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:
import java.util.*;
public class Main
{
	public static void main (String[] args)
	{
	    int i,t,ii,n;
     	Scanner sc=new Scanner(System.in);
	    t=sc.nextInt();
	    for(ii=1;ii<=t;ii++)
	    {
	        n=sc.nextInt();
	        if(n>5)
	        {
	        if(n>448)
	        System.out.println(n+3);
	        else if(n>22)
	        System.out.println(n+2);
	        else if(n>5)
	        System.out.println(n+1);
	        for(i=4;i<n;i++)
	        {
	            if(i==5||i==22||i==448)
	            continue;
	            else
	            System.out.println(i+" "+n);
	        }
	        if(n>448)
	        {
	            System.out.println(n+" 448");
	            System.out.println(n+" 448");
	            System.out.println("448 22");
	            System.out.println("448 22");
	            System.out.println("22 5");
	            System.out.println("22 5");
	            System.out.println("5 3");
	            System.out.println("5 3");
	            System.out.println("3 2");
	            System.out.println("3 2");
	        }
	        else if(n>22)
	        {
	            System.out.println(n+" 22");
	            System.out.println(n+" 22");
	            System.out.println("22 5");
	            System.out.println("22 5");
	            System.out.println("5 3");
	            System.out.println("5 3");
	            System.out.println("3 2");
	            System.out.println("3 2");
	        }
	        else if(n>5)
	        {
	            System.out.println(n+" 5");
	            System.out.println(n+" 5");
	            System.out.println("5 3");
	            System.out.println("5 3");
	            System.out.println("3 2");
	            System.out.println("3 2");
	        }
	        }
	        else
	        {
	            if(n==5)
	            {
	                System.out.println("5");
	                System.out.println("4 5");
	                System.out.println("3 5");
	                System.out.println("5 2");
	                System.out.println("5 2");
	                System.out.println("5 2");
	            }
	            if(n==4)
	            {
	                System.out.println("3");
	                System.out.println("3 4");
	                System.out.println("4 2");
	                System.out.println("4 2");
	            }
	            if(n==3)
	            {
	                System.out.println("2");
	                System.out.println("3 2");
	                System.out.println("3 2");
	            }
	        }
	    }
	}
}