description: 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 guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
  
  Output
  
  Print t lines, each line containing the answer to the corresponding test case. The answer to a test case should be a single integer — the minimal possible number of inversions in the deque after executing the described algorithm.
  
  Example
  
  Input
  
  
  6
  4
  3 7 5 5
  3
  3 2 1
  3
  3 1 2
  4
  -1 2 2 -1
  4
  4 5 1 3
  5
  1 3 1 3 2
  
  
  Output
  
  
  2
  0
  1
  0
  1
  2
  
  Note
  
  One of the ways to get the sequence [5, 3, 7, 5] in the deque, containing only two inversions, from the initial array [3, 7, 5, 5] (the first sample test case) is described in the problem statement. 
  
  Also, in this example, you could get the answer of two inversions by simply putting each element of the original array at the end of the deque. In this case, the original sequence [3, 7, 5, 5], also containing exactly two inversions, will be in the deque as-is.
solution: import java.io.*;
  import java.util.*;
  
  
  
  import java.math.*;
  import java.math.BigInteger;
  
  
  public final class A
  {    
  	static PrintWriter out = new PrintWriter(System.out); 
  	static StringBuilder ans=new StringBuilder();
  	static FastReader in=new FastReader();
  	static ArrayList<Integer> g[];
  	static long mod=(long)1e9+7,INF=Long.MAX_VALUE;
  	static boolean set[],col[]; 
  	static int par[],tot[],partial[];
  	static int Days[],P[][];
  	static int dp[][],sum=0,size[];
  	static ArrayList<Long> seg[];
  	static ArrayList<Long> A;
  	//	static HashSet<Integer> set;
  //		static node1 seg[];
  	//static pair moves[]= {new pair(-1,0),new pair(1,0), new pair(0,-1), new pair(0,1)};
  	public static void main(String args[])throws IOException
  	{		
  		int T=i();
  		outer:while(T-->0)
  		{
  			int N=i();
  			seg=new ArrayList[4*N+5];
  			for(int i=0; i<4*N+5; i++)seg[i]=new ArrayList<Long>();
  			
  			long A[]=inputLong(N);
  			build(1,0,N-1,A);
  			ArrayList<Long> X=new ArrayList<>();
  			X.add(A[0]);
  			long min=0;
  			HashMap<Long,Integer> mp=new HashMap<>();
  			mp.put(A[0], 1);
  			for(int i=1; i<N; i++)
  			{
  				int index=ask(1,0,N-1,0,i-1,A[i]);
  				int right=i-index;
  				int f=mp.getOrDefault(A[i],0);
  				index-=f;
  				mp.put(A[i], f+1);
  				min+=Math.min(index, right);
  			}
  			ans.append(min+"\n");
  		}
  		out.println(ans);
  		out.close();
  	}
  	static int ask(int v,int tl,int tr,int l,int r,long x)
  	{
  		if(l>r)return 0;
  		if(tl==l && tr==r)
  		{
  			return f(seg[v],x)+1;
  		}
  		int tm=(tl+tr)/2;
  		return ask(v*2,tl,tm,l,Math.min(tm, r),x)+ask(v*2+1,tm+1,tr,Math.max(tm+1,l),r,x);
  	}
  	static void build(int v,int tl,int tr,long A[])
  	{
  		if(tl==tr)
  		{
  			seg[v].add(A[tl]);
  			return;
  		}
  		int tm=(tl+tr)/2;
  		build(v*2,tl,tm,A);
  		build(v*2+1,tm+1,tr,A);
  		merge(v);
  		//System.out.println(seg[v]);
  	}
  	static void merge(int v)
  	{
  		int i=0,j=0;
  		while(i<seg[v*2].size() && j<seg[v*2+1].size())
  		{
  			if(seg[v*2].get(i)<seg[v*2+1].get(j))
  			seg[v].add(seg[v*2].get(i++));
  			else seg[v].add(seg[v*2+1].get(j++));
  		}
  		while(i<seg[v*2].size())
  		{
  			
  			seg[v].add(seg[v*2].get(i++));
  			
  		}
  		while( j<seg[v*2+1].size())
  		{
  			
  			 seg[v].add(seg[v*2+1].get(j++));
  		}
  	}
  	static int f(ArrayList<Long> X,long x)
  	{
  		int l=-1,r=X.size();
  		while(r-l>1)
  		{
  			int m=(l+r)/2;
  			long a=X.get(m);
  			if(a<=x)l=m;
  			else r=m;
  		}
  		return l;
  	}
  	static int f(char X[][],int i,int j,int N,int M)
  	{
  		int c1=0,c2=0;
  		int x=i,y=j;
  		while(i>=0 && j>=0 && X[i][j]=='*')
  		{
  			c1++;
  			i--;
  			j--;
  		}
  		i=x;
  		j=y;
  		while(i>=0 && j<M && X[i][j]=='*')
  		{
  			c2++;
  			i--;
  			j++;
  		}	
  		return Math.min(c1,c2)-1;
  	}
  	static void update(char X[][],int min[][],int i,int j,int N,int M,int d)
  	{
  		int x=i,y=j;
  		while(i>=0 && j>=0 && X[i][j]=='*')
  		{
  			min[i][j]=Math.max(min[i][j],d);
  			i--;
  			j--;
  		}
  		i=x;
  		j=y;
  		while(i>=0 && j<M && X[i][j]=='*')
  		{
  			min[i][j]=Math.max(min[i][j],d);
  			i--;
  			j++;
  		}	
  	}
  
  	static long and(int i,int j)
  	{
  		System.out.println("and "+i+" "+j);
  		return l();
  	}
  	static long or(int i,int j)
  	{
  		System.out.println("or "+i+" "+j);
  		return l();
  	}
  	static boolean is_Sorted(int A[])
  	{
  		int N=A.length;
  		for(int i=1; i<=N; i++)if(A[i-1]!=i)return false;
  		return true;
  	}
  	static boolean f(StringBuilder sb,String Y,String order)
  	{
  		StringBuilder res=new StringBuilder(sb.toString());
  		HashSet<Character> set=new HashSet<>();
  		for(char ch:order.toCharArray())
  		{
  			set.add(ch);
  			for(int i=0; i<sb.length(); i++)
  			{
  				char x=sb.charAt(i);
  				if(set.contains(x))continue;
  				res.append(x);
  			}
  		}
  
  		String str=res.toString();
  		return str.equals(Y);
  	}
  	static boolean all_Zero(int f[])
  	{
  		for(int a:f)if(a!=0)return false;
  		return true;
  	}
  	static long form(int a,int l)
  	{
  		long x=0;
  		while(l-->0)
  		{
  			x*=10;
  			x+=a;
  		}
  		return x;
  	}
  	static int count(String X)
  	{
  		HashSet<Integer> set=new HashSet<>();
  		for(char x:X.toCharArray())set.add(x-'0');
  		return set.size();
  	}
  
  
  	//	static void build(int v,int tl,int tr,long A[])
  	//	{
  	//		if(tl==tr)
  	//		{
  	//			seg[v]=A[tl];
  	//		}
  	//		else
  	//		{
  	//			int tm=(tl+tr)/2;
  	//			build(v*2,tl,tm,A);
  	//			build(v*2+1,tm+1,tr,A);
  	//			seg[v]=Math.min(seg[v*2], seg[v*2+1]);
  	//		}
  	//	}
  	
  	static int [] sub(int A[],int B[])
  	{
  		int N=A.length;
  		int f[]=new int[N];
  		for(int i=N-1; i>=0; i--)
  		{
  			if(B[i]<A[i])
  			{
  				B[i]+=26;
  				B[i-1]-=1;
  			}
  			f[i]=B[i]-A[i];
  		}
  		for(int i=0; i<N; i++)
  		{
  			if(f[i]%2!=0)f[i+1]+=26;
  			f[i]/=2;
  		}
  		return f;
  	}
  
  
  
  
  
  	static int max(int a ,int b,int c,int d)
  	{
  		a=Math.max(a, b);
  		c=Math.max(c,d);
  		return Math.max(a, c);
  	}
  	static int min(int a ,int b,int c,int d)
  	{
  		a=Math.min(a, b);
  		c=Math.min(c,d);
  		return Math.min(a, c);
  	}
  
  
  
  	static HashMap<Integer,Integer> Hash(int A[])
  	{
  		HashMap<Integer,Integer> mp=new HashMap<>();
  		for(int a:A)
  		{
  			int f=mp.getOrDefault(a,0)+1;
  			mp.put(a, f);
  		}
  		return mp;
  	}
  	static long mul(long a, long b)
  	{
  		return ( a %mod * 1L * b%mod )%mod;
  	}
  	static void swap(int A[],int a,int b)
  	{
  		int t=A[a];
  		A[a]=A[b];
  		A[b]=t;
  	}
  
  
  	static int find(int a)
  	{
  		if(par[a]<0)return a;
  		return par[a]=find(par[a]);
  	}
  	static void union(int a,int b)
  	{
  		a=find(a);
  		b=find(b);
  		if(a!=b)
  		{
  			par[a]+=par[b];
  			par[b]=a;
  		}
  	}
  	static boolean isSorted(int A[])
  	{
  		for(int i=1; i<A.length; i++)
  		{
  			if(A[i]<A[i-1])return false;
  		}
  		return true;
  	}
  
  	static boolean isDivisible(StringBuilder X,int i,long num)
  	{
  		long r=0;
  		for(; i<X.length(); i++)
  		{
  			r=r*10+(X.charAt(i)-'0');
  			r=r%num;
  		}
  		return r==0;
  	}    
  
  
  
  	static int lower_Bound(int A[],int low,int high, int x) 
  	{ 
  		if (low > high) 
  			if (x >= A[high]) 
  				return A[high]; 
  
  		int mid = (low + high) / 2; 
  
  		if (A[mid] == x) 
  			return A[mid]; 
  
  		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
  			return A[mid - 1]; 
  
  		if (x < A[mid]) 
  			return lower_Bound( A, low, mid - 1, x); 
  
  		return lower_Bound(A, mid + 1, high, x); 
  	} 
  
  	static String f(String A)
  	{
  		String X="";
  		for(int i=A.length()-1; i>=0; i--)
  		{
  			int c=A.charAt(i)-'0';
  			X+=(c+1)%2;
  		}
  		return X;
  	}
  
  	static void sort(long[] a) //check for long
  	{
  		ArrayList<Long> l=new ArrayList<>();
  		for (long i:a) l.add(i);
  		Collections.sort(l);
  		for (int i=0; i<a.length; i++) a[i]=l.get(i);
  	}
  
  	static String swap(String X,int i,int j)
  	{
  		char ch[]=X.toCharArray();
  		char a=ch[i];
  		ch[i]=ch[j];
  		ch[j]=a;
  		return new String(ch);
  	}
  
  	static int sD(long n)  
  	{  
  
  		if (n % 2 == 0 )  
  			return 2;  
  
  		for (int i = 3; i * i <= n; i += 2) {  
  			if (n % i == 0 )  
  				return i;  
  		}  
  
  		return (int)n;  
  	}  
  
  	static void setGraph(int N)
  	{
  		tot=new int[N+1];
  		partial=new int[N+1];
  		Days=new int[N+1];
  		P=new int[N+1][(int)(Math.log(N)+10)];
  		set=new boolean[N+1];
  		g=new ArrayList[N+1];
  		for(int i=0; i<=N; i++)
  		{
  
  			g[i]=new ArrayList<>();		
  			Days[i]=-1;
  			//D2[i]=INF;
  		}
  	}
  
  
  
  	static  long pow(long a,long b)
  	{
  		//long mod=1000000007;
  		long pow=1;
  		long x=a;
  		while(b!=0)
  		{
  			if((b&1)!=0)pow=(pow*x)%mod;
  			x=(x*x)%mod;
  			b/=2;
  		}
  		return pow;
  	}
  
  	static long toggleBits(long x)//one's complement || Toggle bits
  	{
  		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;
  
  		return ((1<<n)-1)^x;
  	}
  
  	static int countBits(long a)
  	{
  		return (int)(Math.log(a)/Math.log(2)+1);
  	}
  
  	static long fact(long N)
  	{ 
  		long n=2; 
  		if(N<=1)return 1;
  		else
  		{
  			for(int i=3; i<=N; i++)n=(n*i)%mod;
  		}
  		return n;
  	}
  
  	static int kadane(int A[])
  	{
  		int lsum=A[0],gsum=A[0];
  		for(int i=1; i<A.length; i++)
  		{
  			lsum=Math.max(lsum+A[i],A[i]);
  			gsum=Math.max(gsum,lsum);
  		}
  		return gsum;
  	}
  
  	static void sort(int[] a) {
  		ArrayList<Integer> l=new ArrayList<>();
  		for (int i:a) l.add(i);
  		Collections.sort(l);
  		for (int i=0; i<a.length; i++) a[i]=l.get(i);
  	}
  
  	static boolean isPrime(long N)
  	{
  		if (N<=1)  return false; 
  		if (N<=3)  return true; 
  		if (N%2 == 0 || N%3 == 0) return false; 
  		for (int i=5; i*i<=N; i=i+6) 
  			if (N%i == 0 || N%(i+2) == 0) 
  				return false; 
  		return true; 
  	}
  	static void print(char A[])
  	{
  		for(char c:A)System.out.print(c+" ");
  		System.out.println();
  	}
  	static void print(boolean A[])
  	{
  		for(boolean c:A)System.out.print(c+" ");
  		System.out.println();
  	}
  	static void print(int A[])
  	{
  		for(int a:A)System.out.print(a+" ");
  		System.out.println();	
  	}
  	static void print(long A[])
  	{
  		for(long i:A)System.out.print(i+ " ");
  		System.out.println();
  
  	}
  	static void print(boolean A[][])
  	{
  		for(boolean a[]:A)print(a);
  	}
  	static void print(long A[][])
  	{
  		for(long a[]:A)print(a);
  	}
  	static void print(int A[][])
  	{
  		for(int a[]:A)print(a);
  	}
  	static void print(ArrayList<Integer> A)
  	{
  		for(int a:A)System.out.print(a+" ");
  		System.out.println();
  	}
  
  	static int i()
  	{
  		return in.nextInt();
  	}
  
  	static long l()
  	{
  		return in.nextLong();
  	}
  
  	static int[] input(int N){
  		int A[]=new int[N];
  		for(int i=0; i<N; i++)
  		{
  			A[i]=in.nextInt();
  		}
  		return A;
  	}
  
  	static long[] inputLong(int N)     {
  		long A[]=new long[N];
  		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
  		return A;
  	}
  
  	static long GCD(long a,long b) 
  	{
  		if(b==0)
  		{
  			return a;
  		}
  		else return GCD(b,a%b );
  	}
  
  }
  class Pair23 implements Comparable<Pair23>
  {
  	int a,i;
  	Pair23(int a,int f)
  	{
  		this.i=f;
  		this.a=a;
  	}
  	public int compareTo(Pair23 X)
  	{
  		return X.a-this.a;
  	}
  }
  
  
  //Code For FastReader
  //Code For FastReader
  //Code For FastReader
  //Code For FastReader
  class FastReader
  {
  	BufferedReader br;
  	StringTokenizer st;
  	public FastReader()
  	{
  		br=new BufferedReader(new InputStreamReader(System.in));
  	}
  
  	String next()
  	{
  		while(st==null || !st.hasMoreElements())
  		{
  			try
  			{
  				st=new StringTokenizer(br.readLine());
  			}
  			catch(IOException e)
  			{
  				e.printStackTrace();
  			}
  		}
  		return st.nextToken();
  	}
  
  	int nextInt()
  	{
  		return Integer.parseInt(next());
  	}
  
  	long nextLong()
  	{
  		return Long.parseLong(next());
  	}
  
  	double nextDouble()
  	{
  		return Double.parseDouble(next());
  	}
  
  	String nextLine()
  	{
  		String str="";
  		try
  		{
  			str=br.readLine();
  		}
  		catch (IOException e)
  		{
  			e.printStackTrace();
  		}
  		return str;
  	}
  
  }