Problem: Luyi has n circles on the plane. The i-th circle is centered at (xi, yi). At the time zero circles start to grow simultaneously. In other words, the radius of each circle at time t (t > 0) is equal to t. The circles are drawn as black discs on an infinite white plane. So at each moment the plane consists of several black and white regions. Note that the circles may overlap while growing.

<image>

We define a hole as a closed, connected white region. For instance, the figure contains two holes shown by red border. During growing some holes may be created and it is easy to see that each created hole will disappear eventually. Luyi asks you to find moment of time such that the last hole disappears. In other words, you should find the first moment such that no hole can be seen after that.

Input

The first line of the input contains integer n (1 ≤ n ≤ 100). Each of the next n lines contains two integers xi and yi ( - 104 ≤ xi, yi ≤ 104), indicating the location of i-th circle.

It's guaranteed that no two circles are centered at the same point.

Output

Print the moment where the last hole disappears. If there exists no moment in which we can find holes print -1.

The answer will be considered correct if the absolute or relative error does not exceed 10 - 4.

Examples

Input

3
0 0
1 1
2 2


Output

-1


Input

4
0 0
0 2
2 2
2 0


Output

1.414214


Input

4
0 1
0 -1
-2 0
4 0


Output

2.125000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
class PT {
 public:
  double x, y;
  PT() {}
  PT(double x, double y) : x(x), y(y) {}
  PT(const PT &p) : x(p.x), y(p.y) {}
  double Magnitude() { return sqrt(x * x + y * y); }
  PT operator+(const PT &p) const { return PT(x + p.x, y + p.y); }
  PT operator-(const PT &p) const { return PT(x - p.x, y - p.y); }
  PT operator*(double c) const { return PT(x * c, y * c); }
  PT operator/(double c) const { return PT(x / c, y / c); }
};
double dot(PT p, PT q) { return p.x * q.x + p.y * q.y; }
double dist2(PT p, PT q) { return dot(p - q, p - q); }
double dist(PT p, PT q) { return sqrt(dist2(p, q)); }
double cross(PT p, PT q) { return p.x * q.y - p.y * q.x; }
double myAsin(double a, double b) {
  if (a / b > 1) return pi * 0.5;
  if (a / b < -1) return -pi * 0.5;
  return asin(a / b);
}
double myAtan(double a, double b) {
  if (b == 0) return pi * 0.5;
  return atan(a / b);
}
ostream &operator<<(ostream &os, const PT &p) {
  os << "(" << p.x << "," << p.y << ")";
}
PT scale(PT p, PT pivot, double c) {
  PT trans = p - pivot;
  trans = (trans * c) / trans.Magnitude();
  return trans + pivot;
}
PT RotateCCW90(PT p) { return PT(-p.y, p.x); }
PT RotateCW90(PT p) { return PT(p.y, -p.x); }
PT RotateCCW(PT p, double t) {
  return PT(p.x * cos(t) - p.y * sin(t), p.x * sin(t) + p.y * cos(t));
}
PT RotateAroundPointCCW(PT p, PT pivot, double t) {
  PT trans = p - pivot;
  PT ret = RotateCCW(trans, t);
  ret = ret + pivot;
  return ret;
}
PT Reflection(PT ray, PT normal) {
  ray = ray / ray.Magnitude();
  normal = normal / normal.Magnitude();
  return normal * (2 * dot(ray, normal)) - ray;
}
PT ProjectPointLine(PT a, PT b, PT c) {
  return a + (b - a) * dot(c - a, b - a) / dot(b - a, b - a);
}
double DistancePointLine(PT a, PT b, PT c) {
  return dist(c, ProjectPointLine(a, b, c));
}
PT ProjectPointSegment(PT a, PT b, PT c) {
  double r = dot(b - a, b - a);
  if (fabs(r) < 1e-7) return a;
  r = dot(c - a, b - a) / r;
  if (r < 0) return a;
  if (r > 1) return b;
  return a + (b - a) * r;
}
double DistancePointSegment(PT a, PT b, PT c) {
  return sqrt(dist2(c, ProjectPointSegment(a, b, c)));
}
double DistancePointPlane(double x, double y, double z, double a, double b,
                          double c, double d) {
  return fabs(a * x + b * y + c * z - d) / sqrt(a * a + b * b + c * c);
}
bool LinesParallel(PT a, PT b, PT c, PT d) {
  return fabs(cross(b - a, c - d)) < 1e-7;
}
bool LinesCollinear(PT a, PT b, PT c, PT d) {
  return LinesParallel(a, b, c, d) && fabs(cross(a - b, a - c)) < 1e-7 &&
         fabs(cross(c - d, c - a)) < 1e-7;
}
bool SegmentsIntersect(PT a, PT b, PT c, PT d) {
  if (LinesCollinear(a, b, c, d)) {
    if (dist2(a, c) < 1e-7 || dist2(a, d) < 1e-7 || dist2(b, c) < 1e-7 ||
        dist2(b, d) < 1e-7)
      return true;
    if (dot(c - a, c - b) > 0 && dot(d - a, d - b) > 0 && dot(c - b, d - b) > 0)
      return false;
    return true;
  }
  if (cross(d - a, b - a) * cross(c - a, b - a) > 0) return false;
  if (cross(a - c, d - c) * cross(b - c, d - c) > 0) return false;
  return true;
}
PT ComputeLineIntersection(PT a, PT b, PT c, PT d) {
  b = b - a;
  d = c - d;
  c = c - a;
  assert(dot(b, b) > 1e-7 && dot(d, d) > 1e-7);
  return a + b * cross(c, d) / cross(b, d);
}
PT ComputeCircleCenter(PT a, PT b, PT c) {
  b = (a + b) / 2;
  c = (a + c) / 2;
  return ComputeLineIntersection(b, b + RotateCW90(a - b), c,
                                 c + RotateCW90(a - c));
}
bool PointInPolygon(const vector<PT> &p, PT q) {
  bool c = 0;
  for (int i = 0; i < p.size(); i++) {
    int j = (i + 1) % p.size();
    if ((p[i].y <= q.y && q.y < p[j].y || p[j].y <= q.y && q.y < p[i].y) &&
        q.x < p[i].x + (p[j].x - p[i].x) * (q.y - p[i].y) / (p[j].y - p[i].y))
      c = !c;
  }
  return c;
}
bool PointOnPolygon(const vector<PT> &p, PT q) {
  for (int i = 0; i < p.size(); i++)
    if (dist2(ProjectPointSegment(p[i], p[(i + 1) % p.size()], q), q) < 1e-7)
      return true;
  return false;
}
vector<PT> CircleLineIntersection(PT a, PT b, PT c, double r) {
  vector<PT> ret;
  b = b - a;
  a = a - c;
  double A = dot(b, b);
  double B = dot(a, b);
  double C = dot(a, a) - r * r;
  double D = B * B - A * C;
  if (D < -1e-7) return ret;
  ret.push_back(c + a + b * (-B + sqrt(D + 1e-7)) / A);
  if (D > 1e-7) ret.push_back(c + a + b * (-B - sqrt(D)) / A);
  return ret;
}
vector<PT> CircleCircleIntersection(PT a, PT b, double r, double R) {
  vector<PT> ret;
  double d = sqrt(dist2(a, b));
  if (d > r + R || d + min(r, R) < max(r, R)) return ret;
  double x = (d * d - R * R + r * r) / (2 * d);
  double y = sqrt(r * r - x * x);
  PT v = (b - a) / d;
  ret.push_back(a + v * x + RotateCCW90(v) * y);
  if (y > 0) ret.push_back(a + v * x - RotateCCW90(v) * y);
  return ret;
}
double ComputeSignedArea(const vector<PT> &p) {
  double area = 0;
  for (int i = 0; i < p.size(); i++) {
    int j = (i + 1) % p.size();
    area += p[i].x * p[j].y - p[j].x * p[i].y;
  }
  return area / 2.0;
}
double ComputeArea(const vector<PT> &p) { return fabs(ComputeSignedArea(p)); }
PT ComputeCentroid(const vector<PT> &p) {
  PT c(0, 0);
  double scale = 6.0 * ComputeSignedArea(p);
  for (int i = 0; i < p.size(); i++) {
    int j = (i + 1) % p.size();
    c = c + (p[i] + p[j]) * (p[i].x * p[j].y - p[j].x * p[i].y);
  }
  return c / scale;
}
bool IsSimple(const vector<PT> &p) {
  for (int i = 0; i < p.size(); i++) {
    for (int k = i + 1; k < p.size(); k++) {
      int j = (i + 1) % p.size();
      int l = (k + 1) % p.size();
      if (i == l || j == k) continue;
      if (SegmentsIntersect(p[i], p[j], p[k], p[l])) return false;
    }
  }
  return true;
}
double PAngle(PT a, PT b, PT c) {
  PT temp1(a.x - b.x, a.y - b.y), temp2(c.x - b.x, c.y - b.y);
  double ans = asin((temp1.x * temp2.y - temp1.y * temp2.x) /
                    (temp1.Magnitude() * temp2.Magnitude()));
  if ((ans < 0 && (temp1.x * temp2.x + temp1.y * temp2.y) < 0) ||
      (ans >= 0 && (temp1.x * temp2.x + temp1.y * temp2.y) < 0))
    ans = pi - ans;
  ans = ans < 0 ? 2 * pi + ans : ans;
  return ans;
}
PT circumcentre(PT a, PT b, PT c) {
  PT mid1 = (a + b) / 2.0;
  PT mid11 = RotateAroundPointCCW(a, mid1, pi / 2.0);
  PT mid2 = (b + c) / 2.0;
  PT mid22 = RotateAroundPointCCW(b, mid2, pi / 2.0);
  PT mid3 = (c + a) / 2.0;
  PT mid33 = RotateAroundPointCCW(c, mid3, pi / 2.0);
  PT now = ComputeLineIntersection(mid1, mid11, mid2, mid22);
  return now;
}
vector<PT> v, points;
bool check(PT p, double dist) {
  int i, j;
  for (i = 0; i < v.size(); i++) {
    if (dist2(p, v[i]) < dist - 1e-7) return false;
  }
  return true;
}
int main() {
  int n, i, j, k, x, y, l;
  PT p;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> x >> y;
    p.x = x;
    p.y = y;
    v.push_back(p);
  }
  if (n <= 2) {
    cout << -1 << endl;
    return 0;
  }
  for (i = 0; i < v.size(); i++) {
    for (j = i + 1; j < v.size(); j++) {
      for (k = j + 1; k < v.size(); k++) {
        double ang1 = PAngle(v[i], v[j], v[k]);
        if (ang1 > pi) ang1 = 2.0 * pi - ang1;
        double ang2 = PAngle(v[i], v[k], v[j]);
        if (ang2 > pi) ang2 = 2.0 * pi - ang2;
        double ang3 = PAngle(v[j], v[i], v[k]);
        if (ang3 > pi) ang3 = 2.0 * pi - ang3;
        if (LinesParallel(v[i], v[j], v[j], v[k])) {
          continue;
        }
        if (ang1 < pi / 2.0 - 1e-7 && ang2 < pi / 2.0 - 1e-7 &&
            ang3 < pi / 2.0 - 1e-7) {
          PT cen = circumcentre(v[i], v[j], v[k]);
          if (check(cen, dist2(cen, v[i]))) {
            points.push_back(cen);
          }
        }
      }
    }
  }
  for (i = 0; i < v.size(); i++) {
    for (j = 0; j < v.size(); j++) {
      if (i == j) continue;
      for (k = 0; k < v.size(); k++) {
        if (k == i || k == j) continue;
        for (l = 0; l < v.size(); l++) {
          if (l == i || l == j || l == k) continue;
          if (LinesParallel(v[i], v[j], v[j], v[k]) &&
              LinesParallel(v[j], v[k], v[k], v[l])) {
            continue;
          }
          if (dist2(v[i], v[j]) == dist2(v[k], v[l]) &&
              dist2(v[i], v[k]) == dist2(v[j], v[l]) &&
              dist2(v[i], v[j]) + dist2(v[j], v[k]) == dist2(v[i], v[k])) {
            PT cen = (v[i] + v[k]) / 2.0;
            if (check(cen, dist2(cen, v[i]))) {
              points.push_back(cen);
            }
          }
        }
      }
    }
  }
  if (points.size() == 0) {
    cout << -1 << endl;
    return 0;
  }
  double maxx = 0, minn = 1e30;
  for (i = 0; i < points.size(); i++) {
    minn = 1e30;
    for (j = 0; j < v.size(); j++) {
      double dist = dist2(points[i], v[j]);
      minn = min(minn, dist);
    }
    maxx = max(maxx, minn);
  }
  maxx = sqrt(maxx);
  if (abs(maxx) < 1e-7) {
    cout << -1 << endl;
    return 0;
  }
  printf("%.10f\n", maxx);
  return 0;
}