The chef has one array of N natural numbers (might be in sorted order). Cheffina challenges chef to find the total number of inversions in the array.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains two lines of input, $N$.
- N space-separated natural numbers. 

-----Output:-----
For each test case, output in a single line answer as the total number of inversions.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $1 \leq arr[i] \leq 10^5$

-----Sample Input:-----
1
5
5 4 1 3 2

-----Sample Output:-----
8

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "def merge(A, aux, low, mid, high):\r\n \r\n    k = i = low\r\n    j = mid + 1\r\n    inversionCount = 0\r\n \r\n    # While there are elements in the left and right runs\r\n    while i <= mid and j <= high:\r\n        if A[i] <= A[j]:\r\n            aux[k] = A[i]\r\n            i = i + 1\r\n        else:\r\n            aux[k] = A[j]\r\n            j = j + 1\r\n            inversionCount += (mid - i + 1)  # NOTE\r\n \r\n        k = k + 1\r\n \r\n    # Copy remaining elements\r\n    while i <= mid:\r\n        aux[k] = A[i]\r\n        k = k + 1\r\n        i = i + 1\r\n \r\n    # Don't need to copy second half\r\n \r\n    # copy back to the original list to reflect sorted order\r\n    for i in range(low, high + 1):\r\n        A[i] = aux[i]\r\n \r\n    return inversionCount\r\n \r\n \r\n# Sort list [low..high] using auxiliary space aux\r\ndef mergeSort(A, aux, low, high):\r\n \r\n    # Base case\r\n    if high == low:  # if run size == 1\r\n        return 0\r\n \r\n    # find mid point\r\n    mid = low + ((high - low) >> 1)\r\n    inversionCount = 0\r\n \r\n    # recursively split runs into two halves until run size == 1,\r\n    # then merge them and return back up the call chain\r\n \r\n    inversionCount += mergeSort(A, aux, low, mid)        # split / merge left half\r\n    inversionCount += mergeSort(A, aux, mid + 1, high)   # split / merge right half\r\n    inversionCount += merge(A, aux, low, mid, high)      # merge the two half runs\r\n \r\n    return inversionCount\r\n \r\nfor _ in range(int(input())):\r\n    n=int(input())\r\n    l=list(map(int,input().split()))\r\n    aux=l.copy()\r\n    print(mergeSort(l,aux,0,len(l)-1))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13383