Problem: You have an array a_1, a_2, ..., a_n where a_i = i.

In one step, you can choose two indices x and y (x ≠ y) and set a_x = \left⌈ (a_x)/(a_y) \right⌉ (ceiling function).

Your goal is to make array a consist of n - 1 ones and 1 two in no more than n + 5 steps. Note that you don't have to minimize the number of steps.

Input

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

The first and only line of each test case contains the single integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the length of array a.

It's guaranteed that the sum of n over test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case, print the sequence of operations that will make a as n - 1 ones and 1 two in the following format: firstly, print one integer m (m ≤ n + 5) — the number of operations; next print m pairs of integers x and y (1 ≤ x, y ≤ n; x ≠ y) (x may be greater or less than y) — the indices of the corresponding operation.

It can be proven that for the given constraints it's always possible to find a correct sequence of operations.

Example

Input


2
3
4


Output


2
3 2
3 2
3
3 4
4 2
4 2

Note

In the first test case, you have array a = [1, 2, 3]. For example, you can do the following: 

  1. choose 3, 2: a_3 = \left⌈ (a_3)/(a_2) \right⌉ = 2 and array a = [1, 2, 2]; 
  2. choose 3, 2: a_3 = \left⌈ 2/2 \right⌉ = 1 and array a = [1, 2, 1]. 

You've got array with 2 ones and 1 two in 2 steps.

In the second test case, a = [1, 2, 3, 4]. For example, you can do the following: 

  1. choose 3, 4: a_3 = \left⌈ 3/4 \right⌉ = 1 and array a = [1, 2, 1, 4]; 
  2. choose 4, 2: a_4 = \left⌈ 4/2 \right⌉ = 2 and array a = [1, 2, 1, 2]; 
  3. choose 4, 2: a_4 = \left⌈ 2/2 \right⌉ = 1 and array a = [1, 2, 1, 1]. 

Solution (in JAVA):

Solution:
//created by Whiplash99
import java.io.*;
import java.util.*;
public class D
{
    public static void main(String[] args) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        int T=Integer.parseInt(br.readLine().trim());
        StringBuilder sb=new StringBuilder();
        StringBuilder sb2=new StringBuilder();

        while (T-->0)
        {
            N=Integer.parseInt(br.readLine().trim());
            int M=0; sb2.setLength(0);

            ArrayList<Integer> list=new ArrayList<>();
            int[] mark=new int[N+1];

            for(i=N;i>2;)
            {
                list.add(i); mark[i]=1;
                i = (int) Math.ceil(Math.sqrt(i));
            }

            for(i=3;i<=N;i++)
            {
                if(mark[i]==1) continue;
                sb2.append(i).append(" ").append(i+1).append("\n");
                M++;
            }
            for(i=0;i<list.size()-1;i++)
            {
                M+=2;
                sb2.append(list.get(i)).append(" ").append(list.get(i+1)).append("\n");
                sb2.append(list.get(i)).append(" ").append(list.get(i+1)).append("\n");
            }
            M+=2;
            sb2.append(list.get(list.size()-1)).append(" ").append(2).append("\n");
            sb2.append(list.get(list.size()-1)).append(" ").append(2).append("\n");

            if(M<=N+5) sb.append(M).append("\n").append(sb2);
            else sb.append("WA\n");
        }
        System.out.println(sb);
    }
}