Laura Bassi was the first female professor at a European university.  
Despite her immense intellect, she was not always allowed to lecture publicly.

One day a professor with very strong beliefs against women in academia sent some `agents` to find Bassi and end her career.

Help her escape by telling her the safest places in town!

Task

```if:python,javascript
Implement the function `advice(agents, n)` where
```
```if:haskell
Implement the function `advice agents n :: [(Int,Int)] -> Int -> [(Int,Int)]` where
```
```if:swift
Implement the function `advice(agents: [[Int]], n: Int) -> [[Int]]` where
```

- `agents` is an array of agent coordinates.
- `n` defines the size of the city that Bassi needs to hide in, in other words the side length of the square grid. 

The function should return a list of coordinates that are the furthest away (by Manhattan distance) from all agents.

As an example, say you have a 6x6 map, and agents at locations

```python
[(0, 0), (1, 5), (5, 1)]
```

The distances to the nearest agent look like this.



The safest spaces are the ones with distance `4`, marked in bright red. So the function should return

```python
[(2, 2), (3, 3), (4, 4), (5, 5)]
```

in any order.

Edge cases:
- If there is an agent on every grid cell, there is no safe space, so return an empty list.
- If there are no agents, then every cell is a safe spaces, so return all coordinates.
- if `n` is `0`, return an empty list.
- If agent coordinates are outside of the map, they are simply not considered.
- There are no duplicate agents on the same square.

Performance

All reference solutions run in around 6 seconds.
You might not pass the tests if you use a brute-force solution.

```if-not:swift,javascript
There are `200` random tests with `n <= 50`. Inefficient solutions might time out.
```
```if:javascript
There are `300` random tests with `n <= 70`. Inefficient solutions might time out.
```
```if:swift
There are `200` random tests with `n <= 70`. Inefficient solutions might time out.
```

This kata is inspired by ThoughtWorks' coding challenge

```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 advice(agents, n):\n    # Remove agents outside of bounds\n    agents = [(r, c) for r, c in agents if 0 <= r < n and 0 <= c < n]\n    \n    # Check for degenerate cases, no agents, or all positions filled\n    if n == 0 or len(set(agents)) == n * n:\n        return []\n    \n    # Place the agents in the field\n    field = [[0 for _ in range(n)] for _ in range(n)]\n    edges = []\n    for r, c in agents:\n        field[r][c] = 1\n        edges.append((r, c))\n    \n    # Flood fill the field in cardinal directions from each edge location that is unfilled\n    # Initial edge locations are the positions of the agents\n    # Default is all locations if we have no agents\n    previous_edges = [(r, c) for r in range(n) for c in range(n)]\n    while edges:\n        new_edges = []\n        for r, c in edges:\n            for dr, dc in [(0, 1), (1, 0), (0, -1), (-1, 0)]:\n                rr, cc = r + dr, c + dc\n                if 0 <= rr < n and 0 <= cc < n and field[rr][cc] == 0:\n                    field[rr][cc] = 1\n                    new_edges.append((rr, cc))\n        previous_edges, edges = edges, new_edges\n    \n    # Return the last round of unfilled positions\n    return previous_edges\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'advice'
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: 6872