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 $y+x-1 = 0$.
t = int(input())
for _ in range(t):
 n = int(input())
 co = []
 suma = []
 diff = []
 for i in range(n):
  x,y = map(int,input().strip().split())
  co.append([x,y])
  suma.append(x+y)
  diff.append(x-y)
 # print(co)
 suma.sort()
 diff.sort()
 # print(suma)
 # print(diff)
 mina = 10**9
 mina = (abs((suma[0]-suma[1])/2))
 mina = min(mina,abs((diff[0]-diff[1])/2))
 # print(mina)
 for i in range(1,n-1):
  mina = min(mina,abs((suma[i]-suma[i+1])/2),abs((diff[i]-diff[i+1])/2))
  # print(i,mina)
  if(mina == 0.0):
   break
 print(mina)
t = int(input())
for _ in range(t):
 n = int(input())
 co = []
 suma = []
 diff = []
 for i in range(n):
  x,y = map(int,input().strip().split())
  co.append([x,y])
  suma.append(x+y)
  diff.append(x-y)
 # print(co)
 suma.sort()
 diff.sort()
 # print(suma)
 # print(diff)
 mina = 10**9
 mina = (abs((suma[0]-suma[1])/2))
 mina = min(mina,abs((diff[0]-diff[1])/2))
 # print(mina)
 for i in range(1,n-1):
  mina = min(mina,abs((suma[i]-suma[i+1])/2),abs((diff[i]-diff[i+1])/2))
  # print(i,mina)
  if(mina == 0.0):
   break
 print(mina)