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.Scanner;

public class CeilDivisions {

    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int t = scan.nextInt();
        StringBuilder s = new StringBuilder();
        while (t-- > 0) {
            int n = scan.nextInt();
            int c = 0;
            int a = n - 1;
            StringBuilder sb = new StringBuilder();
            if (n > 64) {
                while (a != 64) {
                    ++c;
                    sb.append(a + " " + n + "\n");
                    --a;
                }
                sb.append(n + " " + 64 + "\n");
                sb.append(n + " " + 64 + "\n");
                sb.append(n + " " + 64 + "\n");
                c += 3;
                n = 64;
                a = 63;
                while (a != 4) {
                    sb.append(a + " " + n + "\n");
                    --a;
                    ++c;
                }
                sb.append(n + " " + 4 + "\n");
                sb.append(n + " " + 4 + "\n");
                sb.append(n + " " + 4 + "\n");
                sb.append(3 + " " + 4 + "\n");
                sb.append(4 + " " + 2 + "\n");
                sb.append(4 + " " + 2 + "\n");
                c += 6;

            } else {
                
                while (a >= 3) {
                    sb.append(a + " " + n + "\n");
                    --a;
                    ++c;
                }
                sb.append(n + " " + 2 + "\n");
                sb.append(n + " " + 2 + "\n");
                sb.append(n + " " + 2 + "\n");
                sb.append(n + " " + 2 + "\n");
                sb.append(n + " " + 2 + "\n");
                sb.append(n + " " + 2 + "\n");
                sb.append(n + " " + 2 + "\n");
                c += 7;

            }
            s.append(c + "\n");
            s.append(sb );
        }
        System.out.println(s);

    }
}