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 PYTHON3):

Solution:
from sys import stdout
from math import ceil

t=int(input())
for i in range(t):
	n=int(input())
	if(n<=256):
		temp=n
		count=0
		while(temp>1):
			count+=1
			temp=ceil(temp/2)
		print(count+(n-3))
		for i in range(3,n):
			stdout.write(str(i)+" "+str(n)+"\n")
		for i in range(count):
			stdout.write(str(n)+" "+str(2)+"\n")
	else:
		for i in range(0,11):
			if(pow(2,2*i)>=n):
				p1=pow(2,i)
				break
		for i in range(0,11):
			if(pow(2,2*i)>=p1):
				p2=pow(2,i)
				break
		temp=p2
		count=0
		while(temp>1):
			count+=1
			temp=ceil(temp/2)
		print(count+4+(n-5))
		for i in range(3,n):
			if(i!=p1 and i!=p2):
				stdout.write(str(i)+" "+str(n)+"\n")
		stdout.write(str(n)+" "+str(p1)+"\n")
		stdout.write(str(n)+" "+str(p1)+"\n")
		stdout.write(str(p1)+" "+str(p2)+"\n")
		stdout.write(str(p1)+" "+str(p2)+"\n")
		for i in range(count):
			stdout.write(str(p2)+" "+str(2)+"\n")