Chef bought a huge (effectively infinite) planar island and built $N$ restaurants (numbered $1$ through $N$) on it. For each valid $i$, the Cartesian coordinates of restaurant $i$ are $(X_i, Y_i)$.
Now, Chef wants to build $N-1$ straight narrow roads (line segments) on the island. The roads may have arbitrary lengths; restaurants do not have to lie on the roads. The slope of each road must be $1$ or $-1$, i.e. for any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the same road, $|x_1-x_2| = |y_1-y_2|$ must hold.
Let's denote the minimum distance Chef has to walk from restaurant $i$ to reach a road by $D_i$. Then, let's denote $a = \mathrm{max}\,(D_1, D_2, \ldots, D_N)$; Chef wants this distance to be minimum possible.
Chef is a busy person, so he decided to give you the job of building the roads. You should find a way to build them that minimises $a$ and compute $a \cdot \sqrt{2}$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains two space-separated integers $X_i$ and $Y_i$.

-----Output-----
For each test case, print a single line containing one real number — the minimum distance $a$ multiplied by $\sqrt{2}$. Your answer will be considered correct if its absolute or relative error does not exceed $10^{-6}$.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le N \le 10^4$
- $|X_i|, |Y_i| \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (10 points):
- $1 \le T \le 10$
- $2 \le N \le 5$
- $|X_i|, |Y_i| \le 10$ for each valid $i$
- $a \cdot \sqrt{2}$ is an integer
Subtask #2 (90 points): original constraints

-----Example Input-----
2
3
0 0
0 1
0 -1
3
0 1
1 0
-1 0

-----Example Output-----
0.5
0

-----Explanation-----
Example case 1: We should build roads described by equations $y-x+0.5 = 0$ and $y-x-0.5 = 0$.
Example case 2: We should build roads described by equations $y-x-1 = 0$ and $y+x-1 = 0$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 't=int(input())\nfor _ in range(0,t):\n intercept1=[]\n intercept2=[]\n n=int(input())\n for i in range(0,n):\n  x,y=map(int,input().split())\n  intercept1.append(y+x)\n  intercept2.append(y-x)\n intercept1.sort()\n intercept2.sort()\n mn1=10**10\n mn2=10**10\n for i in range(1,n):\n  diff1=intercept1[i]-intercept1[i-1]\n  mn1=min(mn1,diff1)\n  diff2=intercept2[i]-intercept2[i-1]\n  mn2=min(mn2,diff2)\n  ans=min(mn1,mn2)\n print(ans/2)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13355