human
What is a Python code to find the minimal possible number of inversions in the deque after the whole array is processed given the following:
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...
impor
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#Here is Python code to find the minimal possible number of inversions in the deque after the whole array is processed.
t sys
input = sys.stdin.readline

t=int(input())
for tests in range(t):
    n=int(input())
    A=list(map(int,input().split()))

    compression_dict={a: ind+2 for ind, a in enumerate(sorted(set(A)))}
    A=[compression_dict[a] for a in A]

    LEN=len(A)+10

    BIT=[0]*(LEN+1) # 1-indexedなtree. 配列BITの長さはLEN+1にしていることに注意。

    def update(v,w): # index vにwを加える
        while v<=LEN:
            BIT[v]+=w
            v+=(v&(-v)) # v&(-v)で、最も下の立っているビット. 自分を含む大きなノードへ. たとえばv=3→v=4

    def getvalue(v): # [1,v]の区間の和を求める
        ANS=0
        while v!=0:
            ANS+=BIT[v]
            v-=(v&(-v)) # 自分より小さい自分の和を構成するノードへ. たとえばv=14→v=12へ
        return ANS

    ALL=0
    ANS=0

    for a in A:
        x=getvalue(a-1)
        y=getvalue(a)

        z=ALL-y

        ANS+=min(x,z)
        update(a,1)
        ALL+=1

    print(ANS)