#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const double eps = 1e-12;
const int step[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <class T>
inline T max1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a > b ? a : b;
  if (c != -1234567) ans = max1(ans, c);
  if (d != -1234567) ans = max1(ans, d);
  return ans;
}
template <class T>
inline T min1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a < b ? a : b;
  if (c != -1234567) ans = min(ans, c);
  if (d != -1234567) ans = min(ans, d);
  return ans;
}
template <class T>
inline T gcd1(T a, T b) {
  if (a < b) swap(a, b);
  if (a % b == 0) return b;
  return gcd1(b, a % b);
}
template <class T>
inline T lb(T num) {
  return num & (-num);
}
inline int jud(double a, double b) {
  if (abs1(a - b) < eps) return 0;
  if (a < b) return -1;
  return 1;
}
template <typename it, typename t1>
inline int find(t1 val, it a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 1) return 0;
  int be = 0, en = na - 1;
  if (*a <= *(a + na - 1)) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(*(a + be), val) == 1 && be != 0) be--;
    if (!f_small && jud(*(a + be), val) == -1 && be != na - 1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(*(a + be), val) == -1 && be != 0) be--;
    if (f_small && jud(*(a + be), val) == 1 && be != na - 1) be++;
  }
  return be;
}
inline int bitnum(unsigned long long nValue) {
  nValue = ((0xaaaaaaaaaaaaaaaaull & nValue) >> 1) +
           (0x5555555555555555ull & nValue);
  nValue = ((0xccccccccccccccccull & nValue) >> 2) +
           (0x3333333333333333ull & nValue);
  nValue = ((0xf0f0f0f0f0f0f0f0ull & nValue) >> 4) +
           (0x0f0f0f0f0f0f0f0full & nValue);
  nValue = ((0xff00ff00ff00ff00ull & nValue) >> 8) +
           (0x00ff00ff00ff00ffull & nValue);
  nValue = ((0xffff0000ffff0000ull & nValue) >> 16) +
           (0x0000ffff0000ffffull & nValue);
  nValue = ((0xffffffff00000000ull & nValue) >> 32) +
           (0x00000000ffffffffull & nValue);
  return nValue;
}
long long pow(long long n, long long m, long long mod = 0) {
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
const int maxn = 200100;
struct node {
  int he, cha, no;
  bool operator<(const node &no) const { return cha < no.cha; }
  bool operator>(const node &no) const { return cha > no.cha; }
} orig[2][maxn];
priority_queue<node, vector<node>, greater<node> > pq_min;
priority_queue<node> pq_max;
bool f[maxn];
inline bool cmp1(const node &a, const node &b) { return a.no < b.no; }
inline bool cmp2(const node &a, const node &b) { return a.he < b.he; }
int n;
const long long inf = 2000000000;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    orig[0][i].he = x + y;
    orig[0][i].cha = x - y;
    orig[0][i].no = i;
    orig[1][i] = orig[0][i];
  }
  sort(orig[0], orig[0] + n, cmp2);
  for (int i = 0; i < n; i++) {
    pq_min.push(orig[0][i]);
    pq_max.push(orig[0][i]);
  }
  int be = 0, en = 0;
  double ans = 1e300;
  for (int i = 0; i < n; i++) f[i] = 1;
  for (int i = 0; i < n; i++) {
    f[orig[0][i].no] = 0;
    while (!f[pq_min.top().no]) pq_min.pop();
    while (!f[pq_max.top().no]) pq_max.pop();
    en = i;
    while (be < en && pq_max.top().cha - pq_min.top().cha <
                          orig[0][en].he - orig[0][be].he) {
      ans = min1((double)max1(pq_max.top().cha - pq_min.top().cha,
                              orig[0][en].he - orig[0][be].he),
                 ans);
      pq_min.push(orig[0][be]);
      pq_max.push(orig[0][be]);
      f[orig[0][be].no] = 1;
      be++;
    }
    ans = min1((double)max1(pq_max.top().cha - pq_min.top().cha,
                            orig[0][en].he - orig[0][be].he),
               ans);
  }
  printf("%.10lf\n", ans / 2);
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

Sereja placed n points on a plane. Now Sereja wants to place on the plane two straight lines, intersecting at a right angle, so that one of the straight lines intersect the Ox axis at an angle of 45 degrees and the maximum distance from the points to the straight lines were minimum. 

In this problem we consider the distance between points (x1, y1) and (x2, y2) equal |x1 - x2| + |y1 - y2|. The distance between the point and the straight lines is the minimum distance from the point to some point belonging to one of the lines.

Help Sereja, find the maximum distance from the points to the optimally located straight lines.

Input

The first line contains integer n (1 ≤ n ≤ 105). Next n lines contain the coordinates of the lines. The i-th line contains two integers xi, yi (|xi|, |yi| ≤ 109).

Output

In a single line print a real number — the answer to the problem. Your answer will be considered correct iff its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

4
0 0
2 0
0 2
2 2


Output

0.000000000000000


Input

4
1 0
0 1
2 1
1 2


Output

1.000000000000000

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const double eps = 1e-12;
const int step[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <class T>
inline T max1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a > b ? a : b;
  if (c != -1234567) ans = max1(ans, c);
  if (d != -1234567) ans = max1(ans, d);
  return ans;
}
template <class T>
inline T min1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a < b ? a : b;
  if (c != -1234567) ans = min(ans, c);
  if (d != -1234567) ans = min(ans, d);
  return ans;
}
template <class T>
inline T gcd1(T a, T b) {
  if (a < b) swap(a, b);
  if (a % b == 0) return b;
  return gcd1(b, a % b);
}
template <class T>
inline T lb(T num) {
  return num & (-num);
}
inline int jud(double a, double b) {
  if (abs1(a - b) < eps) return 0;
  if (a < b) return -1;
  return 1;
}
template <typename it, typename t1>
inline int find(t1 val, it a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 1) return 0;
  int be = 0, en = na - 1;
  if (*a <= *(a + na - 1)) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(*(a + be), val) == 1 && be != 0) be--;
    if (!f_small && jud(*(a + be), val) == -1 && be != na - 1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(*(a + be), val) == -1 && be != 0) be--;
    if (f_small && jud(*(a + be), val) == 1 && be != na - 1) be++;
  }
  return be;
}
inline int bitnum(unsigned long long nValue) {
  nValue = ((0xaaaaaaaaaaaaaaaaull & nValue) >> 1) +
           (0x5555555555555555ull & nValue);
  nValue = ((0xccccccccccccccccull & nValue) >> 2) +
           (0x3333333333333333ull & nValue);
  nValue = ((0xf0f0f0f0f0f0f0f0ull & nValue) >> 4) +
           (0x0f0f0f0f0f0f0f0full & nValue);
  nValue = ((0xff00ff00ff00ff00ull & nValue) >> 8) +
           (0x00ff00ff00ff00ffull & nValue);
  nValue = ((0xffff0000ffff0000ull & nValue) >> 16) +
           (0x0000ffff0000ffffull & nValue);
  nValue = ((0xffffffff00000000ull & nValue) >> 32) +
           (0x00000000ffffffffull & nValue);
  return nValue;
}
long long pow(long long n, long long m, long long mod = 0) {
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
const int maxn = 200100;
struct node {
  int he, cha, no;
  bool operator<(const node &no) const { return cha < no.cha; }
  bool operator>(const node &no) const { return cha > no.cha; }
} orig[2][maxn];
priority_queue<node, vector<node>, greater<node> > pq_min;
priority_queue<node> pq_max;
bool f[maxn];
inline bool cmp1(const node &a, const node &b) { return a.no < b.no; }
inline bool cmp2(const node &a, const node &b) { return a.he < b.he; }
int n;
const long long inf = 2000000000;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    orig[0][i].he = x + y;
    orig[0][i].cha = x - y;
    orig[0][i].no = i;
    orig[1][i] = orig[0][i];
  }
  sort(orig[0], orig[0] + n, cmp2);
  for (int i = 0; i < n; i++) {
    pq_min.push(orig[0][i]);
    pq_max.push(orig[0][i]);
  }
  int be = 0, en = 0;
  double ans = 1e300;
  for (int i = 0; i < n; i++) f[i] = 1;
  for (int i = 0; i < n; i++) {
    f[orig[0][i].no] = 0;
    while (!f[pq_min.top().no]) pq_min.pop();
    while (!f[pq_max.top().no]) pq_max.pop();
    en = i;
    while (be < en && pq_max.top().cha - pq_min.top().cha <
                          orig[0][en].he - orig[0][be].he) {
      ans = min1((double)max1(pq_max.top().cha - pq_min.top().cha,
                              orig[0][en].he - orig[0][be].he),
                 ans);
      pq_min.push(orig[0][be]);
      pq_max.push(orig[0][be]);
      f[orig[0][be].no] = 1;
      be++;
    }
    ans = min1((double)max1(pq_max.top().cha - pq_min.top().cha,
                            orig[0][en].he - orig[0][be].he),
               ans);
  }
  printf("%.10lf\n", ans / 2);
  return 0;
}

```