human
In fact, the problems E1 and E2 do not have much in common. You should probably think of them as two separate problems.

You are given an integer array a[1 … n] = [a_1, a_2, …, a_n].

Let us consider an empty [deque](https://tinyurl.com/pfeucbux) (double-ended queue). A deque is a data structure that supports adding elements to both the beginning and the end. So, if there are elements [3, 4, 4] currently in the deque, adding an element 1 to the beginning will produce the sequence [\color{red}{1}, 3, 4, 4], and adding the same element to the end will produce [3, 4, 4, \color{red}{1}].

The elements of the array are sequentially added to the initially empty deque, starting with a_1 and finishing with a_n. Before adding each element to the deque, you may choose whether to add it to the beginning or to the end.

For example, if we consider an array a = [3, 7, 5, 5], one of the possible sequences of actions looks like this:    1. |  add 3 to the beginning of the deque: |  deque has a sequence [\color{red}{3}] in it.
  
---|---|---  
  2. |  add 7 to the end of the deque: |  deque has a sequence [3, \color{red}{7}] in it.
  
  3. |  add 5 to the end of the deque: |  deque has a sequence [3, 7, \color{red}{5}] in it.
  
  4. |  add 5 to the beginning of the deque: |  deque has a sequence [\color{red}{5}, 3, 7, 5] in it.
  
  
Find the minimal possible number of inversions in the deque after the whole array is processed. 

An inversion in sequence d is a pair of indices (i, j) such that i < j and d_i > d_j. For example, the array d = [5, 3, 7, 5] has exactly two inversions — (1, 2) and (3, 4), since d_1 = 5 > 3 = d_2 and d_3 = 7 > 5 = d_4.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain descriptions of the test cases. 

The first line of each test case description contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — array size. The second line of the description contains n space-separated integers a_i (-10^9 ≤ a_i ≤ 10^9) — elements of the array.

It is...
Using python3 can you solve the prior task?
 ... What is a Python code to find the minimal possible number of inversions in the deque after the whole array is processed?
assistant
#Here is Python code to find the minimal possible number of inversions in the deque after the whole array is processed.

import sys
readline = sys.stdin.readline

class FenwickTree: # (BinaryIndexedTree)
  def __init__(self, n):
    self.size = n
    self.tree = [0] * (n + 1)
 
  def sum(self, i):
    out = 0
    while i > 0:
      out += self.tree[i]
      i -= (i & -i)
    return out
 
  def add(self, i, x):
    while i <= self.size:
      self.tree[i] += x
      i += (i & -i)

T = int(readline())

for t in range(T):
  N = int(readline())
  A = list(map(int,readline().split()))
  za = sorted(list(set(A)))
  n = len(za)
  dic = {}
  for i, z in enumerate(za):
    dic[z] = i
  for i in range(len(A)):
    A[i] = dic[A[i]] + 1
  
  BIT = FenwickTree(n + 1)
  ans = 0
  for a in A:
    small = BIT.sum(a - 1)
    large = BIT.sum(n + 1) - BIT.sum(a)
    if small < large:
      ans += small
    else:
      ans += large
    BIT.add(a, 1)
  print(ans)