In computer science and discrete mathematics, an [inversion](https://en.wikipedia.org/wiki/Inversion_%28discrete_mathematics%29) is a pair of places in a sequence where the elements in these places are out of their natural order. So, if we use ascending order for a group of numbers, then an inversion is when larger numbers appear before lower number in a sequence.

Check out this example sequence: ```(1, 2, 5, 3, 4, 7, 6)``` and we can see here three inversions
```5``` and ```3```; ```5``` and ```4```; ```7``` and ```6```.

You are given a sequence of numbers and you should count the number of inversions in this sequence.

```Input```: A sequence as a tuple of integers.

```Output```: The inversion number as an integer.

Example:
```python
  count_inversion((1, 2, 5, 3, 4, 7, 6)) == 3
  count_inversion((0, 1, 2, 3)) == 0
```

```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 merge(a, left_index, mid, right_index, aux):\n    i, j = left_index, mid + 1\n    inversions = 0\n\n    for k in range(left_index, right_index + 1):\n        aux[k] = a[k]\n\n    for k in range(left_index, right_index + 1):\n        if i > mid:\n            a[k] = aux[j]\n            j += 1\n        elif j > right_index:\n            a[k] = aux[i]\n            i += 1\n        elif aux[i] <= aux[j]:\n            a[k] = aux[i]\n            i += 1\n        elif aux[j] < aux[i]:\n            a[k] = aux[j]\n            j += 1\n\n            inversions += mid - i + 1\n    return inversions\n\ndef count(a, left_index, right_index, aux):\n    if right_index <= left_index:\n        return 0\n    mid = left_index + (right_index - left_index) // 2\n    left_inversions = count(a, left_index, mid, aux)\n    right_inversions = count(a, mid + 1, right_index, aux)\n    return left_inversions + right_inversions + merge(a, left_index, mid, right_index, aux)\n\ndef count_inversion(sequence):\n    if len(sequence) < 2:\n        return 0\n    aux = [None for _ in range(len(sequence))]\n    sequence_list = list(sequence)\n    return count(sequence_list, 0, len(sequence) - 1, aux)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'count_inversion'
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: 6466