Problem: Gena doesn't like geometry, so he asks you to solve this problem for him.

A rectangle with sides parallel to coordinate axes contains n dots. Let's consider some point of the plane. Let's count the distances from this point to the given n points. Let's sort these numbers in the non-decreasing order. We'll call the beauty of the point the second element of this array. If there are two mimimum elements in this array, the beaty will be equal to this minimum.

Find the maximum beauty of a point inside the given rectangle.

Input

The first line contains three integers w, h, n (1 ≤ w, h ≤ 106, 2 ≤ n ≤ 1000) — the lengths of the rectangle sides and the number of points. Next n lines contain two integers xi, yi (0 ≤ xi ≤ w, 0 ≤ yi ≤ h) each — the coordinates of a point. It is possible that it will be coincident points.

Output

Print a single number — the maximum beauty of a point with the absolute or relative error of at most 10 - 9.

Examples

Input

5 5 4
0 0
5 0
0 5
5 5


Output

4.99999999941792340


Input

5 5 3
4 0
2 5
4 1


Output

5.65685424744772010

Note

The point which beauty we need to find must have coordinates (x, y), where 0 ≤ x ≤ w, 0 ≤ y ≤ h. Some of the n points can coincide.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
namespace geom {
template <typename T>
struct Point {
  Point() {}
  Point(T _x, T _y) : x(_x), y(_y) {}
  T x, y;
  template <typename U>
  explicit Point(const Point<U> &p) : x(p.x), y(p.y) {}
  Point &operator+=(const Point &b) {
    x += b.x;
    y += b.y;
    return *this;
  }
  Point &operator-=(const Point &b) {
    x -= b.x;
    y -= b.y;
    return *this;
  }
  Point &operator*=(T f) {
    x *= f;
    y *= f;
    return *this;
  }
  Point &operator/=(T f) {
    x /= f;
    y /= f;
    return *this;
  }
  Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }
  Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }
  Point operator*(T f) const { return Point(x * f, y * f); }
  Point operator/(T f) const { return Point(x / f, y / f); }
  friend Point operator*(T f, const Point &p) {
    return Point(f * p.x, f * p.y);
  }
  T operator*(const Point &b) const { return x * b.x + y * b.y; }
  T vec_mult(const Point &b) const { return x * b.y - y * b.x; }
  T sqr() const { return x * x + y * y; }
  Point operator-() const { return Point(-x, -y); }
  bool operator==(const Point &b) const { return x == b.x && y == b.y; }
  bool operator!=(const Point &b) const { return x != b.x || y != b.y; }
};
}  // namespace geom
namespace geom {
template <typename T>
bool angle_cmp(Point<T> a, Point<T> b) {
  bool u = a.y > 0 || (a.y == 0 && a.x > 0);
  bool v = b.y > 0 || (b.y == 0 && b.x > 0);
  return u != v ? u : a.vec_mult(b) > 0;
}
}  // namespace geom
namespace util {
inline size_t bits(int x) { return __builtin_popcount(x); }
inline size_t flog(int x) { return 8 * sizeof(int) - 1 - __builtin_clz(x); }
template <typename T>
inline void mini(T &a, T b) {
  if (a > b) a = b;
}
template <typename T>
inline void maxi(T &a, T b) {
  if (a < b) a = b;
}
template <typename T>
inline T abs(T a) {
  return a < 0 ? -a : a;
}
template <typename T>
int sign(T a) {
  return (a > 0) - (a < 0);
}
};  // namespace util
const double eps = 1e-10;
struct Dir {
  geom::Point<double> v;
  int s;
  bool operator<(const Dir &b) const { return geom::angle_cmp(v, b.v); }
};
geom::Point<double> rot(geom::Point<double> v, double c, double s) {
  return {c * v.x - s * v.y, s * v.x + c * v.y};
}
geom::Point<double> proj(geom::Point<double> a, geom::Point<double> b,
                         geom::Point<double> c) {
  c -= a;
  b -= a;
  return a + c * b / b.sqr() * b;
}
std::mt19937 rnd(7629834);
bool check(geom::Point<double> p, double r,
           std::vector<geom::Point<double> > &P,
           std::vector<geom::Point<double> > &F) {
  std::vector<Dir> V;
  int count = 0;
  for (geom::Point<double> q : P)
    if (p != q) {
      q -= p;
      double c = sqrt(q.sqr()) / (2 * r);
      if (c > 1 - eps) continue;
      double s = sqrt(1 - c * c);
      geom::Point<double> v1 = rot(q, c, -s), v2 = rot(q, c, s);
      if (geom::angle_cmp(v2, v1)) count++;
      V.push_back(Dir{v1, 1});
      V.push_back(Dir{v2, -1});
    }
  for (int i = 0; i < (4); ++i) {
    geom::Point<double> q = proj(F[i], F[i + 1], p) - p;
    double c = sqrt(q.sqr()) / r;
    q = rot(F[i + 1] - F[i], 0, -1);
    if (c > 1 - eps) continue;
    double s = sqrt(1 - c * c);
    geom::Point<double> v1 = rot(q, c, -s), v2 = rot(q, c, s);
    if (geom::angle_cmp(v2, v1)) count += 2;
    V.push_back(Dir{v1, 2});
    V.push_back(Dir{v2, -2});
  }
  std::sort(V.begin(), V.end());
  bool ok = count <= 1;
  for (Dir d : V) ok |= (count += d.s) <= 1;
  return ok;
}
int main() {
  int w, h, n;
  scanf("%d%d%d", &w, &h, &n);
  std::vector<geom::Point<double> > P(n);
  for (geom::Point<double> &p : P) scanf("%lf%lf", &p.x, &p.y);
  for (int i = 0; i < (n); ++i) std::swap(P[i], P[rnd() % n]);
  std::vector<geom::Point<double> > F{
      geom::Point<double>{0, 0}, geom::Point<double>{double(w), 0},
      geom::Point<double>{double(w), double(h)},
      geom::Point<double>{0, double(h)}, geom::Point<double>{0, 0}};
  double res = 0;
  for (geom::Point<double> p : P) {
    if (!check(p, std::max(res * (1 + eps), res + eps), P, F)) continue;
    double l = res, r = std::max(w, h) * 1.5;
    while (r - l > std::max(eps * l, eps)) {
      double m = (l + r) * .5;
      if (check(p, m, P, F))
        l = m;
      else
        r = m;
    }
    util::maxi(res, l);
  }
  printf("%.10lf\n", res);
  return 0;
}