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;
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> v) {
  os << "[";
  for (int i = 0; i < int((v).size()); i++) os << v[i] << " ";
  return os << "]";
}
double INF = 1e50;
long double EPS = 1e-9;
long double PI = acos(-1.0);
struct pt {
  double x, y;
  pt() {}
  pt(double x, double y) : 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 norm() { return sqrt(x * x + y * y); }
  bool operator==(const pt &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
  bool operator<(const pt &p) const {
    return make_pair(x, y) < make_pair(p.x, p.y);
  }
};
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 cross(pt p, pt q) { return p.x * q.y - p.y * q.x; }
ostream &operator<<(ostream &os, const pt &p) {
  return os << "(" << p.x << "," << p.y << ")";
}
bool intersect(const pt &a, const pt &b, const pt &p, const pt &q, pt &ret) {
  double d1 = cross(p - a, b - a);
  double d2 = cross(q - a, b - a);
  if (fabs(d1 - d2) <= EPS) return 0;
  ret = (q * d1 - p * d2) / (d1 - d2);
  return 1;
}
vector<pt> polygonCut(vector<pt> &p, const pt &a, const pt &b) {
  vector<pt> res;
  for (int i = 0; i < int((p).size()); i++) {
    int j = (i + 1) % int((p).size());
    bool in1 = cross(b - a, p[i] - a) > EPS;
    bool in2 = cross(b - a, p[j] - a) > EPS;
    if (in1) {
      res.push_back(p[i]);
    }
    if (in1 ^ in2) {
      pt r;
      intersect(a, b, p[i], p[j], r);
      res.push_back(r);
    }
  }
  return res;
}
double distAnAn(double a, double b, bool directed = 0) {
  double p = fmod(2 * PI + fmod(b - a, 2 * PI), 2 * PI);
  if (directed) p = p > PI ? 2 * PI - p : p;
  return p;
}
bool comp(pt &p1, pt &p2) {
  return make_pair(p1.y, p1.x) < make_pair(p2.y, p2.x);
}
int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  vector<pt> rect = {pt(1e9, 1e9), pt(-1e9, 1e9), pt(-1e9, -1e9),
                     pt(1e9, -1e9)};
  int n;
  cin >> n;
  vector<pt> c(n);
  for (int i = 0; i < n; i++) {
    cin >> c[i].x >> c[i].y;
  }
  if (n < 3) {
    cout << -1 << '\n';
    return 0;
  }
  set<pt> holes;
  for (int i = 0; i < n; i++) {
    vector<pt> poly = rect;
    for (int j = 0; j < n; j++) {
      if (i != j) {
        pt m = (c[i] + c[j]) / 2;
        pt v = c[j] - c[i];
        swap(v.x, v.y);
        v.x *= -1;
        poly = polygonCut(poly, m, m + v);
      }
    }
    for (auto &k : poly) {
      if (fabs(k.x) < 1e8 && fabs(k.y) < 1e8) {
        holes.insert(k);
      }
    }
  }
  double ans = 0;
  for (auto &k : holes) {
    vector<pt> phis;
    for (int i = 0; i < n; i++) {
      pt v = c[i] - k;
      double phi = atan2(v.y, v.x);
      if (phi < 0) phi += 2 * PI;
      phis.push_back(pt((c[i] - k).norm(), phi));
    }
    sort(phis.begin(), phis.end());
    int j = 3;
    while (j < n && fabs(phis[j].x - phis[j - 1].x) < EPS) j++;
    phis.resize(j);
    sort(phis.begin(), phis.end(), comp);
    bool b = true;
    for (int i = 0; i < j; i++) {
      int k = (i + 1) % j;
      double dphi = distAnAn(phis[i].y, phis[k].y);
      b = b && dphi < (PI - EPS);
    }
    if (b) {
      ans = max(ans, phis[0].x);
    }
  }
  cout << setprecision(10) << (fabs(ans) < EPS ? -1 : ans) << '\n';
  return 0;
}