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;

public class A {
    public static void main(String [] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int not = Integer.parseInt(br.readLine());
        while(not--!=0) {
            int n = Integer.parseInt(br.readLine());
            StringBuilder sb = new StringBuilder();
            boolean flag = false;
            if(n > (1 << 16)) {
                if(!flag) {
                    sb.append(n + 3).append("\n");
                    flag = true;
                }
                function(1 << 16, n, sb);
                n = 1 << 16;
                
            }
            if(n > (1 << 8)) {
                if(!flag) {
                    sb.append(n + 2).append("\n");
                    flag = true;
                }
                function(1 << 8, n, sb);
                n = 1 << 8;
            }
            if(n > (1 << 4)) {
                if(!flag) {
                    sb.append(n + 1).append("\n");
                    flag = true;
                }
                function(1 << 4, n, sb);
                n = 1 << 4;
            }
            if(n > (1 << 2)) {
                if(!flag) {
                    sb.append(n).append("\n");
                    flag = true;
                }
                function(1 << 2, n, sb);
                n = 1 << 2;
            }
            if(n > (1 << 1)) {
                if(!flag) {
                    sb.append(n - 1).append("\n");
                    flag = true;
                }
                function(1 << 1, n, sb);
                n = 1 << 1;
            }
            sb.append("\n");
            System.out.println(sb);
        }
    }
    public static void function(int a, int b, StringBuilder sb) {
        for(int i = a + 1; i < b; i++) {
            sb.append(i+" "+b).append("\n");
        }
        sb.append(b + " " + a).append("\n");
        sb.append(b + " " + a).append("\n");
    }
}