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);
const double EPS = 1E-8;
bool zero(double x) { return -EPS < x && x < EPS; }
int sgn(double x) { return x > EPS ? 1 : (x < -EPS ? -1 : 0); }
class Point {
 public:
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  void init() { scanf("%lf%lf", &x, &y); }
  void print() const { printf("Point(%lf %lf)\n", x, y); }
  bool operator<(const Point &rhs) const {
    return x < rhs.x - EPS || (zero(x - rhs.x) && y < rhs.y - EPS);
  }
  bool operator==(const Point &rhs) const {
    return zero(x - rhs.x) && zero(y - rhs.y);
  }
  Point operator-(const Point &rhs) const {
    return Point(x - rhs.x, y - rhs.y);
  }
  Point operator+(const Point &rhs) const {
    return Point(x + rhs.x, y + rhs.y);
  }
  Point operator*(const double scale) const {
    return Point(x * scale, y * scale);
  }
  Point operator/(const double scale) const {
    return Point(x / scale, y / scale);
  }
  double operator*(const Point &rhs) const { return x * rhs.y - rhs.x * y; }
  double operator^(const Point &rhs) const { return x * rhs.x + y * rhs.y; }
  Point rotate(double angle) const {
    Point p(sin(angle), cos(angle));
    return Point((*this) * p, (*this) ^ p);
  }
  double length2() const { return x * x + y * y; }
  double length() const { return sqrt(this->length2()); }
  Point trunc(const double scale) const {
    return (*this) / this->length() * scale;
  }
  double angle() const { return atan2(y, x); }
  Point perpendicular() const { return Point(-y, x); }
};
class Line {
 public:
  Point l1, l2;
  Line() {}
  Line(Point l1, Point l2) : l1(l1), l2(l2) {}
  void init() {
    l1.init();
    l2.init();
  }
  void print() const {
    printf("Line[(%lf %lf)--(%lf %lf)]\n", l1.x, l1.y, l2.x, l2.y);
  }
  bool cross(const Point &p) const { return zero((p - l2) * (l1 - l2)); }
  bool cross(const Line &rhs) const { return !this->parallel(rhs); }
  bool parallel(const Line &rhs) const {
    return zero((l1 - l2) * (rhs.l1 - rhs.l2));
  }
  Point intersection(const Line &rhs) const {
    return l1 + (l2 - l1) * (((l1 - rhs.l1) * (rhs.l1 - rhs.l2)) /
                             ((l1 - l2) * (rhs.l1 - rhs.l2)));
  }
  Point projection(const Point &p) const {
    return this->intersection(Line(p, p + (l1 - l2).perpendicular()));
  }
  double distance(const Point &p) const {
    return fabs((p - l1) * (l2 - l1)) / (l1 - l2).length();
  }
};
const int MAXN = 100;
int n;
Point point[MAXN];
vector<int> idx;
vector<double> angle;
Line getLine(const Point &u, const Point &v) {
  Point l1 = (u + v) / 2;
  return Line(l1, l1 + (u - v).perpendicular());
}
bool acute(double a, double b, double c) {
  return a + b > c - EPS && a + c > b - EPS && b + c > a - EPS;
}
bool isValid(const Point &p) {
  angle = vector<double>(idx.size());
  for (int i = (0); i < ((int)angle.size()); i++) {
    angle[i] = (point[idx[i]] - p).angle();
  }
  sort(angle.begin(), angle.end());
  angle.push_back(angle.front() + PI * 2);
  for (int i = (1); i < ((int)angle.size()); i++) {
    if (angle[i] - angle[i - 1] > PI - EPS) {
      return false;
    }
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = (0); i < (n); i++) {
    point[i].init();
  }
  double res = -1;
  for (int i = (0); i < (n); i++) {
    for (int j = (i + 1); j < (n); j++) {
      Line l1 = getLine(point[i], point[j]);
      for (int k = (j + 1); k < (n); k++) {
        Line l2 = getLine(point[i], point[k]);
        if (!acute((point[i] - point[j]).length2(),
                   (point[i] - point[k]).length2(),
                   (point[j] - point[k]).length2()) ||
            !l1.cross(l2))
          continue;
        Point p = l1.intersection(l2);
        double dist = 1E100;
        for (int l = (0); l < (n); l++) {
          double tmpdist = (p - point[l]).length2();
          if (dist > tmpdist + EPS) {
            dist = tmpdist;
            idx = vector<int>(1, l);
          } else if (tmpdist - EPS < dist) {
            idx.push_back(l);
          }
        }
        if (res < dist && isValid(p)) {
          res = dist;
        }
      }
    }
  }
  if (res < 0) {
    puts("-1");
  } else {
    printf("%.13lf\n", sqrt(res));
  }
  return 0;
}