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, p1, p2, p3, p4):\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         \n         p1 = [p1[0]*4, p1[1]*4]\n         p2 = [p2[0]*4, p2[1]*4]\n         p3 = [p3[0]*4, p3[1]*4]\n \n         p4 = [p4[0]*4, p4[1]*4]\n \n         \n         center_x = (p1[0] + p2[0] + p3[0] + p4[0]) / 4\n         center_y = (p1[1] + p2[1] + p3[1] + p4[1]) / 4\n         #print(center_x, " ", center_y)\n \n         #if center_x != center_y:\n             #return False\n         #print(center_x, " ", center_y)\n \n         if p1 == [center_x, center_y]:\n             return False\n         \n         #print(center_x, " ", center_y)\n         \n         center_to_p1 = [center_x - p1[0], center_y - p1[1]]\n         e_p2 = [(int)(center_x - (center_y - p1[1])), (int)(center_y + (center_x - p1[0]))]\n         e_p3 = [(int)(center_x + center_x - p1[0]), (int)(center_y + center_y - p1[1])]\n         e_p4 = [(int)(center_x + (center_y - p1[1])), (int)(center_y - (center_x - p1[0]))]\n         \n         #print ("e_p2 ", e_p2, " e_p3 ", e_p3, " e_p4 ", e_p4)\n         \n         #print ("p2 ", p2, " p3 ", p3, " p4 ", p4)\n         \n         if (e_p2 == p2 or e_p2 == p3 or e_p2 == p4) and (e_p3 == p2 or e_p3 == p3 or e_p3 == p4) and (e_p4 == p2 or e_p4 == p3 or e_p4 == p4):\n             return True\n         else:\n             return False\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: 6702