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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.function.Supplier;
import java.util.stream.IntStream;



public class Main {
    
    
    
    static void test(MyScanner sc) {
        int n = sc.nextInt();
        List<Integer> high = new ArrayList<Integer>();
        List<Integer> low = new ArrayList<Integer>();
        int pivot = n;
        int number = n-1;
        while(pivot >= 5) {
            if(number < 1000 && (number - 1) * (number - 1) < pivot) {
                low.add(pivot);
                low.add(pivot);
                high.add(number);
                high.add(number);
                pivot = number;
            } else {
                low.add(number);
                high.add(pivot);
            }
            number--;
        }
        if(pivot == 4) {
            low.add(3);
            low.add(4);
            low.add(4);
            high.add(4);
            high.add(2);
            high.add(2);
        } 
        
        if(pivot == 3) {
            low.add(3);
            low.add(3);
            high.add(2);
            high.add(2);
        }

        System.out.println(low.size());
        for(int i = 0; i < low.size(); i++) {
            System.out.println(low.get(i) + " " + high.get(i));
        }
    }
    
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        int t = sc.nextInt();
        while(t-- > 0) test(sc);
        
    }
    

static class MyScanner {
    BufferedReader br;
    StringTokenizer st;

    public MyScanner() {
       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;
    }

 }


}