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.*;
import java.util.StringTokenizer;

public class D_ {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    private static StringTokenizer st;

    private static int readInt() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }

    public static void main(String[] args) throws IOException {
        int T = readInt();
        while (T-- > 0) {
            int n = readInt();
            assert n >= 3;
            StringBuilder sb = new StringBuilder();
            int count = 0;
            long i = 2;
            for (; i < n; i *= i) {
                for (int j = (int) (i + 1), limit = (int) Math.min(i * i, n); j < limit; j++) {
                    sb.append(j).append(" ").append(j + 1).append('\n');
                    count++;
                }
            }
            i = (int) Math.sqrt(i);
            sb.append(n).append(" ").append(i).append('\n');
            sb.append(n).append(" ").append(i).append('\n');
            count += 2;
            for (; i > 2; i = (int) Math.sqrt(i)) {
                int j = (int) Math.sqrt(i);
                sb.append(i).append(" ").append(j).append('\n');
                sb.append(i).append(" ").append(j).append('\n');
                count += 2;
            }
            pw.println(count);
            pw.print(sb);
        }
        pw.close();
    }
}