With a friend we used to play the following game on a chessboard
(8, rows, 8 columns).
On the first row at the *bottom* we put numbers:

`1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9`

On row 2 (2nd row from the bottom) we have:

`1/3, 2/4, 3/5, 4/6, 5/7, 6/8, 7/9, 8/10`

On row 3:

`1/4, 2/5, 3/6, 4/7, 5/8, 6/9, 7/10, 8/11`

until last row:

`1/9, 2/10, 3/11, 4/12, 5/13, 6/14, 7/15, 8/16`


When all numbers are on the chessboard each in turn we toss a coin. The one who get "head" wins and
the other gives him, in dollars, the **sum of the numbers on the chessboard**.
We play for fun, the dollars come from a monopoly game! 

### Task
How much can I (or my friend) win or loses for each game if the chessboard has n rows and n columns? Add all of the fractional values on an n by n sized board and give the answer as a simplified fraction.
  
- Ruby, Python, JS, Coffee, Clojure, PHP, Elixir, Crystal, Typescript, Go:

The function called 'game' with parameter n (integer >= 0) returns as result an irreducible fraction written as an array of integers: [numerator, denominator].
If the denominator is 1 return [numerator].

- Haskell:

'game' returns either a "Left Integer" if denominator is 1 otherwise 
"Right (Integer, Integer)" 

- Prolog:
'game' returns an irreducible fraction written as an array of integers: [numerator, denominator].
If the denominator is 1 return [numerator, 1].

- Java, C#, C++, F#, Swift, Reason, Kotlin:

'game' returns a string that mimicks the array returned in Ruby, Python, JS, etc...

- Fortran, Bash: 'game' returns a string


- Forth: return on the stack the numerator and the denominator (even if the denominator is 1)


- In Fortran - as in any other language - the returned string is not permitted
to contain any redundant trailing whitespace: you can use dynamically allocated character strings.

#### See Example Test Cases for each language

```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 = "'''\n        n    t(i)     n-1  (n + i + 1) * (n - i)\ns(n) =  Σ   -----  +   Σ   ---------------------\n       i=1  i + 1     i=1     2 * (n + i + 1)\n\n        n    i      n-1   n - i\n     =  Σ   ---  +   Σ    -----\n       i=1   2      i=1     2\n\n        n    i      n-1    i\n     =  Σ   ---  +   Σ    ---\n       i=1   2      i=1    2\n\n         n      n-1\n     =  ---  +   Σ   i\n         2      i=1\n\n         n      n * (n - 1)\n     =  ---  +  -----------\n         2          2\n\n     =  n^2 / 2\n'''\n\ndef game(n):\n    return [n**2, 2] if n % 2 else [n**2 // 2]"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'game'
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: 5368