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 long double EPS = 1e-9;
const long double PI = acos(-1);
inline int sign(long double a) { return (a < -EPS) ? -1 : ((a > EPS) ? 1 : 0); }
struct point {
  long double x, y;
  point(long double _x = 0.0, long double _y = 0.0) : x(_x), y(_y) {}
  point operator+(const point &a) const { return point(x + a.x, y + a.y); }
  point operator-(const point &a) const { return point(x - a.x, y - a.y); }
  point operator*(long double k) const { return point(x * k, y * k); }
  point operator/(long double k) const { return point(x / k, y / k); }
  long double operator*(const point &a) const { return x * a.x + y * a.y; }
  long double operator^(const point &a) const { return x * a.y - y * a.x; }
  bool operator==(const point &X) const { return x == X.x && y == X.y; }
  bool operator!=(const point &X) const { return !(*this == X); }
  bool operator<(const point &X) const { return x == X.x ? y < X.y : x < X.x; }
  point rotate(long double angle) {
    long double cosa = cos(angle), sina = cos(angle);
    return point(x * cosa - y * sina, x * sina + y * cosa);
  }
  long double norm() { return x * x + y * y; };
  long double len() { return sqrt(norm()); };
  long double angle() {
    long double res = atan2(y, x);
    if (res < 0) res = PI * 2 + res;
    return res;
  };
};
struct circle : point {
  long double r;
  circle(long double _x = 0, long double _y = 0, long double _r = 0)
      : point(_x, _y), r(_r) {}
  circle(point p, long double _r = 0) : point(p), r(_r) {}
};
struct line {
  long double a, b, c;
  point u, v;
  line(long double aa = 0.0, long double bb = 0.0, long double cc = 0.0)
      : a(aa), b(bb), c(cc) {}
  line(point _u, point _v) : u(_u), v(_v) {
    a = v.y - u.y;
    b = u.x - v.x;
    c = -(a * u.x + b * v.y);
  }
  line(point P, long double m) {
    a = -m;
    b = 1;
    c = -((a * P.x) + (b * P.y));
  }
  long double f(const point &p) { return a * p.x + b * p.y + c; }
};
long double angle(point a, point o, point b) {
  return acos(((a - o) * (b - o)) / (a - o).len() / (b - o).len());
};
long double directedAngle(point a, point o, point b) {
  long double t = -(a - o).angle() + (b - o).angle();
  while (t < 0) t += PI * 2;
  while (t >= PI * 2) t -= PI * 2;
  return t;
}
namespace geometry {
bool areParallel(line l1, line l2) {
  return sign(l1.a * l2.b == l1.b * l2.a) == 0;
}
bool areSame(line l1, line l2) {
  return areParallel(l1, l2) && sign(l1.c * l2.a - l2.c * l1.a) == 0 &&
         sign(l1.c * l2.b - l1.b * l2.c) == 0;
}
bool areIntersect(line l1, line l2, point &p) {
  if (areParallel(l1, l2)) return false;
  long double dx = l1.b * l2.c - l2.b * l1.c;
  long double dy = l1.c * l2.a - l2.c * l1.a;
  long double d = l1.a * l2.b - l2.a * l1.b;
  p = point(dx, dy) / d;
  return true;
}
void closestPoint(line l, point p, point &ans) {
  if (fabs(l.b) < EPS) {
    ans.x = -(l.c) / l.a;
    ans.y = p.y;
    return;
  }
  if (fabs(l.a) < EPS) {
    ans.x = p.x;
    ans.y = -(l.c) / l.b;
    return;
  }
  line perp(l.b, -l.a, -(l.b * p.x - l.a * p.y));
  areIntersect(l, perp, ans);
}
void reflectionPoint(line l, point p, point &ans) {
  point b;
  closestPoint(l, p, b);
  ans = p + (b - p) * 2;
}
circle getCircumcircle(point a, point b, point c) {
  long double d =
      2.0 * (a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y));
  assert(fabs(d) > EPS);
  long double x = (a.norm() * (b.y - c.y) + b.norm() * (c.y - a.y) +
                   c.norm() * (a.y - b.y)) /
                  d;
  long double y = (a.norm() * (c.x - b.x) + b.norm() * (a.x - c.x) +
                   c.norm() * (b.x - a.x)) /
                  d;
  point p(x, y);
  return circle(p, (p - a).len());
}
}  // namespace geometry
int n;
point p[105];
bool check(point a, point b, point c) {
  if (sign((b - a) * (c - a)) > 0 && sign((a - b) * (c - b)) > 0 &&
      sign((a - c) * (b - c)) > 0)
    return 1;
  if (sign((a - b) * (c - b)) == 0) swap(a, b);
  if (sign((a - c) * (b - c)) == 0) swap(a, c);
  if (sign((b - a) * (c - a)) == 0) {
    point cool = b + c - a;
    for (int i = 1; i <= n; i++) {
      if (sign((p[i] - cool).len()) == 0) return 1;
    }
  }
  return 0;
}
bool check2(circle a) {
  for (int i = 1; i <= n; i++) {
    if (sign((a - p[i]).len() - a.r) < 0) return 0;
  }
  return 1;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> p[i].x >> p[i].y;
  long double ans = -1;
  for (int i = 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++)
      for (int k = j + 1; k <= n; k++) {
        if (check(p[i], p[j], p[k]) &&
            check2(geometry::getCircumcircle(p[i], p[j], p[k]))) {
          ans = max(ans, geometry::getCircumcircle(p[i], p[j], p[k]).r);
        }
      }
  if (ans < 0)
    cout << -1;
  else
    cout << fixed << setprecision(5) << ans;
}