norm_sq(vec v) { return v.x * v.x + v.y * v.y; }
double distToLineOrSeg(point P, point A, point B, point &C, bool _segment) {
  vec AP = toVector(A, P), AB = toVector(A, B);
  double u = dotProduct(AP, AB) / norm_sq(AB);
  if (_segment) {
    if (u < 0.0)
      C = A;
    else if (u > 1.0)
      C = B;
    else
      C = translate(A, scale(AB, u));
  } else
    C = translate(A, scale(AB, u));
  return dist(C, P);
}
point mirrorPoint(point P, point A, point B) {
  point C, R;
  distToLineOrSeg(P, A, B, C, false);
  R = translate(P, scale(toVector(P, C), 2.0));
  return R;
}
double angle(point A, point O, point B) {
  vec OA = toVector(O, A), OB = toVector(O, B);
  return acos(dotProduct(OA, OB) / (sqrt(norm_sq(OA) * norm_sq(OB))));
}
double angleWRTx(vec v) {
  double rad = atan2(v.y, v.x);
  if (rad < 0.0) rad = 2.0 * pi + rad;
  return rad;
}
bool collinear(point P, point Q, point R) {
  return fabs(crossProduct(toVector(P, Q), toVector(P, R))) < eps;
}
bool ccw(point P, point Q, point R) {
  if (collinear(P, Q, R))
    return crossProduct(toVector(P, Q), toVector(P, R)) >= 0;
  return crossProduct(toVector(P, Q), toVector(P, R)) > 0;
}
double angleFromLength(double A, double B, double C) {
  return acos((A * A + B * B - C * C) / (2.0 * A * B));
}
double areaFromLength(double A, double B, double C) {
  double s = (A + B + C) / 2.0;
  return sqrt(s * (s - A) * (s - B) * (s - C));
}
double rCircumCircle(double ab, double bc, double ca) {
  return ab * bc * ca / (4.0 * areaFromLength(ab, bc, ca));
}
double rCircumCircle(point A, point B, point C) {
  return rCircumCircle(dist(A, B), dist(B, C), dist(C, A));
}
double rInCircle(double ab, double bc, double ca) {
  return areaFromLength(ab, bc, ca) / (0.5 * (ab + bc + ca));
}
double rInCircle(point A, point B, point C) {
  return rInCircle(dist(A, B), dist(B, C), dist(C, A));
}
int inCircle(point p1, point p2, point p3, point &ctr, double &r) {
  r = rInCircle(p1, p2, p3);
  if (fabs(r) < eps) return 0;
  double ration = dist(p1, p2) / dist(p1, p3);
  point p = translate(p2, scale(toVector(p2, p3), ration / (1 + ration)));
  ration = dist(p2, p1) / dist(p2, p3);
  p = translate(p1, scale(toVector(p1, p3), ration / (1 + ration)));
  doIntersect(p1, p, p2, p, ctr);
  return 1;
}
double overlapCircleArea(point c1, double r1, point c2, double r2) {
  double d, rad1, rad2, area1, area2, chord;
  if (r1 > r2) {
    swap(c1, c2);
    swap(r1, r2);
  }
  d = dist(c1, c2);
  if (d >= r1 + r2) return 0;
  if (d <= r2 - r1) return pi * r1 * r1;
  rad1 = angleFromLength(r1, d, r2), rad2 = angleFromLength(r2, d, r1);
  chord = 2.0 * r1 * sin(rad1);
  area1 = (r1 * r1 * rad1) -
          ((2 * rad1 > pi) ? -1 : 1) * areaFromLength(r1, r1, chord);
  area2 = (r2 * r2 * rad2) - areaFromLength(r2, r2, chord);
  return area1 + area2;
}
bool inPolygon(point poly[], int n, point p) {
  int i, j, k;
  double totAngle = 0;
  for (i = 0; i < n; ++i)
    if (poly[i].x == p.x && poly[i].y == p.y) return true;
  for (i = 1; i < n; ++i)
    if (collinear(p, poly[i - 1], poly[i]) &&
        onSegment(p, poly[i - 1], poly[i]))
      return true;
  for (i = 1; i < n; ++i) {
    if (ccw(poly[i - 1], p, poly[i]))
      totAngle -= angle(poly[i - 1], p, poly[i]);
    else
      totAngle += angle(poly[i - 1], p, poly[i]);
  }
  return fabs(totAngle - 2.0 * pi) < eps;
}
double cross(point p1, point p2, point p3) {
  return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
}
vector<point> ConvexHull(int n, point ara[]) {
  int i, j, k;
  vector<point> cnvx(2 * n);
  sort(ara, ara + n);
  for (i = 0, k = 0; i < n; ++i) {
    while (k >= 2 && cross(cnvx[k - 2], cnvx[k - 1], ara[i]) <= 0) k--;
    cnvx[k++] = ara[i];
  }
  for (i = n - 2, j = k + 1; i >= 0; --i) {
    while (k >= j && cross(cnvx[k - 2], cnvx[k - 1], ara[i]) <= 0) k--;
    cnvx[k++] = ara[i];
  }
  cnvx.resize(k - 1);
  return cnvx;
}
int main() {
  int n;
  cin >> n;
  point p[n + 5];
  for (int i = 0; i < n; i++) cin >> p[i].x >> p[i].y;
  p[n] = p[0];
  p[n + 1] = p[1];
  p[n + 2] = p[2];
  p[n + 3] = p[3];
  double mx = 1e11;
  for (int i = 2; i <= n + 2; i++) {
    point a = p[i - 2];
    point b = p[i - 1];
    point c = p[i];
    point d;
    double res = distToLineOrSeg(b, a, c, d, true);
    mx = min(mx, res);
  }
  cout << fixed << setprecision(7) << mx / 2.0 << endl;
  return 0;
}

```