Given the coordinates of four points in 2D space, return whether the four points could construct a square.

The coordinate (x,y) of a point is represented by an integer array with two integers.

Example:

Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: True



 Note: 

All the input integers are in the range [-10000, 10000].
A valid square has four equal sides with positive length and four equal angles (90-degree angles).
Input points have no order.

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class Solution:\n     def validSquare(self, A, B, C, D):\n         """\n         A B   A D   A C\n         C D   B C   D B\n     \n         A C   A B   A D     \n         B D   D C   C B     \n         \n         - figure out which orientation this is\n         - B-A == D-C and C-A == D-B\n         - D-A == C-B and B-A == C-D \n         - C-A == B-D and D-A == B-C\n         \n         - if one of those is true, just need to check angles\n         - check length of two perpendicular sides is same\n             - enough to check -y, x?\n             \n         4     A(2,4)\n         3\n         2 C(0,2)  B(4,2)\n         1\n         0     D(2,0)\n           0 1 2 3 4\n           \n         [1,0]\n         [-1,0]\n         [0,-1]\n         [0,1]\n         \n         1       D\n         \n         0  B         A\n         \n        -1       C\n         \n           -1    0    1\n         \n         \n         :type p1: List[int]\n         :type p2: List[int]\n         :type p3: List[int]\n         :type p4: List[int]\n         :rtype: bool\n         """\n         def sub(p2, p1):\n             return [p2[0]-p1[0], p2[1]-p1[1]]\n         \n #         def add(p1, p2):\n #             return [p1[0]+p2[0], p1[1]+p2[1]]\n             \n         if sub(A, B) == [0, 0]:\n             return False\n         \n         if sub(B, A) == sub(D, C) and sub(C, A) == sub(D, B):\n             print((1))\n             diff1 = sub(B, A)\n             diff2 = sub(A, C)\n             print((diff1, diff2))\n             if diff1 == [-diff2[1], diff2[0]] or diff1 == [diff2[1], -diff2[0]]:\n                 return True\n             \n         elif sub(D, A) == sub(C, B) and sub(B, A) == sub(C, D):\n             print((2))\n             diff1 = sub(D, A)\n             diff2 = sub(A, B)\n             print((diff1, diff2))\n             if diff1 == [-diff2[1], diff2[0]] or diff1 == [diff2[1], -diff2[0]]:\n                 return True\n             \n             \n         elif sub(C, A) == sub(B, D) and sub(D, A) == sub(B, C):\n             print((3))\n             diff1 = sub(C, A)\n             diff2 = sub(A, D)\n             print((diff1, diff2))  # [-1, -1] [1, -1]\n             if diff1 == [-diff2[1], diff2[0]] or diff1 == [diff2[1], -diff2[0]]:\n                 return True\n             \n         else:\n             print((0))\n             \n         return False\n             \n         \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'validSquare'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 7032