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<iostream>
#include<math.h>
#include<bits/stdc++.h>
#define ll long long int
#define hell 1000000007LL
using namespace std;
ll power(ll x, ll y){
    ll z=hell;
    if(y==0)
     return 1;
    else
    {
        ll p=power(x,y/2);
        ll w=(p*p)%z;
        if(y%2==0)
         return w;
        else
        return (x*w)%z;
    }}
ll gcd(ll x,ll y)
{
    if(y==0)
     return x;
    else
    return gcd(y,x%y);
}
bool comp(pair<ll,ll>&a,pair<ll,ll>&b)
{
    if(a.first==b.first)
    return a.second>b.second;
    return a.first<b.first;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.precision(20);
    ll t;
    cin>>t;
    while(t--)
    {
       ll n;
       cin>>n;
       if(n==3)
       {
           cout<<2<<"\n";
           cout<<3<<" "<<2<<"\n";
           cout<<3<<" "<<2<<"\n";
       }
       else if(n==4)
       {
           cout<<3<<"\n";
           cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<2<<"\n";
           cout<<4<<" "<<2<<"\n";
           
       }
       else if(n==5)
       {
           cout<<5<<"\n";
           cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<2<<"\n";
           cout<<5<<" "<<2<<"\n";
           cout<<5<<" "<<2<<"\n";
           
       }
       else if(n==6)
       {
           cout<<6<<"\n";
           cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<6<<"\n";
           cout<<6<<" "<<2<<"\n";
           cout<<6<<" "<<2<<"\n";
           cout<<6<<" "<<2<<"\n";
       }
       else if(n==7)
       {
           cout<<7<<"\n";
           cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<6<<"\n";
           cout<<6<<" "<<7<<"\n";
           cout<<7<<" "<<2<<"\n";
           cout<<7<<" "<<2<<"\n";
           cout<<7<<" "<<2<<"\n";
           
       }
       else if(n==8)
       {
           cout<<8<<"\n";
            cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<6<<"\n";
           cout<<6<<" "<<7<<"\n";
           cout<<7<<" "<<8<<"\n";
           cout<<8<<" "<<2<<"\n";
            cout<<8<<" "<<2<<"\n";
             cout<<8<<" "<<2<<"\n";
             
           
       }
       else if(n==9)
       {
           cout<<10<<"\n";
            cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<6<<"\n";
           cout<<6<<" "<<7<<"\n";
           cout<<7<<" "<<8<<"\n";
           cout<<8<<" "<<9<<"\n";
           cout<<9<<" "<<2<<"\n";
           cout<<9<<" "<<2<<"\n";
           cout<<9<<" "<<2<<"\n";
           cout<<9<<" "<<2<<"\n";
       }
       else if(n==10)
       {
           cout<<11<<"\n";
           cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<6<<"\n";
           cout<<6<<" "<<7<<"\n";
           cout<<7<<" "<<8<<"\n";
           cout<<8<<" "<<9<<"\n";
           cout<<9<<" "<<10<<"\n";
            cout<<10<<" "<<2<<"\n";
             cout<<10<<" "<<2<<"\n";
              cout<<10<<" "<<2<<"\n";
               cout<<10<<" "<<2<<"\n";
           
       }
       else
       {
           ll x=n,c=0;
           while(x>1)
           {
              if(x%8==0)
              x=x/8;
              else
              x=x/8+1;
              c++;
           }
           cout<<c+n-4+3<<"\n";
           cout<<3<<" "<<4<<"\n";
           cout<<4<<" "<<5<<"\n";
           cout<<5<<" "<<6<<"\n";
           cout<<6<<" "<<7<<"\n";
           cout<<7<<" "<<8<<"\n";
           for(int i=9;i<=n-1;i++)
           cout<<i<<" "<<i+1<<"\n";
           //n-9 + 5
           for(int i=1;i<=c;i++)
           cout<<n<<" "<<8<<"\n";
           cout<<8<<" "<<2<<"\n";
           cout<<8<<" "<<2<<"\n";
           cout<<8<<" "<<2<<"\n";
           
       }
       }

    }