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 = "# Function to Use Inversion Count \r\ndef mergeSort(arr, n):\r\n    # A temp_arr is created to store \r\n    # sorted array in merge function \r\n    temp_arr = [0] * n\r\n    return _mergeSort(arr, temp_arr, 0, n - 1)\r\n\r\n\r\n# This Function will use MergeSort to count inversions \r\n\r\ndef _mergeSort(arr, temp_arr, left, right):\r\n    # A variable inv_count is used to store \r\n    # inversion counts in each recursive call \r\n\r\n    inv_count = 0\r\n\r\n    # We will make a recursive call if and only if \r\n    # we have more than one elements \r\n\r\n    if left < right:\r\n        # mid is calculated to divide the array into two subarrays \r\n        # Floor division is must in case of python \r\n\r\n        mid = (left + right) // 2\r\n\r\n        # It will calculate inversion  \r\n        # counts in the left subarray \r\n\r\n        inv_count += _mergeSort(arr, temp_arr,\r\n                                left, mid)\r\n\r\n        # It will calculate inversion  \r\n        # counts in right subarray \r\n\r\n        inv_count += _mergeSort(arr, temp_arr,\r\n                                mid + 1, right)\r\n\r\n        # It will merge two subarrays in  \r\n        # a sorted subarray \r\n\r\n        inv_count += merge(arr, temp_arr, left, mid, right)\r\n    return inv_count\r\n\r\n\r\n# This function will merge two subarrays  \r\n# in a single sorted subarray \r\ndef merge(arr, temp_arr, left, mid, right):\r\n    i = left  # Starting index of left subarray \r\n    j = mid + 1  # Starting index of right subarray \r\n    k = left  # Starting index of to be sorted subarray \r\n    inv_count = 0\r\n\r\n    # Conditions are checked to make sure that  \r\n    # i and j don't exceed their \r\n    # subarray limits. \r\n\r\n    while i <= mid and j <= right:\r\n\r\n        # There will be no inversion if arr[i] <= arr[j] \r\n\r\n        if arr[i] <= arr[j]:\r\n            temp_arr[k] = arr[i]\r\n            k += 1\r\n            i += 1\r\n        else:\r\n            # Inversion will occur. \r\n            temp_arr[k] = arr[j]\r\n            inv_count += (mid - i + 1)\r\n            k += 1\r\n            j += 1\r\n\r\n    # Copy the remaining elements of left  \r\n    # subarray into temporary array \r\n    while i <= mid:\r\n        temp_arr[k] = arr[i]\r\n        k += 1\r\n        i += 1\r\n\r\n    # Copy the remaining elements of right  \r\n    # subarray into temporary array \r\n    while j <= right:\r\n        temp_arr[k] = arr[j]\r\n        k += 1\r\n        j += 1\r\n\r\n    # Copy the sorted subarray into Original array \r\n    for loop_var in range(left, right + 1):\r\n        arr[loop_var] = temp_arr[loop_var]\r\n\r\n    return inv_count\r\n\r\nfor _ in range(int(input())):\r\n    n=int(input())\r\n    arr = list(map(int,input().split()))\r\n    print(mergeSort(arr, n))\r\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13449