A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum.
Given a row x col grid of integers, how many 3 x 3 "magic square" subgrids are there?  (Each subgrid is contiguous).
 
Example 1:

Input: grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
Output: 1
Explanation: 
The following subgrid is a 3 x 3 magic square:

while this one is not:

In total, there is only one magic square inside the given grid.

Example 2:
Input: grid = [[8]]
Output: 0

Example 3:
Input: grid = [[4,4],[3,3]]
Output: 0

Example 4:
Input: grid = [[4,7,8],[9,5,1],[2,3,6]]
Output: 0

 
Constraints:

row == grid.length
col == grid[i].length
1 <= row, col <= 10
0 <= grid[i][j] <= 15

```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    \n    def isMagicSquare(self, grid):\n        '''\n        Check whether the given grid is a magic square\n        '''\n        # Check the elements\n        flat = [num for row in grid for num in row]\n        if sorted(flat) != [1, 2, 3, 4, 5, 6, 7, 8, 9]:\n            return False\n        \n        # Check the row, column and diagnal sums\n        row_sums = [sum(row) for row in grid]\n        col_sums = [sum([row[i] for row in grid]) for i in range(3)]\n        diag_sums = [sum([grid[i][i] for i in range(3)]), (grid[0][2] + grid[1][1] + grid[2][0])]\n        row_sums.extend(col_sums)\n        row_sums.extend(diag_sums)\n        return len(set(row_sums)) == 1\n    \n    \n    def numMagicSquaresInside(self, grid: List[List[int]]) -> int:\n        # 9:37 --> 9:52 --> 10:31 9/14/20\n        cnt = 0\n        # Construct the 3x3 square\n        for i in range(len(grid)-2):\n            for j in range(len(grid)-2):\n                temp_grid = [grid[i+k][j:j+3] for k in range(3)]\n                if self.isMagicSquare(temp_grid):\n                    cnt += 1\n        \n        return cnt\n        \n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numMagicSquaresInside'
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: 7886