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.io.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class D {
    public static void main(String[] args) throws IOException {
        Scanner in = new Scanner(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out), 1 << 20);
        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            int n = in.nextInt();

            ArrayList<Integer> xs = new ArrayList<>();
            for (int x = n; x > 2; x = (int) Math.ceil(Math.sqrt(x))) {
                xs.add(x);
            }
            xs.add(2);
            Collections.sort(xs);

            out.write((n + xs.size() - 3) + "\n");
            for (int j = 2; j <= n; j++) {
                if (!xs.contains(j)) {
                    out.write(j + " " + n + "\n");
                }
            }

            for (int j = xs.size() - 1; j > 0; --j) {
                Integer x = xs.get(j);
                Integer nextX = xs.get(j - 1);
                out.write(x + " " + nextX + "\n");
                out.write(x + " " + nextX + "\n");
            }
        }
        out.flush();
    }
}