### Preface
You are currently working together with a local community to build a school teaching children how to code. First plans have been made and the community wants to decide on the best location for the coding school.
In order to make this decision data about the location of students and potential locations is collected. 

### Problem
In order to be able to attract and teach as many students as possible we want to minimize the total traveling distance for potential students. The streets system is organized in a traditional grid system and students can only travel horizontally or vertically (not diagonal).

The locations of interested students is given as an array with the first value of each entry presenting the x coordinate and the second value presenting the y coordinate:
```python
students = [[3,7],[2,2],[14,1], ...];
```
Potential locations are passed as an array of objects with an unique id, a x and y coordinate:
```python
locations = [{"id": 1, "x": 3, "y": 4}, {"id": 2, "x": 8, "y": 2}, ...];
```

Your task is now to evaluate which of the school locations would be best to minimize the distance for all potential students to the school.

The desired output should consist of a string indicating the ID of the best suitable location and the x and y coordinates in the following form:

```
"The best location is number 1 with the coordinates x = 3 and y = 4"
```

```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 optimum_location(students, locations):\n    def total_distance(loc):\n        x_dist = sum(abs(loc[\'x\'] - x) for x, y in students)\n        y_dist = sum(abs(loc[\'y\'] - y) for x, y in students)\n        return x_dist + y_dist\n    best_loc = min(locations, key=total_distance)\n    template = "The best location is number {id} with the coordinates x = {x} and y = {y}"\n    return template.format(**best_loc)\n    \n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'optimum_location'
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: 6410