Given the coordinates of four points in 2D space p1, p2, p3 and p4, return true if the four points construct a square. The coordinate of a point pi is represented as [xi, yi]. The input is not given in any order.

A valid square has four equal sides with positive length and four equal angles (90-degree angles).

```
Example 1:
Input: p1 = [2,6], p2 = [5,1], p3 = [0,-2], p4 = [-3,3]
Output: true
Example 2:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
Output: false
```

import math A=list(map(int,input('Point p1: ').split(','))) B=list(map(int,input('Point p2: ').split(','))) C=list(map(int,input('Point p3: ').split(','))) D=list(map(int,input('Point p4: ').split(','))) LIST=[A,B,C,D] M=sorted(LIST , key=lambda X: [X[1], X[0]]) p1,p2,p3,p4 = M[0],M[1],M[2],M[3] def length(x,y): return (((y[0]-x[0])**2) + ((y[1]-x[1])**2)) flag=0 if length(p1,p2)==length(p2,p4): if length(p2,p4) == length(p4,p3): if length(p4,p3) == length(p3,p1): if length(p2,p3) == length(p1,p4): flag=1 else: flag=0 else: flag=0 else: flag=0 else: flag=0 print(True) if flag==1 else print(False)

YOU CAN INPUT THE COORDINATES(POINTS) IN ANY ORDER.

PRACTICAL SAMPLE IMAGE BELOW

Input_1:

Point p1: 2,6

Point p2: 5,1

Point p3: 0,-2

Point p4: -3,3

Output:

True

Input_2:

Point p1: 0,0

Point p2: 1,1

Point p3: 1,0

Point p4: 0,12

Output:

False

Input_3:

Point p1: 0,0

Point p2: 1,1

Point p3: 1,0

Point p4: 0,1

Output:

True

Input_4:

Point p1: 1,0

Point p2: -1,0

Point p3: 0,1

Point p4: 0,-1

Output:

True

Input_5:

Point p1: 10,20

Point p2: 20,20

Point p3: 10,10

Point p4: 20,10

Output:

True

Sample Image of Output and the Execution of the Code.

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