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.util.*;
public class Main{
    static Scanner sc = new Scanner(System.in);
    static int MOD = 1_000_000_007;
    static int mod = 1_000_000_007;
    public static void main(String[] args){
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            solve();
        }
    }

    static int[]X = new int[]{1,-1,0,0};
    static int[]Y = new int[]{0,0,1,-1};

    // 1 2 3
    // 2 1 3
    private static void solve(){
        double n = sc.nextDouble();
        List<int[]>list = new ArrayList<>();
        while(n > 2){
             int begin = (int)Math.ceil(Math.sqrt(n));
             for(int i = begin + 1;i < n;i++){
                 list.add(new int[]{i,i + 1});
             }
             list.add(new int[]{(int)n,begin});
             list.add(new int[]{(int)n,begin});
             n = begin;
        }
        System.out.println(list.size());
        for(int[]i : list){
            System.out.print(i[0] + " " + i[1] + " ");
        }
        System.out.println();
    }


    //
    public static boolean sorted(int begin,int[]arr,int len){
        boolean sorted = true;
        for(int i = begin;i <= len;i++){
            if(arr[i] < arr[i - 1])
                sorted = false;
        }
        return sorted;
    }
    public static boolean sorted(int[]arr,int len){
        boolean sorted = true;
        for(int i = 1;i <= len;i++){
            if(arr[i] < arr[i - 1])
                sorted = false;
        }
        return sorted;
    }
    private static ArrayList<ArrayList<Integer>>g(int n){
        ArrayList<ArrayList<Integer>> g = new ArrayList<>();
        for (int i = 0; i < (n + 1); i++) {
            g.add(new ArrayList<>());
        }
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt();
            int v = sc.nextInt();
            g.get(u).add(v);
            g.get(v).add(u);
        }
        return g;
    }
    private static int gcb(int a,int b){
        if(a == b)
            return a;
        if(a < b)
            return gcb(b,a);
        if(a % b == 0)
            return b;
        return gcb(b,a % b);
    }

    private static void printList(List<Integer> arr){
        for(int i : arr){
            System.out.print(i + " ");
        }
        System.out.println();
    }
    private static void printArr(int[]arr){
        for(int i : arr){
            System.out.print(i + " ");
        }
        System.out.println();
    }
    private static int[]readArr(int len){
        int[]ans = new int[len];
        for(int i = 0;i < len;i++){
            ans[i] = sc.nextInt();
        }
        return ans;
    }
    private static long powmod(long a,long b){
        long res=1;
        for(long i=0;i<b;i++){
            res=res*a%mod;
        }
        return res;
    }
}