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>
const int MAXN = 105;
const double EPS = 1e-8;
namespace geometry {
struct Point {
  double x, y;
  Point() {}
  Point(double x_, double y_) : x(x_), y(y_) {}
};
inline Point operator+(const Point &x, const Point &y) {
  return Point(x.x + y.x, x.y + y.y);
}
inline Point operator-(const Point &x, const Point &y) {
  return Point(x.x - y.x, x.y - y.y);
}
inline Point operator*(const Point &x, double y) {
  return Point(x.x * y, x.y * y);
}
inline Point operator*(double x, const Point &y) { return y * x; }
inline Point operator/(const Point &x, double y) { return x * (1 / y); }
inline bool operator<(const Point &x, const Point &y) {
  return x.x + EPS < y.x || (x.x < y.x + EPS && x.y + EPS < y.y);
}
inline double cross(const Point &x, const Point &y) {
  return x.x * y.y - x.y * y.x;
}
inline double cross(const Point &x, const Point &y, const Point &z) {
  return cross(y - x, z - x);
}
inline double dot(const Point &x, const Point &y) {
  return x.x * y.x + x.y * y.y;
}
inline double dot(const Point &x, const Point &y, const Point &z) {
  return dot(y - x, z - x);
}
inline Point rotate_ccw(const Point &x) { return Point(-x.y, x.x); }
inline double len2(const Point &x) { return dot(x, x); }
inline double dist2(const Point &x, const Point &y) { return len2(y - x); }
}  // namespace geometry
int n;
geometry::Point a[MAXN];
std::set<geometry::Point> ps;
void init() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%lf%lf", &a[i].x, &a[i].y);
    ps.insert(a[i]);
  }
}
void solve() {
  double ans = -1e100;
  for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j)
      for (int k = j + 1; k < n; ++k) {
        double d1 = geometry::dot(a[i], a[j], a[k]);
        double d2 = geometry::dot(a[j], a[k], a[i]);
        double d3 = geometry::dot(a[k], a[i], a[j]);
        if (d1 < -EPS || d2 < -EPS || d3 < -EPS) continue;
        if (d1 < EPS || d2 < EPS || d3 < EPS) {
          geometry::Point v;
          if (d1 < EPS)
            v = a[j] + a[k] - a[i];
          else if (d2 < EPS)
            v = a[k] + a[i] - a[j];
          else if (d3 < EPS)
            v = a[i] + a[j] - a[k];
          if (ps.find(v) == ps.end()) continue;
        }
        geometry::Point x1 = (a[i] + a[j]) / 2;
        geometry::Point x2 = x1 + geometry::rotate_ccw(a[j] - a[i]);
        geometry::Point y1 = (a[i] + a[k]) / 2;
        geometry::Point y2 = y1 + geometry::rotate_ccw(a[k] - a[i]);
        double u = cross(x1, y1, y2);
        double v = cross(x2, y1, y2);
        geometry::Point o = x1 + (x2 - x1) / (u - v) * u;
        double t = geometry::dist2(o, a[i]);
        bool flag = true;
        for (int p = 0; p < n; ++p) {
          double tmp = geometry::dist2(o, a[p]);
          if (tmp + EPS < t) {
            flag = false;
            break;
          }
        }
        if (flag && t > ans) ans = t;
      }
  if (ans < 0)
    printf("-1\n");
  else
    printf("%f\n", sqrt(ans));
}
int main() {
  init();
  solve();
  return 0;
}