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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
    static class node
    {
        int x, y;
        public node(int a, int b){
            x = a;
            y = b;
        }
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuffer sb = new StringBuffer();
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
		    int n = Integer.parseInt(br.readLine());
		    int count = 0, last = n, sqrt = (int)Math.ceil(Math.sqrt(n));
		    n--;
		    ArrayList<node> arr = new ArrayList<node>();
		    while(n >= 2){
		        if(n > sqrt){
		            arr.add(new node(n, last));
		            count++;
		            n--;
		        }
		        else{
		            arr.add(new node(last, sqrt));
		            arr.add(new node(last, sqrt));
		            count += 2;
		            last = sqrt;
		            sqrt = (int)Math.ceil(Math.sqrt(n));
		            n--;
		        }
		    }
		    sb.append(count+"\n");
		    for(int i = 0; i < arr.size(); i++){
		        node te = arr.get(i);
		        sb.append(te.x+" "+te.y+"\n");
		    }
		}
		System.out.println(sb);
	}
}