Problem: <image>

While trading on his favorite exchange trader William realized that he found a vulnerability. Using this vulnerability he could change the values of certain internal variables to his advantage. To play around he decided to change the values of all internal variables from a_1, a_2, …, a_n to -a_1, -a_2, …, -a_n. For some unknown reason, the number of service variables is always an even number.

William understands that with his every action he attracts more and more attention from the exchange's security team, so the number of his actions must not exceed 5 000 and after every operation no variable can have an absolute value greater than 10^{18}. William can perform actions of two types for two chosen variables with indices i and j, where i < j:

  1. Perform assignment a_i = a_i + a_j 
  2. Perform assignment a_j = a_j - a_i 

William wants you to develop a strategy that will get all the internal variables to the desired values.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 20). Description of the test cases follows.

The first line of each test case contains a single even integer n (2 ≤ n ≤ 10^3), which is the number of internal variables.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9), which are initial values of internal variables.

Output

For each test case print the answer in the following format:

The first line of output must contain the total number of actions k, which the strategy will perform. Note that you do not have to minimize k. The inequality k ≤ 5 000 must be satisfied. 

Each of the next k lines must contain actions formatted as "type i j", where "type" is equal to "1" if the strategy needs to perform an assignment of the first type and "2" if the strategy needs to perform an assignment of the second type. Note that i < j should hold.

We can show that an answer always exists.

Example

Input


2
4
1 1 1 1
4
4 3 1 2


Output


8
2 1 2
2 1 2
2 1 3
2 1 3
2 1 4
2 1 4
1 1 2
1 1 2
8
2 1 4
1 2 4
1 2 4
1 2 4
1 3 4
1 1 2
1 1 2
1 1 4

Note

For the first sample test case one possible sequence of operations is as follows:

  1. "2 1 2". Values of variables after performing the operation: [1, 0, 1, 1] 
  2. "2 1 2". Values of variables after performing the operation: [1, -1, 1, 1] 
  3. "2 1 3". Values of variables after performing the operation: [1, -1, 0, 1] 
  4. "2 1 3". Values of variables after performing the operation: [1, -1, -1, 1] 
  5. "2 1 4". Values of variables after performing the operation: [1, -1, -1, 0] 
  6. "2 1 4". Values of variables after performing the operation: [1, -1, -1, -1] 
  7. "1 1 2". Values of variables after performing the operation: [0, -1, -1, -1] 
  8. "1 1 2". Values of variables after performing the operation: [-1, -1, -1, -1] 



For the second sample test case one possible sequence of operations is as follows:

  1. "2 1 4". Values of variables after performing the operation: [4, 3, 1, -2] 
  2. "1 2 4". Values of variables after performing the operation: [4, 1, 1, -2] 
  3. "1 2 4". Values of variables after performing the operation: [4, -1, 1, -2] 
  4. "1 2 4". Values of variables after performing the operation: [4, -3, 1, -2] 
  5. "1 3 4". Values of variables after performing the operation: [4, -3, -1, -2] 
  6. "1 1 2". Values of variables after performing the operation: [1, -3, -1, -2] 
  7. "1 1 2". Values of variables after performing the operation: [-2, -3, -1, -2] 
  8. "1 1 4". Values of variables after performing the operation: [-4, -3, -1, -2] 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class B {
    public static void main(String args[])throws IOException{
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int t = sc.nextInt();
        while(t-- > 0){
			int n = sc.nextInt();
			int arr[] = new int[n];
			for(int i = 0; i < n; i++) {
				arr[i] = sc.nextInt();
			}
			out.println(3*n);
			for(int i = 0; i < n; i = i+2) {
				out.println(2 + " " + (i+1) + " " + (i+2));
				out.println(1 + " " + (i+1) + " " + (i+2));
				out.println(2 + " " + (i+1) + " " + (i+2));
				out.println(1 + " " + (i+1) + " " + (i+2));
				out.println(2 + " " + (i+1) + " " + (i+2));
				out.println(1 + " " + (i+1) + " " + (i+2));
			}
		}
        out.flush();
    }

    static 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;
		}
	}

	static void swap(long[] arr, int i, int j)
	{
		long temp = arr[i];
		arr[i] = arr[j];
		arr[j] = temp;
	}
	
	/* This function takes last element as pivot, places
	the pivot element at its correct position in sorted
	array, and places all smaller (smaller than pivot)
	to left of pivot and all greater elements to right
	of pivot */
	static int partition(long[] arr, int low, int high)
	{
		
		// pivot
		long pivot = arr[high];
		
		// Index of smaller element and
		// indicates the right position
		// of pivot found so far
		int i = (low - 1);
	
		for(int j = low; j <= high - 1; j++)
		{
			
			// If current element is smaller
			// than the pivot
			if (arr[j] < pivot)
			{
				
				// Increment index of
				// smaller element
				i++;
				swap(arr, i, j);
			}
		}
		swap(arr, i + 1, high);
		return (i + 1);
	}
	
	/* The main function that implements QuickSort
			arr[] --> Array to be sorted,
			low --> Starting index,
			high --> Ending index
	*/
	static void quickSort(long[] arr, int low, int high)
	{
		if (low < high)
		{
			
			// pi is partitioning index, arr[p]
			// is now at right place
			int pi = partition(arr, low, high);
	
			// Separately sort elements before
			// partition and after partition
			quickSort(arr, low, pi - 1);
			quickSort(arr, pi + 1, high);
		}
	}
}