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.

import java.util.*;
import java.util.concurrent.CompletableFuture;

import javax.swing.text.Segment;

import java.io.*;
import java.math.*;
import java.sql.Array;



public class Main {
	  static class Reader{
		  
			BufferedReader br;
			StringTokenizer st;
			public Reader() {
				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; 
		    } 
		}
	 
	  static long mod = (long)(1e9 + 7);
	 
	static void sort(long[] arr ) {
		 ArrayList<Long> al = new ArrayList<>();
		 for(long e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(int[] arr ) {
		 ArrayList<Integer> al = new ArrayList<>();
		 for(int e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(char[] arr) {
		ArrayList<Character> al = new ArrayList<Character>();
		for(char cc:arr) al.add(cc);
		Collections.sort(al);
		for(int i = 0 ;i<arr.length ;i++) arr[i] = al.get(i);
	}
	static void rvrs(int[] arr) {
		int i =0 , j = arr.length-1;
		while(i>=j) {
			int temp = arr[i];
			arr[i] = arr[j];
			arr[j] = temp;
			i++;
			j--;
		}
	}
	static void rvrs(long[] arr) {
		int i =0 , j = arr.length-1;
		while(i>=j) {
			long temp = arr[i];
			arr[i] = arr[j];
			arr[j] = temp;
			i++;
			j--;
		}
	}

	static long mod_mul(long a , long b ,long mod) {
		return ((a%mod)*(b%mod))%mod;
	}
	 static long gcd(long a, long b)
	  {      
	     if (b == 0)
	        return a;
	     return gcd(b, a % b); 
	  }
	 static boolean[] prime(int num) {
			boolean[] bool = new boolean[num];
		     
		      for (int i = 0; i< bool.length; i++) {
		         bool[i] = true;
		      }
		      for (int i = 2; i< Math.sqrt(num); i++) {
		         if(bool[i] == true) {
		            for(int j = (i*i); j<num; j = j+i) {
		               bool[j] = false;
		            }
		         }
		      }
		      if(num >= 0) {
		    	  bool[0] = false;
		    	  bool[1] = false;
		      }
		      
		      return bool;
		}

	 static long modInverse(long a, long m)
	    {
	        long g = gcd(a, m);
	       
	          return   power(a, m - 2, m);
	        
	    }
	   
	 static long power(long x, long y, long m){
	        if (y == 0) return 1; long p = power(x, y / 2, m) % m; p = (int)((p * (long)p) % m);
	        if (y % 2 == 0) return p; else return (int)((x * (long)p) % m); }
	   
     static class Combinations{
	    	 private long[] z;
	    	 private long[] z1;
	    	 private long[] z2;
	    	  public Combinations(long N , long mod) {
				z = new long[(int)N+1];
				z1 = new long[(int)N+1];
				z[0] = 1;
				for(int i =1 ; i<=N ; i++) z[i] = (z[i-1]*i)%mod;
			     z2 = new long[(int)N+1];
				z2[0] = z2[1] = 1;
			    for (int i = 2; i <= N; i++)
			        z2[i] = z2[(int)(mod % i)] * (mod - mod / i) % mod;
			    
			    
			    z1[0] = z1[1] = 1;
			    
			    for (int i = 2; i <= N; i++)
			        z1[i] = (z2[i] * z1[i - 1]) % mod;
			}
	    	  long fac(long n) {
	    		  return z[(int)n];
	    	  }
	    	  long invrsNum(long n) {
	    		  return z2[(int)n];
	    	  }
	    	  long invrsFac(long n) {
	    		  return invrsFac((int)n);
	    	  }
	    	  long ncr(long N, long R, long mod)
	    	  {		if(R<0 || R>N ) return 0;
	    		    long ans = ((z[(int)N] * z1[(int)R])
	    		              % mod * z1[(int)(N - R)])
	    		             % mod;
	    		    return ans;
	    		}
	      }
	      static class DisjointUnionSets {
			    int[] rank, parent;
			    int n;
			  
			    public DisjointUnionSets(int n)
			    {
			        rank = new int[n];
			        parent = new int[n];
			        this.n = n;
			        makeSet();
			    }
			  
			    void makeSet()
			    {
			        for (int i = 0; i < n; i++) {
			          
			            parent[i] = i;
			        }
			    }
			  
			    int find(int x)
			    {
			        if (parent[x] != x) {
			        
			            parent[x] = find(parent[x]);
			  
			        }
			  
			        return parent[x];
			    }
			  
			    void union(int x, int y)
			    {
			        int xRoot = find(x), yRoot = find(y);
			  
			        if (xRoot == yRoot)
			            return;
			  
			        if (rank[xRoot] < rank[yRoot])
			  
			            parent[xRoot] = yRoot;
			  
			        else if (rank[yRoot] < rank[xRoot])
			  
			            parent[yRoot] = xRoot;
			  
			        else
			        {
			            parent[yRoot] = xRoot;
			  
			            rank[xRoot] = rank[xRoot] + 1;
			        }
			    }
			}
	      static int[] KMP(String str) {
	    	  int n = str.length();
	    	  int[] kmp = new int[n];
	    	  for(int i = 1 ; i<n ; i++) {
	    		  int j = kmp[i-1];
	    		  while(j>0 && str.charAt(i) != str.charAt(j)) {
	    			  j = kmp[j-1];
	    		  }
	    		  if(str.charAt(i) == str.charAt(j)) j++;
	    		  kmp[i] = j;
	    	  }
	    	  
	    	  return kmp;
	      }
	      
	      
/************************************************ Query **************************************************************************************/	  
	 
/***************************************** 		Sparse Table	********************************************************/
	      static class SparseTable{
	    		
	    		private long[][] st;
	    		
	    		SparseTable(long[] arr){
	    			int n = arr.length;
	    			st = new long[n][25];
	    			log = new int[n+2];
	    			build_log(n+1);
	    			build(arr);
	    		}
	    		
	    		private void build(long[] arr) {
	    			int n = arr.length;
	    			
	    			for(int i = n-1 ; i>=0 ; i--) {
	    				for(int j = 0 ; j<25 ; j++) {
	    					int r = i + (1<<j)-1;
	    					if(r>=n) break;
	    					if(j == 0 ) st[i][j] = arr[i];
	    					else st[i][j] = Math.min(st[i][j-1] , st[ i + ( 1 << (j-1) ) ][ j-1 ] );
	    				}
	    			}
	    		}
	    		public long gcd(long a  ,long b) {
	    			if(a == 0) return b;
	    			return gcd(b%a , a);
	    		}
	    		public long query(int l ,int r) {
	    			int w = r-l+1;
	    			int power = log[w];
	    			return Math.min(st[l][power],st[r - (1<<power) + 1][power]);
	    		}
	    		private int[] log;
	    		void build_log(int n) {
	    			log[1] = 0;
	    			for(int i = 2 ; i<=n ; i++) {
	    				log[i] = 1 + log[i/2];
	    			}
	    		}
	    	}
	      
	      
/********************************************************	Segement Tree	*****************************************************/
/**
	 	 static class SegmentTree{
			 long[] tree;
			 long[] arr;
			 int n;
			 SegmentTree(long[] arr){
				 this.n = arr.length;
				 tree = new long[4*n+1];
				 this.arr = arr;
				 buildTree(0, n-1, 1);
			 }
			 
			 
			  void buildTree(int s ,int e  ,int index ) {
					if(s == e) {
						tree[index] = arr[s];
						return;
					}
				
					int mid = (s+e)/2;
					
					buildTree( s,  mid, 2*index);
					buildTree( mid+1, e, 2*index+1);
					
					tree[index] = Math.min(tree[2*index] , tree[2*index+1]);
				}
			  
			 long query(int si ,int ei) {
				 return query(0 ,n-1 , si ,ei , 1   );
			 }
			 private long query( int ss ,int se ,int qs , int qe,int index) {
					
					if(ss>=qs && se<=qe) return tree[index];
					
					if(qe<ss || se<qs) return (long)(1e17);
					
					int mid = (ss + se)/2;
					long left = query( ss , mid , qs ,qe , 2*index);
					long right= query(mid + 1 , se , qs ,qe , 2*index+1);
					return Math.min(left, right);
				}
			 public void update(int index , int val) {
				 arr[index] = val;
				 for(long e:arr) System.out.print(e+" ");
				 update(index , 0 , n-1 , 1);
			 }
			 private void update(int id ,int si , int ei , int index) {
				 if(id < si || id>ei) return;
				 if(si == ei ) { 
					 tree[index] = arr[id];
					 return;
				 }
				 if(si > ei) return;
				 int mid = (ei + si)/2;
					
					update( id,  si, mid , 2*index);
					update( id , mid+1, ei , 2*index+1);
					
					tree[index] = Math.min(tree[2*index] ,tree[2*index+1]);
			 }
			  
		 }
		 */

/* ***************************************************************************************************************************************************/	 
	 
	      static Reader sc = new Reader();
	 static StringBuilder sb = new StringBuilder();
	 public static void main(String args[]) throws IOException {
	
		 int tc = 1;
		  tc = sc.nextInt();

		 for(int i = 1 ; i<=tc ; i++) {

//			 sb.append("Case #" + i + ": "  );	// During KickStart && HackerCup
			 TEST_CASE();
			 
		 }
		 System.out.println(sb);
//		 System.out.println();
	 }
//	 1
//	 5
//	 2 2 2 1 3
	static void TEST_CASE() {
		int n = sc.nextInt();
		int[] arr = new int[n];
		for(int i =0 ; i<n ; i++) arr[i] = sc.nextInt();
		MyTreeSetLong tree = new MyTreeSetLong(true);
		long ans = 0;
		Map<Integer , Long> map  = new HashMap<>();
		for(int e:arr) {
			if(map.containsKey(e)) map.put(e, map.get(e)+1);
			else map.put(e, 1l);
			tree.add(e);
			long c1 = tree.size() - tree.countFloorNodeLongs(e);
			long c2 = tree.size() - c1 - map.get(e);
			ans += Math.min(c1, c2);
		}
		System.out.println(ans);		
	}
}

  class NodeLong {
    NodeLong parent;
    NodeLong left;
    NodeLong right;
    long value;
    int size;
    int height;

    NodeLong(long v) {
        value = v;
        size = height = 1;
    }

    NodeLong finalisePosition(NodeLong root) {
        int lheight = findDepth(left), rheight = findDepth(right);

        if (lheight > rheight + 1) {
            if (findDepth(left.right) > findDepth(left.left))
                root = left.rotateLeft(root);
            root = rotateRight(root);
        } else if (lheight + 1 < rheight) {
            if (findDepth(right.left) > findDepth(right.right))
                root = right.rotateRight(root);
            root = rotateLeft(root);
        } else {
            setParameters();
        }

        return root;
    }

    NodeLong rotateRight(NodeLong root) {
        NodeLong A = this, B = left, P = parent;

        if (P != null) {
            if (P.left == this) P.left = B;
            else if (P.right == this) P.right = B;
            else System.exit(7 / 0);
        } else root = B;
        B.parent = A.parent;

        A.left = B.right;
        if (B.right != null) B.right.parent = A;
        B.right = A;
        A.parent = B;

        A.setParameters();
        B.setParameters();

        return root;
    }

    NodeLong rotateLeft(NodeLong root) {
        NodeLong A = this, B = right, P = parent;

        if (P != null) {
            if (P.left == this) P.left = B;
            else if (P.right == this) P.right = B;
            else System.exit(7 / 0);
        } else root = B;
        B.parent = A.parent;

        A.right = B.left;
        if (B.left != null) B.left.parent = A;
        B.left = A;
        A.parent = B;

        A.setParameters();
        B.setParameters();

        return root;
    }

    void setParameters() {
        size = 1 + findSize(left) + findSize(right);
        height = 1 + Math.max(findDepth(left), findDepth(right));
    }

    int size() {
        return size;
    }

    static int findDepth(NodeLong node) {
        return node == null ? 0 : node.height;
    }

    static int findSize(NodeLong node) {
        return node == null ? 0 : node.size();
    }

    public int compareTo(NodeLong node) {
        return Long.compare(value, node.value);
    }

    public String toString() {
        return value + "";
    }

}
class MyTreeSetLong implements Iterable<Long> {
    NodeLong root;
    boolean allowDuplicates;
    private int itrInd;
    private ArrayList<NodeLong> dfsTrav = new ArrayList<>();

    public MyTreeSetLong() {
        root = null;
    }

    public MyTreeSetLong(boolean allowDupli) {
        root = null;
        allowDuplicates = allowDupli;
    }

    public boolean add(long value) {
        return add(new NodeLong(value));
    }

    public int countFloorNodeLongs(long value) {
        return countFloorNodeLongs(root, new NodeLong(value));
    }

    public int size() {
        return root == null ? 0 : root.size();
    }

    private boolean add(NodeLong toAdd) {
        if (root == null) {
            root = toAdd;
            return true;
        }

        NodeLong tr = root;
        while (true) {
            if (toAdd.compareTo(tr) < 0) {
                if (tr.left == null) {
                    tr.left = toAdd;
                    toAdd.parent = tr;
                    break;
                } else tr = tr.left;
            } else if (allowDuplicates || toAdd.compareTo(tr) > 0) {
                if (tr.right == null) {
                    tr.right = toAdd;
                    toAdd.parent = tr;
                    break;
                } else tr = tr.right;
            } else return false;
        }

        while (toAdd != null) {
            root = toAdd.finalisePosition(root);
            toAdd = toAdd.parent;
        }
        return true;
    }

    private int countFloorNodeLongs(NodeLong node, NodeLong key) {
        if (node == null) return 0;
        else if (node.compareTo(key) > 0)
            return countFloorNodeLongs(node.left, key);
        else
            return NodeLong.findSize(node.left) + 1 + countFloorNodeLongs(node.right, key);
    }

    public Iterator<Long> iterator() {
        dfsTrav.clear();
        dfs(root);
        itrInd = 0;
        Iterator<Long> iterator = new Iterator<Long>() {

            public boolean hasNext() {
                return itrInd < size();
            }


            public Long next() {
                return dfsTrav.get(itrInd++).value;
            }
        };
        return iterator;
    }

    private void dfs(NodeLong node) {
        if (node == null) return;
        dfs(node.left);
        dfsTrav.add(node);
        dfs(node.right);
    }

    public String toString() {
        dfsTrav.clear();
        dfs(root);
        return dfsTrav.toString();
    }

}
 



/*******************************************************************************************************************************************************/

/**

 */






