#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const int iter = 60;
const double eps = 1e-7;
const int size = 100 * 1000 + 100;
const int rms = (1 << 18) - 1;
const int hrms = rms / 2;
const long long inf = (long long)1e15;
long long x[size], y[size];
int n;
bool used[size];
long long lefts[rms + 1];
long long rights[rms + 1];
inline long long mabs(long long d) {
  if (d < 0)
    return -d;
  else
    return d;
}
void turnon(int ps, long long m) {
  lefts[ps + hrms + 1] = x[ps] - y[ps] - m;
  rights[ps + hrms + 1] = x[ps] - y[ps] + m;
  ps += hrms + 1;
  long long ov1, ov2;
  while (ps > 1) {
    ps /= 2;
    ov1 = lefts[ps];
    ov2 = rights[ps];
    if (lefts[ps * 2] > lefts[ps * 2 + 1])
      lefts[ps] = lefts[ps * 2];
    else
      lefts[ps] = lefts[ps * 2 + 1];
    if (rights[ps * 2] < rights[ps * 2 + 1])
      rights[ps] = rights[ps * 2];
    else
      rights[ps] = rights[ps * 2 + 1];
    if (lefts[ps] == ov1 && rights[ps] == ov2) break;
  }
}
void turnoff(int ps) {
  lefts[ps + hrms + 1] = -inf;
  rights[ps + hrms + 1] = inf;
  ps += hrms + 1;
  long long ov1, ov2;
  while (ps > 1) {
    ps /= 2;
    ov1 = lefts[ps];
    ov2 = rights[ps];
    if (lefts[ps * 2] > lefts[ps * 2 + 1])
      lefts[ps] = lefts[ps * 2];
    else
      lefts[ps] = lefts[ps * 2 + 1];
    if (rights[ps * 2] < rights[ps * 2 + 1])
      rights[ps] = rights[ps * 2];
    else
      rights[ps] = rights[ps * 2 + 1];
    if (lefts[ps] == ov1 && rights[ps] == ov2) break;
  }
}
vector<pair<long long, int> > eventOpen, eventClose;
long long eventCloseVal[size];
long long eventCloseNum[size];
long long eventOpenVal[size];
long long eventOpenNum[size];
double check(long long m) {
  for (int i = 0; i <= rms; i++) {
    lefts[i] = -inf;
    rights[i] = inf;
  }
  for (int i = 0; i < n; i++) {
    lefts[i + hrms + 1] = x[i] - y[i] - m;
    rights[i + hrms + 1] = x[i] - y[i] + m;
  }
  for (int i = hrms; i > 0; i--) {
    lefts[i] = max(lefts[i * 2], lefts[i * 2 + 1]);
    rights[i] = min(rights[i * 2], rights[i * 2 + 1]);
  }
  if (lefts[1] <= rights[1]) return true;
  int p = 0, nm;
  for (int i = 0; i < n; i++) {
    turnoff(eventOpenNum[i]);
    while (p < n && eventCloseVal[p] + m < eventOpenVal[i] - m) {
      turnon(eventCloseNum[p], m);
      p++;
    }
    if (lefts[1] <= rights[1]) return true;
  }
  return false;
}
int main() {
  scanf("%d", &n);
  long long lb = 0;
  long long rb = 0;
  for (int i = 0; i < n; i++) {
    scanf("%I64d%I64d", &x[i], &y[i]);
    x[i] *= 2;
    y[i] *= 2;
    rb = max(rb, max(mabs(x[i] + y[i]), mabs(x[i] - y[i])));
  }
  for (int i = 0; i < n; i++) {
    eventOpen.push_back(make_pair(x[i] + y[i], i));
    eventClose.push_back(make_pair(x[i] + y[i], i));
  }
  sort(eventOpen.begin(), eventOpen.end());
  sort(eventClose.begin(), eventClose.end());
  for (int i = 0; i < n; i++) {
    eventOpenNum[i] = eventOpen[i].second;
    eventOpenVal[i] = eventOpen[i].first;
    eventCloseVal[i] = eventClose[i].first;
    eventCloseNum[i] = eventClose[i].second;
  }
  while (lb < rb) {
    long long mid = (lb + rb) / 2;
    cerr << mid << endl;
    if (check(mid))
      rb = mid;
    else
      lb = mid + 1;
  }
  cout.precision(20);
  cout << lb / 2.0 << endl;
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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(-1.0);
const int iter = 60;
const double eps = 1e-7;
const int size = 100 * 1000 + 100;
const int rms = (1 << 18) - 1;
const int hrms = rms / 2;
const long long inf = (long long)1e15;
long long x[size], y[size];
int n;
bool used[size];
long long lefts[rms + 1];
long long rights[rms + 1];
inline long long mabs(long long d) {
  if (d < 0)
    return -d;
  else
    return d;
}
void turnon(int ps, long long m) {
  lefts[ps + hrms + 1] = x[ps] - y[ps] - m;
  rights[ps + hrms + 1] = x[ps] - y[ps] + m;
  ps += hrms + 1;
  long long ov1, ov2;
  while (ps > 1) {
    ps /= 2;
    ov1 = lefts[ps];
    ov2 = rights[ps];
    if (lefts[ps * 2] > lefts[ps * 2 + 1])
      lefts[ps] = lefts[ps * 2];
    else
      lefts[ps] = lefts[ps * 2 + 1];
    if (rights[ps * 2] < rights[ps * 2 + 1])
      rights[ps] = rights[ps * 2];
    else
      rights[ps] = rights[ps * 2 + 1];
    if (lefts[ps] == ov1 && rights[ps] == ov2) break;
  }
}
void turnoff(int ps) {
  lefts[ps + hrms + 1] = -inf;
  rights[ps + hrms + 1] = inf;
  ps += hrms + 1;
  long long ov1, ov2;
  while (ps > 1) {
    ps /= 2;
    ov1 = lefts[ps];
    ov2 = rights[ps];
    if (lefts[ps * 2] > lefts[ps * 2 + 1])
      lefts[ps] = lefts[ps * 2];
    else
      lefts[ps] = lefts[ps * 2 + 1];
    if (rights[ps * 2] < rights[ps * 2 + 1])
      rights[ps] = rights[ps * 2];
    else
      rights[ps] = rights[ps * 2 + 1];
    if (lefts[ps] == ov1 && rights[ps] == ov2) break;
  }
}
vector<pair<long long, int> > eventOpen, eventClose;
long long eventCloseVal[size];
long long eventCloseNum[size];
long long eventOpenVal[size];
long long eventOpenNum[size];
double check(long long m) {
  for (int i = 0; i <= rms; i++) {
    lefts[i] = -inf;
    rights[i] = inf;
  }
  for (int i = 0; i < n; i++) {
    lefts[i + hrms + 1] = x[i] - y[i] - m;
    rights[i + hrms + 1] = x[i] - y[i] + m;
  }
  for (int i = hrms; i > 0; i--) {
    lefts[i] = max(lefts[i * 2], lefts[i * 2 + 1]);
    rights[i] = min(rights[i * 2], rights[i * 2 + 1]);
  }
  if (lefts[1] <= rights[1]) return true;
  int p = 0, nm;
  for (int i = 0; i < n; i++) {
    turnoff(eventOpenNum[i]);
    while (p < n && eventCloseVal[p] + m < eventOpenVal[i] - m) {
      turnon(eventCloseNum[p], m);
      p++;
    }
    if (lefts[1] <= rights[1]) return true;
  }
  return false;
}
int main() {
  scanf("%d", &n);
  long long lb = 0;
  long long rb = 0;
  for (int i = 0; i < n; i++) {
    scanf("%I64d%I64d", &x[i], &y[i]);
    x[i] *= 2;
    y[i] *= 2;
    rb = max(rb, max(mabs(x[i] + y[i]), mabs(x[i] - y[i])));
  }
  for (int i = 0; i < n; i++) {
    eventOpen.push_back(make_pair(x[i] + y[i], i));
    eventClose.push_back(make_pair(x[i] + y[i], i));
  }
  sort(eventOpen.begin(), eventOpen.end());
  sort(eventClose.begin(), eventClose.end());
  for (int i = 0; i < n; i++) {
    eventOpenNum[i] = eventOpen[i].second;
    eventOpenVal[i] = eventOpen[i].first;
    eventCloseVal[i] = eventClose[i].first;
    eventCloseNum[i] = eventClose[i].second;
  }
  while (lb < rb) {
    long long mid = (lb + rb) / 2;
    cerr << mid << endl;
    if (check(mid))
      rb = mid;
    else
      lb = mid + 1;
  }
  cout.precision(20);
  cout << lb / 2.0 << endl;
  return 0;
}

```