Calculate the trace of a square matrix. A square matrix has `n` rows and `n` columns, where `n` is any integer > 0. The entries of the matrix can contain any number of integers. The function should return the calculated trace of the matrix, or `nil/None` if the array is empty or not square; you can otherwise assume the input will be valid (of the form described below).

The trace of an n-by-n square matrix **A** is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of **A**.

A matrix will be defined as an array of arrays, where the 1st entry represents the 1st row, the 2nd entry the 2nd row, and so on.

For example, the following code...
```ruby,python
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
```
represents the matrix
```
|1 2 3|
|4 5 6|
|7 8 9|
```
which has a trace of `1 + 5 + 9 = 15`.

You can read more about the trace of a matrix at these sources:

 * http://en.wikipedia.org/wiki/Trace_(linear_algebra)
 * http://mathworld.wolfram.com/MatrixTrace.html

~~~if:ruby
Note: The `Matrix` class is disabled.
~~~
~~~if:python
Note: `Numpy` is disabled.
~~~

```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 trace(matrix):\n    if matrix and {len(matrix)} == {len(m) for m in matrix}:\n        return sum(matrix[i][i] for i in range(len(matrix)))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'trace'
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: 5726