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.math.*; 

public class Main { 

	public static void main(String[] args) throws IOException 
	{ 
		FastScanner f = new FastScanner(); 
		int t=f.nextInt();
//		int t=1;
		while(t-->0){
			int n=f.nextInt();
			ArrayList<ArrayList<Integer>> list=new ArrayList<>();
			if(n>=65536) {
				for(int i=n-1;i>256;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}
				int curr=n;
				while(true) {
					if(((curr+255)/256)>=256) {
						curr=(curr+255)/256;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(256);
						list.add(a);
					}
					else {
						break;
					}
				}
				

				for(int i=256;i>16;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}

				while(true) {
					if(((curr+15)/16)>=16) {
						curr=(curr+15)/16;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(16);
						list.add(a);
					}
					else {
						break;
					}
				}
				
				for(int i=16;i>4;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}

				while(true) {
					if(((curr+3)/4)>=4) {
						curr=(curr+3)/4;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(4);
						list.add(a);
					}
					else {
						break;
					}
				}
				
				for(int i=4;i>2;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}

				while(true) {
					if(((curr+1)/2)>=2) {
						curr=(curr+1)/2;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(2);
						list.add(a);
					}
					else {
						break;
					}
				}
				ArrayList<Integer> a=new ArrayList<>();
				a.add(n);
				a.add(2);
				list.add(a);
			}
			else if(n>=256) {

				for(int i=n-1;i>16;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}
				int curr=n;
				while(true) {
					if(((curr+15)/16)>=16) {
						curr=(curr+15)/16;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(16);
						list.add(a);
					}
					else {
						break;
					}
				}
				
				for(int i=16;i>4;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}

				while(true) {
					if(((curr+3)/4)>=4) {
						curr=(curr+3)/4;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(4);
						list.add(a);
					}
					else {
						break;
					}
				}
				
				for(int i=4;i>2;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}

				while(true) {
					if(((curr+1)/2)>=2) {
						curr=(curr+1)/2;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(2);
						list.add(a);
					}
					else {
						break;
					}
				}
				ArrayList<Integer> a=new ArrayList<>();
				a.add(n);
				a.add(2);
				list.add(a);
			}
			else if(n>=16) {
				for(int i=n-1;i>4;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}
				int curr=n;
				while(true) {
					if(((curr+3)/4)>=4) {
						curr=(curr+3)/4;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(4);
						list.add(a);
					}
					else {
						break;
					}
				}
				
				for(int i=4;i>2;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}

				while(true) {
					if(((curr+1)/2)>=2) {
						curr=(curr+1)/2;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(2);
						list.add(a);
					}
					else {
						break;
					}
				}
				ArrayList<Integer> a=new ArrayList<>();
				a.add(n);
				a.add(2);
				list.add(a);
			}
			else if(n>=4) {
				for(int i=n-1;i>2;i--) {
					ArrayList<Integer> a=new ArrayList<>();
					a.add(i);
					a.add(n);
					list.add(a);
				}
				int curr=n;
				while(true) {
					if(((curr+1)/2)>=2) {
						curr=(curr+1)/2;
						ArrayList<Integer> a=new ArrayList<>();
						a.add(n);
						a.add(2);
						list.add(a);
					}
					else {
						break;
					}
				}
				ArrayList<Integer> a=new ArrayList<>();
				a.add(n);
				a.add(2);
				list.add(a);
			}
			else {
				ArrayList<Integer> a=new ArrayList<>();
				a.add(3);
				a.add(2);
				list.add(a);
				a=new ArrayList<>();
				a.add(3);
				a.add(2);
				list.add(a);
			}
			System.out.println(list.size());
			for(int i=0;i<list.size();i++) {
				System.out.println(list.get(i).get(0)+" "+list.get(i).get(1));
			}
		}
	} 
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		long[] readLongArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}
}