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 = 'from collections import deque\n\nINF = 1000000\n\nclass Field:\n    def __init__(self, n, agents):\n        self.n = n\n        self.agents = agents\n        self.table = [[INF] * n for _ in range(n)]\n        self._queue = deque()\n        self._calculate_safety()\n    \n    def _calculate_safety(self):\n        for i, j in self.agents:\n            if 0 <= i < self.n and 0 <= j < self.n:\n                self._add_to_queue(i, j, 0)\n        self._process_queue()\n                \n    def _add_to_queue(self, i, j, value):\n        self._queue.append((i, j, value))\n        \n    def _process_queue(self):\n        while self._queue:\n            i, j, value = self._queue.popleft()\n            if self.table[i][j] != INF:\n                continue\n            self.table[i][j] = value\n\n            if i < self.n - 1:\n                self._add_to_queue(i + 1, j, value + 1)\n                \n            if i > 0:\n                self._add_to_queue(i - 1, j, value + 1)\n                \n            if j < self.n - 1:\n                self._add_to_queue(i, j + 1, value + 1)\n                \n            if j > 0:\n                self._add_to_queue(i, j - 1, value + 1)\n      \n    @property\n    def safest_places(self):\n        locations = []\n        max_el = 1\n        for i in range(self.n):\n            for j in range(self.n):\n                if self.table[i][j] > max_el:\n                    max_el = self.table[i][j]\n                    locations = [(i, j)]\n                elif self.table[i][j] == max_el:\n                    locations.append((i, j))\n        return locations\n    \n\ndef advice(agents, n):\n    field = Field(n, agents)\n    return field.safest_places'
_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: 8264