#include <bits/stdc++.h>
using namespace std;
const int M = 1e5 + 228;
const long long Q = 4 * 1e9 + 7.;
const long double eps = 1e-10;
pair<long long, long long> pre[M], suf[M];
vector<pair<pair<long long, long long>, long long> > g2, g1;
long long x[M], y[M];
long long x1[M], y11[M], x2[M], y2[M];
int q1[M], q2[M];
bool is_Q(long long xqw) { return xqw == Q; }
bool pupsik(long long n, long double X) {
  long long l, r, mid, l1, r1, mid1;
  l = 0;
  r = n;
  while (l != r - 1) {
    mid = (l + r) / 2;
    if (g1[mid].first.first <= X)
      l = mid;
    else
      r = mid;
  }
  l1 = -1;
  r1 = n - 1;
  while (l1 != r1 - 1) {
    mid1 = (l1 + r1) / 2;
    if (g1[mid1].first.second >= X)
      r1 = mid1;
    else
      l1 = mid1;
  }
  r = r1;
  l1 = l;
  if (r && is_Q(pre[r - 1].first)) return false;
  if (l1 != n - 1 && is_Q(suf[l1 + 1].first)) return false;
  if (r == 0) return true;
  if (l1 == n - 1) return true;
  if ((pre[r - 1].second < suf[l1 + 1].first) ||
      (suf[l1 + 1].second < pre[r - 1].first))
    return false;
  return true;
}
bool cmp(int i, int j) { return x[i] + y[i] < x[j] + y[j]; }
bool cmp1(int i, int j) { return y[i] - x[i] < y[j] - x[j]; }
int main() {
  srand(time(NULL));
  long long n;
  scanf("%lld", &n);
  for (long long i = 0; i < n; i++) {
    scanf(
        "%lld"
        "%lld",
        &x[i], &y[i]);
    x[i] *= 2;
    y[i] *= 2;
  }
  for (int i = 0; i < n; i++) q1[i] = q2[i] = i;
  sort(q1, q1 + n, cmp);
  sort(q2, q2 + n, cmp1);
  long long l = -1, r = 2000000002.;
  while (r - l > 1) {
    long long mid = (l + r) / 2;
    g2.resize(0);
    g1.resize(0);
    for (long long i = 0; i < n; i++) {
      x1[i] = y[i] + x[i] - mid;
      y11[i] = y[i] + x[i] + mid;
      x2[i] = y[i] - x[i] - mid;
      y2[i] = y[i] - x[i] + mid;
    }
    for (long long i = 0; i < n; i++)
      g1.push_back(make_pair(
          make_pair(y[q1[i]] + x[q1[i]] - mid, y[q1[i]] + x[q1[i]] + mid),
          q1[i]));
    for (long long i = 0; i < n; i++)
      g1.push_back(make_pair(
          make_pair(y[q2[i]] - x[q1[i]] - mid, y[q2[i]] - x[q2[i]] + mid),
          q2[i]));
    pre[0] = make_pair(x2[g1[0].second], y2[g1[0].second]);
    for (long long i = 1; i < n; i++) {
      if (pre[i - 1].first == Q) {
        pre[i] = make_pair(Q, Q);
        continue;
      }
      long long xxx = max(pre[i - 1].first, x2[g1[i].second]);
      long long yyy = min(pre[i - 1].second, y2[g1[i].second]);
      if (xxx <= yyy)
        pre[i] = make_pair(xxx, yyy);
      else
        pre[i] = make_pair(Q, Q);
    }
    suf[n - 1] = make_pair(x2[g1[n - 1].second], y2[g1[n - 1].second]);
    for (long long i = n - 2; i >= 0; i--) {
      if (suf[i + 1].first == Q) {
        suf[i] = make_pair(Q, Q);
        continue;
      }
      long long xxx = max(suf[i + 1].first, x2[g1[i].second]);
      long long yyy = min(suf[i + 1].second, y2[g1[i].second]);
      if (xxx <= yyy)
        suf[i] = make_pair(xxx, yyy);
      else
        suf[i] = make_pair(Q, Q);
    }
    bool ok = false;
    for (long long i = 0; i < n; i++) {
      ok |= pupsik(n, g1[i].first.first);
      ok |= pupsik(n, g1[i].first.second);
      if (ok) break;
    }
    if (ok)
      r = mid;
    else
      l = mid;
  }
  if (r % 2)
    cout << r / 2 << ".5";
  else
    cout << r / 2;
  return 0;
}

### Prompt

Please create a solution in CPP 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 int M = 1e5 + 228;
const long long Q = 4 * 1e9 + 7.;
const long double eps = 1e-10;
pair<long long, long long> pre[M], suf[M];
vector<pair<pair<long long, long long>, long long> > g2, g1;
long long x[M], y[M];
long long x1[M], y11[M], x2[M], y2[M];
int q1[M], q2[M];
bool is_Q(long long xqw) { return xqw == Q; }
bool pupsik(long long n, long double X) {
  long long l, r, mid, l1, r1, mid1;
  l = 0;
  r = n;
  while (l != r - 1) {
    mid = (l + r) / 2;
    if (g1[mid].first.first <= X)
      l = mid;
    else
      r = mid;
  }
  l1 = -1;
  r1 = n - 1;
  while (l1 != r1 - 1) {
    mid1 = (l1 + r1) / 2;
    if (g1[mid1].first.second >= X)
      r1 = mid1;
    else
      l1 = mid1;
  }
  r = r1;
  l1 = l;
  if (r && is_Q(pre[r - 1].first)) return false;
  if (l1 != n - 1 && is_Q(suf[l1 + 1].first)) return false;
  if (r == 0) return true;
  if (l1 == n - 1) return true;
  if ((pre[r - 1].second < suf[l1 + 1].first) ||
      (suf[l1 + 1].second < pre[r - 1].first))
    return false;
  return true;
}
bool cmp(int i, int j) { return x[i] + y[i] < x[j] + y[j]; }
bool cmp1(int i, int j) { return y[i] - x[i] < y[j] - x[j]; }
int main() {
  srand(time(NULL));
  long long n;
  scanf("%lld", &n);
  for (long long i = 0; i < n; i++) {
    scanf(
        "%lld"
        "%lld",
        &x[i], &y[i]);
    x[i] *= 2;
    y[i] *= 2;
  }
  for (int i = 0; i < n; i++) q1[i] = q2[i] = i;
  sort(q1, q1 + n, cmp);
  sort(q2, q2 + n, cmp1);
  long long l = -1, r = 2000000002.;
  while (r - l > 1) {
    long long mid = (l + r) / 2;
    g2.resize(0);
    g1.resize(0);
    for (long long i = 0; i < n; i++) {
      x1[i] = y[i] + x[i] - mid;
      y11[i] = y[i] + x[i] + mid;
      x2[i] = y[i] - x[i] - mid;
      y2[i] = y[i] - x[i] + mid;
    }
    for (long long i = 0; i < n; i++)
      g1.push_back(make_pair(
          make_pair(y[q1[i]] + x[q1[i]] - mid, y[q1[i]] + x[q1[i]] + mid),
          q1[i]));
    for (long long i = 0; i < n; i++)
      g1.push_back(make_pair(
          make_pair(y[q2[i]] - x[q1[i]] - mid, y[q2[i]] - x[q2[i]] + mid),
          q2[i]));
    pre[0] = make_pair(x2[g1[0].second], y2[g1[0].second]);
    for (long long i = 1; i < n; i++) {
      if (pre[i - 1].first == Q) {
        pre[i] = make_pair(Q, Q);
        continue;
      }
      long long xxx = max(pre[i - 1].first, x2[g1[i].second]);
      long long yyy = min(pre[i - 1].second, y2[g1[i].second]);
      if (xxx <= yyy)
        pre[i] = make_pair(xxx, yyy);
      else
        pre[i] = make_pair(Q, Q);
    }
    suf[n - 1] = make_pair(x2[g1[n - 1].second], y2[g1[n - 1].second]);
    for (long long i = n - 2; i >= 0; i--) {
      if (suf[i + 1].first == Q) {
        suf[i] = make_pair(Q, Q);
        continue;
      }
      long long xxx = max(suf[i + 1].first, x2[g1[i].second]);
      long long yyy = min(suf[i + 1].second, y2[g1[i].second]);
      if (xxx <= yyy)
        suf[i] = make_pair(xxx, yyy);
      else
        suf[i] = make_pair(Q, Q);
    }
    bool ok = false;
    for (long long i = 0; i < n; i++) {
      ok |= pupsik(n, g1[i].first.first);
      ok |= pupsik(n, g1[i].first.second);
      if (ok) break;
    }
    if (ok)
      r = mid;
    else
      l = mid;
  }
  if (r % 2)
    cout << r / 2 << ".5";
  else
    cout << r / 2;
  return 0;
}

```