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...
#!/us Give me a Python program to find the minimal possible number of inversions in the deque after the whole array is processed?
assistant
#Here is Python program to find the minimal possible number of inversions in the deque after the whole array is processed.
r/bin/env python3
# from typing import *

import sys
import io
import math
import collections
import decimal
import itertools
import bisect
import heapq

def input():
    return sys.stdin.readline()[:-1]

# sys.setrecursionlimit(1000000)

# _INPUT = """# paste here...
# """
# sys.stdin = io.StringIO(_INPUT)

INF = 10**10

class BIT:
    def __init__(self, n):
        self.size = n
        self.data = [0] * (n+1)
        # self.depth = n.bit_length()
    def add(self, i, x):
        while i <= self.size:
            self.data[i] += x
            i += i & -i
    def get_sum(self, i):
        s = 0
        while i > 0:
            s += self.data[i]
            i -= i & -i
        return s
    def get_rsum(self, l, r):
        """
        [l, r] の sum
        """
        return self.get_sum(r) - self.get_sum(l-1)

def solve(N, A):
    D = {a: i for i, a in enumerate(sorted(set(A)))}
    B = [D[a]+1 for a in A]

    bit = BIT(N+1)

    q = collections.deque()
    rev = 0
    for i in range(N):
        b = B[i]
        if i == 0:
            bit.add(b, 1)
        else:
            r_left = bit.get_rsum(b+1, N+1)
            r_right = 0
            if b > 0:
                r_right = bit.get_sum(b-1)
            
            rev += min(r_left, r_right)
            bit.add(b, 1)

    return rev

T0 = int(input())
for _ in range(T0):
    N = int(input())
    A = list(map(int, input().split()))
    print(solve(N, A))