Write a function that accepts a square matrix (`N x N` 2D array) and returns the determinant of the matrix.

How to take the determinant of a matrix -- it is simplest to start with the smallest cases:

A 1x1 matrix `|a|` has determinant `a`.

A 2x2 matrix `[ [a, b], [c, d] ]` or
```
|a  b|
|c  d|
```
has determinant: `a*d - b*c`.

The determinant of an `n x n` sized matrix is calculated by reducing the problem to the calculation of the determinants of `n` matrices of`n-1 x n-1` size.

For the 3x3 case, `[ [a, b, c], [d, e, f], [g, h, i] ]` or
```
|a b c|  
|d e f|  
|g h i|  
```
the determinant is: `a * det(a_minor) - b * det(b_minor) + c * det(c_minor)` where `det(a_minor)` refers to taking the determinant of the 2x2 matrix created by crossing out the row and column in which the element a occurs:
```
|- - -|
|- e f|
|- h i|  
```
Note the alternation of signs. 

The determinant of larger matrices are calculated analogously, e.g. if M is a 4x4 matrix with first row `[a, b, c, d]`, then:

`det(M) = a * det(a_minor) - b * det(b_minor) + c * det(c_minor) - d * det(d_minor)`

```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 = 'def sub_determinant(matrix, i):\n    sub_matrix = []\n    for j in range(1,len(matrix)):\n        sub_matrix.append(matrix[j][:i] + matrix[j][i+1:])\n    return sub_matrix\n    \ndef determinant(matrix):\n    if len(matrix) == 0:\n        return 0\n    elif len(matrix) == 1:\n        return matrix[0][0]\n    elif len(matrix) == 2:\n        return matrix[0][0] * matrix[1][1] - matrix[0][1]*matrix[1][0]\n    else:\n        sum = 0\n        for i in range(0,len(matrix)):\n            if 1 == i & 1:\n                sum = sum - matrix[0][i] * determinant(sub_determinant(matrix,i))\n            else:\n                sum = sum + matrix[0][i] * determinant(sub_determinant(matrix,i))\n        return sum\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'determinant'
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: 5806