#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void rread(T& num) {
  num = 0;
  T f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') num = num * 10 + ch - '0', ch = getchar();
  num *= f;
}
inline int getgcd(int x, int y) {
  if (!x) return y;
  return getgcd(y % x, x);
}
inline long long getlcm(int x, int y) {
  return (long long)x / getgcd(x, y) * y;
}
inline long long getgcd(long long x, long long y) {
  if (!x) return y;
  return getgcd(y % x, x);
}
inline long long getlcm(long long x, long long y) {
  return x / getgcd(x, y) * y;
}
inline int power(int x, int k, int p) {
  int res = 1;
  for (; k; k >>= 1, x = (long long)x * x % p)
    if (k & 1) res = (long long)res * x % p;
  return res;
}
const int maxn = 2005;
struct point {
  double x, y;
  inline point() { x = y = 0; }
  inline point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  inline friend bool operator!=(point a, point b) {
    return a.x != b.x || a.y != b.y;
  }
  inline friend double dis(point a, point b) {
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
  }
} p[maxn];
int w, h, n, cnt, tot;
double dist[maxn][maxn];
pair<double, int> q[maxn];
const double pi = acos(-1.0);
inline void insert(double l, double r, int flag = 1) {
  if (l < -pi) cnt += flag, l += pi * 2;
  if (r > pi) cnt += flag, r -= pi * 2;
  q[++tot] = make_pair(l, flag);
  q[++tot] = make_pair(r, -flag);
}
inline bool check(int x, double r) {
  tot = cnt = 0;
  point tmp = p[x];
  if (r > tmp.x) {
    double a = -pi, t = acos(tmp.x / r);
    insert(a - t, a + t, 2);
  }
  if (r > tmp.y) {
    double a = -pi / 2, t = acos(tmp.y / r);
    insert(a - t, a + t, 2);
  }
  if (r > w - tmp.x) {
    double a = 0, t = acos((w - tmp.x) / r);
    insert(a - t, a + t, 2);
  }
  if (r > h - tmp.y) {
    double a = pi / 2, t = acos((h - tmp.y) / r);
    insert(a - t, a + t, 2);
  }
  for (int(i) = (1); (i) <= (n); (i)++)
    if (i != x && p[i] != p[x]) {
      double d = dist[i][x];
      if (r + r > d) {
        double a = atan2(p[i].y - tmp.y, p[i].x - tmp.x), t = acos(d / 2 / r);
        insert(a - t, a + t);
      }
    }
  sort(q + 1, q + tot + 1);
  if (cnt <= 1) return 1;
  for (int(i) = (1); (i) <= (tot); (i)++) {
    if (cnt <= 1) return 1;
    cnt += q[i].second;
  }
  return 0;
}
int main() {
  rread(w);
  rread(h);
  rread(n);
  for (int(i) = (1); (i) <= (n); (i)++) rread(p[i].x), rread(p[i].y);
  random_shuffle(p + 1, p + n + 1);
  for (int(i) = (1); (i) <= (n); (i)++)
    for (int(j) = (1); (j) <= (n); (j)++) dist[i][j] = dis(p[i], p[j]);
  double lim = dis(point(0, 0), point(w, h)), ans = 0;
  for (int(i) = (1); (i) <= (n); (i)++) {
    if (check(i, ans + 1e-10)) {
      double l = ans, r = lim;
      for (int(t) = (1); (t) <= (60); (t)++) {
        double m = (l + r) / 2;
        if (check(i, m))
          l = m;
        else
          r = m;
      }
      ans = l;
    }
  }
  printf("%.12f\n", ans);
  return 0;
}

### Prompt

In CPP, your task is to solve 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>
using namespace std;
template <class T>
inline void rread(T& num) {
  num = 0;
  T f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') num = num * 10 + ch - '0', ch = getchar();
  num *= f;
}
inline int getgcd(int x, int y) {
  if (!x) return y;
  return getgcd(y % x, x);
}
inline long long getlcm(int x, int y) {
  return (long long)x / getgcd(x, y) * y;
}
inline long long getgcd(long long x, long long y) {
  if (!x) return y;
  return getgcd(y % x, x);
}
inline long long getlcm(long long x, long long y) {
  return x / getgcd(x, y) * y;
}
inline int power(int x, int k, int p) {
  int res = 1;
  for (; k; k >>= 1, x = (long long)x * x % p)
    if (k & 1) res = (long long)res * x % p;
  return res;
}
const int maxn = 2005;
struct point {
  double x, y;
  inline point() { x = y = 0; }
  inline point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  inline friend bool operator!=(point a, point b) {
    return a.x != b.x || a.y != b.y;
  }
  inline friend double dis(point a, point b) {
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
  }
} p[maxn];
int w, h, n, cnt, tot;
double dist[maxn][maxn];
pair<double, int> q[maxn];
const double pi = acos(-1.0);
inline void insert(double l, double r, int flag = 1) {
  if (l < -pi) cnt += flag, l += pi * 2;
  if (r > pi) cnt += flag, r -= pi * 2;
  q[++tot] = make_pair(l, flag);
  q[++tot] = make_pair(r, -flag);
}
inline bool check(int x, double r) {
  tot = cnt = 0;
  point tmp = p[x];
  if (r > tmp.x) {
    double a = -pi, t = acos(tmp.x / r);
    insert(a - t, a + t, 2);
  }
  if (r > tmp.y) {
    double a = -pi / 2, t = acos(tmp.y / r);
    insert(a - t, a + t, 2);
  }
  if (r > w - tmp.x) {
    double a = 0, t = acos((w - tmp.x) / r);
    insert(a - t, a + t, 2);
  }
  if (r > h - tmp.y) {
    double a = pi / 2, t = acos((h - tmp.y) / r);
    insert(a - t, a + t, 2);
  }
  for (int(i) = (1); (i) <= (n); (i)++)
    if (i != x && p[i] != p[x]) {
      double d = dist[i][x];
      if (r + r > d) {
        double a = atan2(p[i].y - tmp.y, p[i].x - tmp.x), t = acos(d / 2 / r);
        insert(a - t, a + t);
      }
    }
  sort(q + 1, q + tot + 1);
  if (cnt <= 1) return 1;
  for (int(i) = (1); (i) <= (tot); (i)++) {
    if (cnt <= 1) return 1;
    cnt += q[i].second;
  }
  return 0;
}
int main() {
  rread(w);
  rread(h);
  rread(n);
  for (int(i) = (1); (i) <= (n); (i)++) rread(p[i].x), rread(p[i].y);
  random_shuffle(p + 1, p + n + 1);
  for (int(i) = (1); (i) <= (n); (i)++)
    for (int(j) = (1); (j) <= (n); (j)++) dist[i][j] = dis(p[i], p[j]);
  double lim = dis(point(0, 0), point(w, h)), ans = 0;
  for (int(i) = (1); (i) <= (n); (i)++) {
    if (check(i, ans + 1e-10)) {
      double l = ans, r = lim;
      for (int(t) = (1); (t) <= (60); (t)++) {
        double m = (l + r) / 2;
        if (check(i, m))
          l = m;
        else
          r = m;
      }
      ans = l;
    }
  }
  printf("%.12f\n", ans);
  return 0;
}

```