#include <bits/stdc++.h>
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
namespace IO {
const int L = 1 << 15;
char ibuf[L | 1], *iS = ibuf, *iT = ibuf, obuf[L | 1], *oS = obuf,
                  *oT = obuf + L, c, st[66];
int tp = 0, f;
inline char gc() {
  if (iS == iT) iT = (iS = ibuf) + fread(ibuf, sizeof(char), L, stdin);
  return (*iS++);
}
inline void flush() {
  fwrite(obuf, sizeof(char), oS - obuf, stdout);
  oS = obuf;
}
inline void pc(char c) {
  *oS++ = c;
  if (oS == oT) flush();
}
inline long long read() {
  long long x = 0;
  f = 1, c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -1;
  for (; isdigit(c); c = getchar()) x = (x << 1) + (x << 3) + (c & 15);
  return x * f;
}
inline void write(long long x) {
  if (!x) putchar('0');
  if (x < 0) putchar('-'), x = -x;
  while (x) st[++tp] = x % 10 + '0', x /= 10;
  while (tp) putchar(st[tp--]);
}
inline void writeln(long long x) {
  write(x);
  putchar('\n');
}
inline void wri(long long x) { write(x), putchar(' '); }
struct IOflusher {
  ~IOflusher() { flush(); }
} _ioflusher_;
}  // namespace IO
using IO::read;
using IO::wri;
const int maxn = 1e3 + 13;
struct point {
  double x, y;
  point() {}
  point(double x, double y) : x(x), y(y) {}
} p[maxn];
const double pi = acos(-1.0);
double dist(point a, point b) {
  return sqrt(((a.x - b.x) * (a.x - b.x)) + ((a.y - b.y) * (a.y - b.y)));
}
pair<double, int> A[maxn * 4];
int c;
int sum;
void add(double s, double t, int v = 1) {
  if (s <= 0)
    sum += v;
  else
    A[++c] = {s, v};
  if (t < 2 * pi) A[++c] = {t + 1e-12, -v};
}
double w, h;
int n, m;
double _d[maxn], _a[maxn];
bool check(int x, double r) {
  sum = c = 0;
  for (register int i = (1); i <= int(n); ++i)
    if (dist(p[i], p[x]) > 0 && dist(p[i], p[x]) < 2 * r) {
      double r1 = acos(dist(p[i], p[x]) / 2 / r);
      double s1 = atan2(p[i].y - p[x].y, p[i].x - p[x].x);
      double l = s1 - r1, r = s1 + r1;
      while (l < 0) l += 2 * pi;
      while (l >= 2 * pi) l -= 2 * pi;
      while (r < 0) r += 2 * pi;
      while (r >= 2 * pi) r -= 2 * pi;
      if (l <= r)
        add(l, r);
      else
        add(0, r), add(l, 2 * pi);
    }
  double t;
  if (p[x].x < r) {
    t = acos(p[x].x / r);
    add(pi - t, pi + t, 2);
  }
  if (p[x].y < r) {
    t = acos(p[x].y / r);
    add(1.5 * pi - t, 1.5 * pi + t, 2);
  }
  if (p[x].x + r > w) {
    t = acos((w - p[x].x) / r);
    add(0, t, 2);
    add(2 * pi - t, 2 * pi, 2);
  }
  if (p[x].y + r > h) {
    t = acos((h - p[x].y) / r);
    add(pi / 2 - t, pi / 2 + t, 2);
  }
  if (c < 2) return true;
  sort(A + 1, A + 1 + c);
  if (sum < 2 && A[1].first > 1e-9) return true;
  for (register int j = (1); j <= int(c); ++j) {
    sum += A[j].second;
    if (sum < 2) return true;
  }
  if (sum < 2 && A[c].first < 2 * pi - 1e-9) return true;
  return false;
}
int main() {
  double L = 0, R;
  w = read(), h = read(), n = read();
  for (register int i = (1); i <= int(n); ++i) p[i].x = read(), p[i].y = read();
  random_shuffle(p + 1, p + 1 + n);
  for (register int i = (1); i <= int(n); ++i) {
    if (!check(i, L + 1e-9)) continue;
    R = 2e6;
    while (R - L > 1e-9) {
      double mid = (L + R) / 2.0;
      if (check(i, mid))
        L = mid;
      else
        R = mid;
    }
  }
  printf("%.15lf\n", L);
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following 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.

### Response

```cpp
#include <bits/stdc++.h>
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
namespace IO {
const int L = 1 << 15;
char ibuf[L | 1], *iS = ibuf, *iT = ibuf, obuf[L | 1], *oS = obuf,
                  *oT = obuf + L, c, st[66];
int tp = 0, f;
inline char gc() {
  if (iS == iT) iT = (iS = ibuf) + fread(ibuf, sizeof(char), L, stdin);
  return (*iS++);
}
inline void flush() {
  fwrite(obuf, sizeof(char), oS - obuf, stdout);
  oS = obuf;
}
inline void pc(char c) {
  *oS++ = c;
  if (oS == oT) flush();
}
inline long long read() {
  long long x = 0;
  f = 1, c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -1;
  for (; isdigit(c); c = getchar()) x = (x << 1) + (x << 3) + (c & 15);
  return x * f;
}
inline void write(long long x) {
  if (!x) putchar('0');
  if (x < 0) putchar('-'), x = -x;
  while (x) st[++tp] = x % 10 + '0', x /= 10;
  while (tp) putchar(st[tp--]);
}
inline void writeln(long long x) {
  write(x);
  putchar('\n');
}
inline void wri(long long x) { write(x), putchar(' '); }
struct IOflusher {
  ~IOflusher() { flush(); }
} _ioflusher_;
}  // namespace IO
using IO::read;
using IO::wri;
const int maxn = 1e3 + 13;
struct point {
  double x, y;
  point() {}
  point(double x, double y) : x(x), y(y) {}
} p[maxn];
const double pi = acos(-1.0);
double dist(point a, point b) {
  return sqrt(((a.x - b.x) * (a.x - b.x)) + ((a.y - b.y) * (a.y - b.y)));
}
pair<double, int> A[maxn * 4];
int c;
int sum;
void add(double s, double t, int v = 1) {
  if (s <= 0)
    sum += v;
  else
    A[++c] = {s, v};
  if (t < 2 * pi) A[++c] = {t + 1e-12, -v};
}
double w, h;
int n, m;
double _d[maxn], _a[maxn];
bool check(int x, double r) {
  sum = c = 0;
  for (register int i = (1); i <= int(n); ++i)
    if (dist(p[i], p[x]) > 0 && dist(p[i], p[x]) < 2 * r) {
      double r1 = acos(dist(p[i], p[x]) / 2 / r);
      double s1 = atan2(p[i].y - p[x].y, p[i].x - p[x].x);
      double l = s1 - r1, r = s1 + r1;
      while (l < 0) l += 2 * pi;
      while (l >= 2 * pi) l -= 2 * pi;
      while (r < 0) r += 2 * pi;
      while (r >= 2 * pi) r -= 2 * pi;
      if (l <= r)
        add(l, r);
      else
        add(0, r), add(l, 2 * pi);
    }
  double t;
  if (p[x].x < r) {
    t = acos(p[x].x / r);
    add(pi - t, pi + t, 2);
  }
  if (p[x].y < r) {
    t = acos(p[x].y / r);
    add(1.5 * pi - t, 1.5 * pi + t, 2);
  }
  if (p[x].x + r > w) {
    t = acos((w - p[x].x) / r);
    add(0, t, 2);
    add(2 * pi - t, 2 * pi, 2);
  }
  if (p[x].y + r > h) {
    t = acos((h - p[x].y) / r);
    add(pi / 2 - t, pi / 2 + t, 2);
  }
  if (c < 2) return true;
  sort(A + 1, A + 1 + c);
  if (sum < 2 && A[1].first > 1e-9) return true;
  for (register int j = (1); j <= int(c); ++j) {
    sum += A[j].second;
    if (sum < 2) return true;
  }
  if (sum < 2 && A[c].first < 2 * pi - 1e-9) return true;
  return false;
}
int main() {
  double L = 0, R;
  w = read(), h = read(), n = read();
  for (register int i = (1); i <= int(n); ++i) p[i].x = read(), p[i].y = read();
  random_shuffle(p + 1, p + 1 + n);
  for (register int i = (1); i <= int(n); ++i) {
    if (!check(i, L + 1e-9)) continue;
    R = 2e6;
    while (R - L > 1e-9) {
      double mid = (L + R) / 2.0;
      if (check(i, mid))
        L = mid;
      else
        R = mid;
    }
  }
  printf("%.15lf\n", L);
  return 0;
}

```