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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define cp ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define ll long long int  
#define vint vector<int>
#define vllint vector<ll>
#define pair_int pair<int , int>
#define pair_ll_int pair<ll , ll>
#define vector_of_pair_int vector<pair_int>
#define pb push_back 
#define test_case int t; cin>>t; while(t--)
#define umap unordered_map <int,int> 
#define mapint map<int,int>
#define infinity 1000000000
#define mp make_pair

int main() 
{ 
	cp
    
    test_case
    {
       ll n;
       cin>>n;

       if(n<=256)
       {
         int count=0;       	
         ll temp=n;
       	 while(temp!=1)
       	 {
       	 	count++;
       	 	if(temp%2==0)
       	 		temp=temp/2;
       	 	else
       	 		temp=temp/2+1;
       	 }

       	 cout<<count+n-3<<endl;
        
         for (int i = 1; i <=n-3; ++i)
       	 {
       	 	/* code */
       	 	 cout<<3+i-1<<" "<<3+i<<endl;
       	 }

       	 for (int i = 0; i < count; ++i)
       	 {
       	 	/* code */
       	 	cout<<n<<" "<<2<<endl;
       	 }

       	 




       }
       else
       {
       	 int count=0;       	
         ll temp=n;
       	 while(temp!=1)
       	 {
       	 	count++;
       	 	
       	 	temp=ceil(float(temp)/float(16));
       	 }

       	 cout<<count+n<<endl;
         
         for (int i = 3; i <n; ++i)
       	 {
       	 	/* code */
             if(i!=16)
             {
             	cout<<i<<" "<<i+1<<endl;
             }

       	 }
          
           for (int i = 0; i < count; ++i)
       	 {
       	 	/* code */
       	 	cout<<n<<" "<<16<<endl;
       	 }
       	 
       	 for (int i = 0; i < 4; ++i)
       	 {
       	 	/* code */
       	 	cout<<16<<" "<<2<<endl;
       	 }
       	 
       	
       }
    }

    return 0; 
}