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 = "# Python 3 program to count inversions in an array \n\n# Function to Use Inversion Count \ndef mergeSort(arr, n): \n\t# A temp_arr is created to store \n\t# sorted array in merge function \n\ttemp_arr = [0]*n \n\treturn _mergeSort(arr, temp_arr, 0, n-1) \n\n# This Function will use MergeSort to count inversions \n\ndef _mergeSort(arr, temp_arr, left, right): \n\n\t# A variable inv_count is used to store \n\t# inversion counts in each recursive call \n\n\tinv_count = 0\n\n\t# We will make a recursive call if and only if \n\t# we have more than one elements \n\n\tif left < right: \n\n\t\t# mid is calculated to divide the array into two subarrays \n\t\t# Floor division is must in case of python \n\n\t\tmid = (left + right)//2\n\n\t\t# It will calculate inversion \n\t\t# counts in the left subarray \n\n\t\tinv_count += _mergeSort(arr, temp_arr, \n\t\t\t\t\t\t\t\t\tleft, mid) \n\n\t\t# It will calculate inversion \n\t\t# counts in right subarray \n\n\t\tinv_count += _mergeSort(arr, temp_arr, \n\t\t\t\t\t\t\t\tmid + 1, right) \n\n\t\t# It will merge two subarrays in \n\t\t# a sorted subarray \n\n\t\tinv_count += merge(arr, temp_arr, left, mid, right) \n\treturn inv_count \n\n# This function will merge two subarrays \n# in a single sorted subarray \ndef merge(arr, temp_arr, left, mid, right): \n\ti = left\t # Starting index of left subarray \n\tj = mid + 1 # Starting index of right subarray \n\tk = left\t # Starting index of to be sorted subarray \n\tinv_count = 0\n\n\t# Conditions are checked to make sure that \n\t# i and j don't exceed their \n\t# subarray limits. \n\n\twhile i <= mid and j <= right: \n\n\t\t# There will be no inversion if arr[i] <= arr[j] \n\n\t\tif arr[i] <= arr[j]: \n\t\t\ttemp_arr[k] = arr[i] \n\t\t\tk += 1\n\t\t\ti += 1\n\t\telse: \n\t\t\t# Inversion will occur. \n\t\t\ttemp_arr[k] = arr[j] \n\t\t\tinv_count += (mid-i + 1) \n\t\t\tk += 1\n\t\t\tj += 1\n\n\t# Copy the remaining elements of left \n\t# subarray into temporary array \n\twhile i <= mid: \n\t\ttemp_arr[k] = arr[i] \n\t\tk += 1\n\t\ti += 1\n\n\t# Copy the remaining elements of right \n\t# subarray into temporary array \n\twhile j <= right: \n\t\ttemp_arr[k] = arr[j] \n\t\tk += 1\n\t\tj += 1\n\n\t# Copy the sorted subarray into Original array \n\tfor loop_var in range(left, right + 1): \n\t\tarr[loop_var] = temp_arr[loop_var] \n\t\t\n\treturn inv_count \n\nfor i in range(int(input())):\n    n=int(input())\n    arr=list(map(int,input().split()))\n    result = mergeSort(arr, n) \n    print( result) \n\n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13453