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.*;
import java.io.*; 

public class Test {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int testCases = sc.nextInt();
        while (testCases > 0) {
            testCases--;
            int n = sc.nextInt();
            int length = n;
            int[] arr = new int[n];
            boolean[] flag = new boolean[n];
            int operations = 0;
            StringBuilder sb = new StringBuilder();
            Queue<Integer> queue = new LinkedList<>();
            for (int i = 0; i < length; i++) {
                arr[i] = i + 1;
            }
            while (n > 2) {
                n = (int) Math.floor(Math.sqrt(n));
                flag[n] = true;
                if (n > 2) {
                    queue.offer(n);
                }
            }
            for (int i = 2; i < length - 1; i++) {
                if (flag[i + 1]) {
                    continue;
                } else {
                    sb.append(i + 1 + " " + (i + 2) + "\n");
                    operations++;
                }
            }
            while (queue.size() != 0) {
                int num = queue.poll();
                sb.append(length + " " + num + "\n");
                sb.append(num + " " + length + "\n");
                operations += 2;
            }
            sb.append(length + " " + 2 + "\n");
            sb.append(length + " " + 2 + "\n");
            sb.append(length + " " + 2 + "\n");
            sb.append(length + " " + 2 + "\n");
            sb.append(length + " " + 2 + "\n");
            operations += 5;
            sb.insert(0, operations + "\n");
            System.out.println(sb.toString());
        }
 
    
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //FAST READER ENDS

}