Problem: This is an easy version of the problem. In this version, all numbers in the given array are distinct and the constraints on n are less than in the hard version of the problem.

You are given an array a of n integers (there are no equals elements in the array). You can perform the following operations on array elements:

  1. choose any index i (1 ≤ i ≤ n) and move the element a[i] to the begin of the array; 
  2. choose any index i (1 ≤ i ≤ n) and move the element a[i] to the end of the array. 



For example, if n = 5, a = [4, 7, 2, 3, 9], then the following sequence of operations can be performed: 

  * after performing the operation of the first type to the second element, the array a will become [7, 4, 2, 3, 9]; 
  * after performing the operation of the second type to the second element, the array a will become [7, 2, 3, 9, 4]. 



You can perform operations of any type any number of times in any order.

Find the minimum total number of operations of the first and second type that will make the a array sorted in non-decreasing order. In other words, what is the minimum number of operations that must be performed so the array satisfies the inequalities a[1] ≤ a[2] ≤ … ≤ a[n].

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases in the test. Then t test cases follow.

Each test case starts with a line containing an integer n (1 ≤ n ≤ 3000) — length of the array a.

Then follow n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — an array that needs to be sorted by the given operations. All numbers in the given array are distinct.

The sum of n for all test cases in one test does not exceed 3000.

Output

For each test case output one integer — the minimum total number of operations of the first and second type, which will make the array sorted in non-decreasing order.

Example

Input


4
5
4 7 2 3 9
5
3 5 8 1 7
5
1 4 5 7 12
4
0 2 1 3


Output


2
2
0
2

Note

In the first test case, you first need to move 3, and then 2 to the beginning of the array. Therefore, the desired sequence of operations: [4, 7, 2, 3, 9] → [3, 4, 7, 2, 9] → [2, 3, 4, 7, 9].

In the second test case, you need to move the 1 to the beginning of the array, and the 8 — to the end. Therefore, the desired sequence of operations: [3, 5, 8, 1, 7] → [1, 3, 5, 8, 7] → [1, 3, 5, 7, 8].

In the third test case, the array is already sorted.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
 
public class Main {
    static final long MOD = 1000000007L;
    static final int INF = 50000000;
    static final int NINF = -50000000;
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        
        int Q = sc.ni();
        for (int q = 0; q < Q; q++) {
            int N = sc.ni();
            int[][] input = new int[N][2];
            int[] ints = new int[N];
            for (int i = 0; i < N; i++) {
            	input[i][0] = sc.ni();
            	ints[i] = input[i][0];
            	input[i][1] = i;
            }
            input = sort(input);
            int M = 0;
            int cur = input[0][0];
            for (int i = 0; i < N; i++) {
            	if (input[i][0]!=cur) {
            		cur = input[i][0];
            		M++;
            	}
            	input[i][0] = M;
            }
            M++;
            int[] nums = new int[N];
            for (int i = 0; i < N; i++) {
            	nums[input[i][1]] = input[i][0];
            }
            int[][] ranges = new int[M][2];
            ArrayList<Integer>[] indices = new ArrayList[M];
            for (int i = 0; i < M; i++) {
            	Arrays.fill(ranges[i], -1);
            	indices[i] = new ArrayList<Integer>();
            }
            	
            
            for (int i = 0; i < N; i++) {
            	if (ranges[nums[i]][0]==-1)
            		ranges[nums[i]][0] = i;
            	ranges[nums[i]][1] = i;
            	indices[nums[i]].add(i);
            }
            int[] curInd = new int[M];
            
            int[][] dp = new int[N][3]; //first,midd,last
            for (int i = 0; i < N; i++) {
            	int ind = curInd[nums[i]];
            	dp[i][0] = 1+ind;
            	
            	if (i == ranges[nums[i]][1]) {
            		if (nums[i] > 0 && ranges[nums[i]][0] > ranges[nums[i]-1][1]) {
            			dp[i][1] = dp[ranges[nums[i]-1][1]][1]+(1+ind);
            		} else {
            			dp[i][1] = 1+ind;
            			if (nums[i] > 0 && indices[nums[i]-1].get(0) < ranges[nums[i]][0]) {
                    		int low = 0;
                    		int high = indices[nums[i]-1].size()-1;
                    		while (low < high) {
                    			int med = (low+high+1)/2;
                    			if (indices[nums[i]-1].get(med) < ranges[nums[i]][0]) {
                    				low = med;
                    			} else {
                    				high = med-1;
                    			}
                    		}
                    		dp[i][1] += (1+low);
            			}
            		}
            	}
            	
            	if (nums[i] > 0) {
            		dp[i][2] = 1;
            		if (ind > 0) {
            			dp[i][2] = 1+dp[indices[nums[i]].get(ind-1)][2];
            		}
            		if (i > ranges[nums[i]-1][1]) {
            			dp[i][2] = Math.max(dp[i][2], 1+dp[ranges[nums[i]-1][1]][1]);
            		}
        			if (indices[nums[i]-1].get(0) < i) {
                		int low = 0;
                		int high = indices[nums[i]-1].size()-1;
                		while (low < high) {
                			int med = (low+high+1)/2;
                			if (indices[nums[i]-1].get(med) < i) {
                				low = med;
                			} else {
                				high = med-1;
                			}
                		}
                		dp[i][2] = Math.max(dp[i][2],(low+1)+1);
        			}
            	}
            	
            	curInd[nums[i]] += 1;
            }
            
            int take = 0;
            for (int i = 0; i < N; i++) {
            	for (int j = 0; j < 3; j++)
            		take = Math.max(take, dp[i][j]);
            }
            
            pw.println(N-take);
        }
        
        pw.close();
    }
    
    public static int[][] sort(int[][] arr) {
    	//Sort an array (immune to quicksort TLE)
    	Random rgen = new Random();
    	for (int i = 0; i < arr.length; i++) {
    		int randomPosition = rgen.nextInt(arr.length);
    		int[] temp = arr[i];
    		arr[i] = arr[randomPosition];
    		arr[randomPosition] = temp;
    	}
    	Arrays.sort(arr, new Comparator<int[]>() {
    		@Override
    		public int compare(int[] arr1, int[] arr2) {
    			return arr1[0]-arr2[0];
    		}
    	});
    	return arr;
    }
    
    //No lazy propagation. 0 indexed. Very fast.
    static class SegmentTree {
    	public int[] tree;
    	public int[] arr;
    	public int NONE;
    	public int N;

    	//Zero initialization
    	public SegmentTree(int n) {
    		N = n;
    		tree = new int[4*N+1];
    		arr = new int[N];
    		NONE = 0;
    	}

    	public int merge(int a, int b) {
    		return (a+b); //set this manually
    	}

    	public int query(int i, int j) {
    		return query(0,0,N-1,i,j);
    	}

    	public void add(int arrIndex, int val) {
    		arr[arrIndex] += val;
    		update(0,0,N-1,arrIndex,arr[arrIndex]);
    	}

    	private int query(int treeIndex, int lo, int hi, int i, int j) {
    		// query for arr[i..j]
    		if (lo > j || hi < i)
    			return NONE;
    		if (i <= lo && j >= hi)
    			return tree[treeIndex];
    		int mid = lo + (hi - lo) / 2;

    		if (i > mid)
    			return query(2 * treeIndex + 2, mid + 1, hi, i, j);
    		else if (j <= mid)
    			return query(2 * treeIndex + 1, lo, mid, i, j);

    		int leftQuery = query(2 * treeIndex + 1, lo, mid, i, mid);
    		int rightQuery = query(2 * treeIndex + 2, mid + 1, hi, mid + 1, j);

    		// merge query results
    		return merge(leftQuery, rightQuery);
    	}

    	private void update(int treeIndex, int lo, int hi, int arrIndex, int val) {
    		if (lo == hi) {
    			tree[treeIndex] = val;
    			return;
    		}

    		int mid = lo + (hi - lo) / 2;

    		if (arrIndex > mid)
    			update(2 * treeIndex + 2, mid + 1, hi, arrIndex, val);
    		else if (arrIndex <= mid)
    			update(2 * treeIndex + 1, lo, mid, arrIndex, val);

    		// merge updates
    		tree[treeIndex] = merge(tree[2 * treeIndex + 1], tree[2 * treeIndex + 2]);
    	}
    }
    
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            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 ni() {
            return Integer.parseInt(next());
        }
 
        long nl() {
            return Long.parseLong(next());
        }
 
        double nd() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}