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 A {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();
        int testCases = sc.nextInt();

        for (int t = 0; t < testCases; t++) {
            int n = sc.nextInt();

            StringBuilder ans = new StringBuilder();
            int count = 0;

            if (n == 3) {
                sb.append(2).append("\n");
                sb.append(3 + " " + 2).append("\n");
                sb.append(3 + " " + 2).append("\n");
                continue;
            }

            for (int i = 3; i <= n - 1; i++) {
                if (i == 4 || i == 8) {
                    continue;
                }
                ans.append(i + " " + n).append("\n");
                count++;
            }

            if (n > 8) {
                int temp = n;
                while (temp != 1) {
                    ans.append(n + " " + 8).append("\n");
                    temp = (temp + 7) / 8;
                    count++;
                }
            }

            if (n >= 8) {
                ans.append(8 + " " + 4).append("\n");
                ans.append(8 + " " + 4).append("\n");
                count = count + 2;
            }

            if (n > 4 && n < 8) {
                int temp = n;
                while (temp != 1) {
                    ans.append(n + " " + 4).append("\n");
                    temp = (temp + 3) / 4;
                    count++;
                }
            }

            if (n >= 4) {
                ans.append(4 + " " + 2).append("\n");
                ans.append(4 + " " + 2).append("\n");
                count = count + 2;
            }

            sb.append(count).append("\n");

            sb.append(ans).append("\n");

        }

        System.out.print(sb);
    }
}