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 <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T, class T1>
inline void gn(T &first, T1 &second) {
  gn(first);
  gn(second);
}
template <class T, class T1, class T2>
inline void gn(T &first, T1 &second, T2 &z) {
  gn(first);
  gn(second);
  gn(z);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
template <class T, class U>
inline void print(T first, U second) {
  printsp(first);
  println(second);
}
template <class T, class U, class V>
inline void print(T first, U second, V z) {
  printsp(first);
  printsp(second);
  println(z);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
struct point {
  double first, second;
  point(double first = 0, double second = 0) : first(first), second(second) {}
  point operator-(point a) { return point(first - a.first, second - a.second); }
  point operator+(point a) { return point(first + a.first, second + a.second); }
  point operator*(double a) { return point(first * a, second * a); }
  point operator/(double a) { return point(first / a, second / a); }
  point operator&(point a) {
    return point(first * a.first - second * a.second,
                 first * a.second + second * a.first);
  }
  point rotate(double al) { return *this & point(cos(al), sin(al)); }
  double operator^(point a) { return first * a.second - second * a.first; }
  double operator*(point a) { return first * a.first + second * a.second; }
  point norm() {
    double s = nor();
    if (s < 1e-8) return *this;
    return point(first / s, second / s);
  }
  point conj() { return point(-second, first); }
  double nor() { return sqrt(*this * *this); }
  double al() { return atan2(second, first); }
  bool operator<(const point &a) const {
    if (fabs(first - a.first) > 1e-8) return first < a.first;
    return second < a.second - 1e-8;
  }
  bool operator>(const point &a) const {
    if (fabs(first - a.first) > 1e-8) return first > a.first;
    return second > a.second + 1e-8;
  }
  bool operator==(const point &a) const {
    if (fabs(first - a.first) > 1e-8) return 0;
    return fabs(second - a.second) < 1e-8;
  }
  bool operator!=(const point &a) const {
    if (*this == a) return false;
    return true;
  }
  void input() { scanf("%lf %lf", &first, &second); }
  void print() { printf("%lf %lf\n", first, second); }
};
double dist(point a, point b) {
  return sqrt((a.first - b.first) * (a.first - b.first) +
              (a.second - b.second) * (a.second - b.second));
}
int sgn(double a) { return (a > 1e-8) - (a < -1e-8); }
bool is_on(point a, point b, point c) {
  if (sgn(a - b ^ b - c)) return 0;
  return sgn((a - c) * (b - c)) <= 0;
}
bool intersect(point a, point b, point c, point d, point &ans) {
  if (min(a.first, b.first) > max(c.first, d.first) + 1e-8) return 0;
  if (max(a.first, b.first) < min(c.first, d.first) - 1e-8) return 0;
  if (min(a.second, b.second) > max(c.second, d.second) + 1e-8) return 0;
  if (max(a.second, b.second) < min(c.second, d.second) - 1e-8) return 0;
  if (sgn((a - b) ^ (c - b)) * sgn((a - b) ^ (d - b)) >= 0) return 0;
  if (sgn((c - d) ^ (a - d)) * sgn((c - d) ^ (b - d)) >= 0) return 0;
  double sc = fabs((a - b) ^ (b - c)), sd = fabs((a - b) ^ (b - d));
  ans = (c * sd + d * sc) / (sc + sd);
  return 1;
}
double angle(point a, point b) {
  double res = a * b / a.nor() / b.nor();
  res = acos(res);
  return res;
}
double angle(point a, point b, point c) { return angle(a - c, b - c); }
double pdist(point c, point a, point b) {
  point aa = c - a, bb = c - b, ab = a - b;
  if (sgn(aa * ab) >= 0) return aa.nor();
  if (sgn(bb * ab) <= 0) return bb.nor();
  return fabs(aa ^ bb) / ab.nor();
}
bool is_in_poly(point a, point *p, int n) {
  for (int i = 0; i < n; i++)
    if (is_on(p[i], p[i + 1], a)) return 1;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    point b = p[i], c = p[i + 1];
    if (b > c) swap(b, c);
    if (sgn(c - b ^ a - b) < 0 && b.first < a.first - 1e-8 &&
        a.first < c.first + 1e-8)
      cnt++;
  }
  return cnt & 1;
}
point capture_centre(point &a, point &b, point &c) {
  point bb = (a + b) / 2, cc = (a + c) / 2;
  point bbb = (b - a).conj(), ccc = (c - a).conj();
  double s = (bbb ^ ccc), t = (cc - bb) ^ ccc;
  return bb + bbb * (t / s);
}
point p[111];
int main() {
  int n;
  gn(n);
  for (int i = 1; i <= n; i++) p[i].input();
  int tag = 0;
  double ans = 0;
  for (int i1 = 1; i1 <= n; i1++)
    for (int i2 = i1 + 1; i2 <= n; i2++)
      for (int i3 = i2 + 1; i3 <= n; i3++) {
        point a = p[i1], b = p[i2], c = p[i3];
        if ((b - a) * (c - a) < -1e-8 || (a - b) * (c - b) < -1e-8 ||
            (a - c) * (b - c) < -1e-8)
          continue;
        point d = capture_centre(a, b, c);
        double r = (d - a).nor();
        if (is_on(a, c, d)) swap(c, b);
        if (is_on(b, c, d)) swap(c, a);
        if (is_on(a, b, d)) {
          int flag = 0, cnt = 0;
          for (int i = 1; i <= n; i++)
            if (i != i1 && i != i2 && i != i3) {
              if ((p[i] - d).nor() < r - 1e-8) flag++;
              if (fabs((p[i] - d).nor() - r) < 1e-8 &&
                  sgn(p[i] - a ^ b - a) == sgn(b - a ^ c - a))
                cnt++;
            }
          if (!flag && cnt) {
            smax(ans, r);
            tag++;
          }
        } else {
          int flag = 0;
          for (int i = 1; i <= n; i++)
            if (i != i1 && i != i2 && i != i3) {
              if ((p[i] - d).nor() < r - 1e-8) flag++;
            }
          if (!flag) {
            smax(ans, r);
            tag++;
          }
        }
      }
  if (tag)
    printf("%.9lf\n", ans);
  else
    puts("-1");
  return 0;
}