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 = 'from sys import stdin, stdout\nfrom math import floor, gcd, fabs, factorial, fmod, sqrt, inf, log\nfrom collections import defaultdict as dd, deque\nfrom heapq import merge, heapify, heappop, heappush, nsmallest\nfrom bisect import bisect_left as bl, bisect_right as br, bisect\nmod = pow(10, 9) + 7\nmod2 = 998244353\ndef inp(): return stdin.readline().strip()\ndef out(var, end="\\n"): stdout.write(str(var)+"\\n")\ndef outa(*var, end="\\n"): stdout.write(\' \'.join(map(str, var)) + end)\ndef lmp(): return list(mp())\ndef mp(): return map(int, inp().split())\ndef smp(): return map(str, inp().split())\ndef l1d(n, val=0): return [val for i in range(n)]\ndef l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]\ndef remadd(x, y): return 1 if x%y else 0\ndef ceil(a,b): return (a+b-1)//b\n\ndef isprime(x):\n    if x<=1: return False\n    if x in (2, 3): return True\n    if x%2 == 0: return False\n    for i in range(3, int(sqrt(x))+1, 2):\n        if x%i == 0: return False\n    return True\n\ndef mergeSort(arr, n): \n    temp_arr = [0]*n \n    return _mergeSort(arr, temp_arr, 0, n-1) \n  \ndef _mergeSort(arr, temp_arr, left, right): \n    inv_count = 0\n    if left < right: \n        mid = (left + right)//2\n        inv_count += _mergeSort(arr, temp_arr,  \n                                    left, mid) \n        inv_count += _mergeSort(arr, temp_arr,  \n                                  mid + 1, right) \n        inv_count += merge(arr, temp_arr, left, mid, right) \n    return inv_count \n\ndef merge(arr, temp_arr, left, mid, right): \n    i = left    \n    j = mid + 1\n    k = left    \n    inv_count = 0\n    while i <= mid and j <= right: \n        if arr[i] <= arr[j]: \n            temp_arr[k] = arr[i] \n            k += 1\n            i += 1\n        else: \n            temp_arr[k] = arr[j] \n            inv_count += (mid-i + 1) \n            k += 1\n            j += 1\n    while i <= mid: \n        temp_arr[k] = arr[i] \n        k += 1\n        i += 1\n    while j <= right: \n        temp_arr[k] = arr[j] \n        k += 1\n        j += 1\n    for loop_var in range(left, right + 1): \n        arr[loop_var] = temp_arr[loop_var] \n    return inv_count     \n\nfor _ in range(int(inp())):\n    n = int(inp())\n    arr = lmp()\n    print(mergeSort(arr, n))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16321