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.*;
import java.lang.*;


public class Main {
    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while (t-- != 0) {
            int n = sc.nextInt();
            int count=0;

            if(n>256)
            {
                count=n;
                double y=n;
                while(y!=1)
                {
                    y=Math.ceil(y/16);
                    count++;
                }
                System.out.println(count);

                for(int i=n-1;i>=3;i--){
                    if(i!=16)
                    System.out.println(i + " " + n);
                }
                double f=n;
                while(f!=1)
                {
                    f=Math.ceil(f/16);
                    System.out.println(n + " " + 16);
                }
                int x=16;
                while(x!=1)
                {
                    x=(int)Math.ceil(x/2);
                    System.out.println(16 + " " + 2);
                }
                



            }
            else
            {
                double x=n;
                count=n-3;
                while(x!=1)
                {
                    x=Math.ceil(x/2);
                    count++;
                }
                System.out.println(count);
                for(int i=n-1;i>=3;i--){
                    System.out.println( i + " " + n);
                }
                x=n;
                while(x!=1)
                {
                    x=Math.ceil(x/2);
                    System.out.println(n + " " + 2);
                }
            }

        }
    }

    static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    // method to return LCM of two numbers
    static long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }

    public 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;
        }
    }

}