The new generation external memory contains an array of integers a[1 … n] = [a_1, a_2, …, a_n].

This type of memory does not support changing the value of an arbitrary element. Instead, it allows you to cut out any segment of the given array, cyclically shift (rotate) it by any offset and insert it back into the same place.

Technically, each cyclic shift consists of two consecutive actions: 

  1. You may select arbitrary indices l and r (1 ≤ l < r ≤ n) as the boundaries of the segment. 
  2. Then you replace the segment a[l … r] with it's cyclic shift to the left by an arbitrary offset d. The concept of a cyclic shift can be also explained by following relations: the sequence [1, 4, 1, 3] is a cyclic shift of the sequence [3, 1, 4, 1] to the left by the offset 1 and the sequence [4, 1, 3, 1] is a cyclic shift of the sequence [3, 1, 4, 1] to the left by the offset 2. 



For example, if a = [1, \color{blue}{3, 2, 8}, 5], then choosing l = 2, r = 4 and d = 2 yields a segment a[2 … 4] = [3, 2, 8]. This segment is then shifted by the offset d = 2 to the left, and you get a segment [8, 3, 2] which then takes the place of of the original elements of the segment. In the end you get a = [1, \color{blue}{8, 3, 2}, 5].

Sort the given array a using no more than n cyclic shifts of any of its segments. Note that you don't need to minimize the number of cyclic shifts. Any method that requires n or less cyclic shifts will be accepted.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain the descriptions of the test cases. 

The first line of each test case description contains an integer n (2 ≤ n ≤ 50) — the length of the array. The second line consists of space-separated elements of the array a_i (-10^9 ≤ a_i ≤ 10^9). Elements of array a may repeat and don't have to be unique.

Output

Print t answers to all input test cases. 

The first line of the answer of each test case should contain an integer k (0 ≤ k ≤ n) — the number of actions to sort the array. The next k lines should contain descriptions of the actions formatted as "l r d" (without quotes) where l and r (1 ≤ l < r ≤ n) are the boundaries of the segment being shifted, while d (1 ≤ d ≤ r - l) is the offset value. Please remember that only the cyclic shifts to the left are considered so the chosen segment will be shifted by the offset d to the to the left.

Note that you are not required to find the minimum number of cyclic shifts needed for sorting. Any sorting method where the number of shifts does not exceed n will be accepted.

If the given array a is already sorted, one of the possible answers is k = 0 and an empty sequence of cyclic shifts.

If there are several possible answers, you may print any of them.

Example

Input


4
2
2 1
3
1 2 1
4
2 4 1 3
5
2 5 1 4 3


Output


1
1 2 1
1
1 3 2
3
2 4 1
2 3 1
1 3 2
4
2 4 2
1 5 3
1 2 1
1 3 1

Note

Explanation of the fourth data set in the example: 

  1. The segment a[2 … 4] is selected and is shifted to the left by 2: [2, \color{blue}{5, 1, 4}, 3] \longrightarrow [2, \color{blue}{4, 5, 1}, 3] 
  2. The segment a[1 … 5] is then selected and is shifted to the left by 3: [\color{blue}{2, 4, 5, 1, 3}] \longrightarrow [\color{blue}{1, 3, 2, 4, 5}] 
  3. After that the segment a[1 … 2] is selected and is shifted to the left by 1: [\color{blue}{1, 3}, 2, 4, 5] \longrightarrow [\color{blue}{3, 1}, 2, 4, 5] 
  4. And in the end the segment a[1 … 3] is selected and is shifted to the left by 1: [\color{blue}{3, 1, 2}, 4, 5] \longrightarrow [\color{blue}{1, 2, 3}, 4, 5] 
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.Map.Entry;

import javafx.beans.binding.StringBinding;

public class Solution {
	InputStream is;
	FastWriter out;
	String INPUT = "";
	
	public static void main(String[] args) throws Exception 
	{
		new Solution().run();// Here run assign I/O calls solve also tell total time invested
	}
	
	void solve()
	{
		int t=ni();
		while(t-->0)
			go();
	}
	
	void go()
	{
		int i,j;
		int n=ni(),arr[]=ni(n);
		Map<Integer,Integer> map=new HashMap<>();
		PriorityQueue<Integer> pq=new PriorityQueue<>((o1,o2)->o2-o1);
		for(i=0;i<n;i++)
		{
			pq.add(arr[i]);
			map.put(arr[i], i);
		}
//		List<Entry<Integer, Integer>> list=new ArrayList<>(map.entrySet());
//		Collections.sort(list,(o1,o2)->o1.getKey()-o2.getKey());
//		for(i=n-1;i>=0;i--)
//		{
//			if(i==list.get(i).getValue())
//				continue;
//			System.out.println(1+" "+(i+1)+" "+(i-list.get(i).getValue()));
//		}
		
		int k=n,q=0;
		int temp[]=new int[n];
		StringBuilder str=new StringBuilder();
		while(!pq.isEmpty())
		{
			i=pq.poll();
			if(map.get(i)>=k-1)
			{
				k--;
				continue;
			}
			q++;
//			out.println(map.get(i)+" "+k);
			str.append(1+" "+k+" "+(map.get(i)+1)+"\n");
			int p=map.get(i)+1;
			for(j=0;j<k;j++)
			{
				map.put(arr[p%k], j);
				temp[j]=arr[p++%k];
			}
			arr=Arrays.copyOf(temp, n);
			k--;
		}
		out.println(q);
		out.print(str.toString());
	}
	
	static boolean prime[];
	static int count=0;
	void sieve(int n)
	{
		prime=new boolean[n+1];
		Arrays.fill(prime, true);
		for(int i=2;i<=Math.sqrt(n);i++)
			if(prime[i])
				for(int j=i*i;j<=n;j+=i)
					prime[j]=false;
	}
	
	boolean isPrime(int n)
	{
		for(int i=2;i<=Math.sqrt(n);i++)
			if(n%i==0)
				return false;
		return true;
	}
	
	long gcd(long a,long b)
	{
		if(a==0)
			return b;
		return gcd(b%a,a);
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private int[] ni(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private long[] nl(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
	
	private Long[] nL(int n) {
		Long[] a = new Long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}
	
	private Integer[] nI(int n) {
		Integer[] a = new Integer[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	
	private char[][] ns(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[][] ni(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = ni(m);
		return map;
	}
	
	private long[][] nl(int n, int m) {
		long[][] map = new long[n][];
		for(int i = 0;i < n;i++)map[i] = nl(m);
		return map;
	}
	
	private Integer[][] nI(int n, int m) {
		Integer[][] map = new Integer[n][];
		for(int i = 0;i < n;i++)map[i] = nI(m);
		return map;
	}
	
	private Long[][] nL(int n, int m) {
		Long[][] map = new Long[n][];
		for(int i = 0;i < n;i++)map[i] = nL(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;
		
		private FastWriter(){out = null;}
		
		public FastWriter(OutputStream os)
		{
			this.out = os;
		}
		
		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}
		
		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}
		
		public FastWriter write(char c)
		{
			return write((byte)c);
		}
		
		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}
		
		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}
		
		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}
		
		private static int countDigits(int l) 
		{
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}
		
		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}
		
		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}
		
		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}
		
		public FastWriter writeln(char c){
			return write(c).writeln();
		}
		
		public FastWriter writeln(int x){
			return write(x).writeln();
		}
		
		public FastWriter writeln(long x){
			return write(x).writeln();
		}
		
		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}
		
		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}
		
		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}
		
		public FastWriter writeln()
		{
			return write((byte)'\n');
		}
		
		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}
		
		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}
		
		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}
		
		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}
		
		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}
		
		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}
		
		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}
		
		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}
	
	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}
	
	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}
	
	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}
	
	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}
	
	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}
	
	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}