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 math import ceil, log2, sqrt
t = int(input())
for testCaseCounter in range(t):
	n = int(input())
	origN = n

	extraTwos = 0
	extraTwos += 1
	endpoints = list()
	
	index = n
	
	while index >= 3:
		endpoints.append(index)
		index = int(ceil(sqrt(index)))
	endpoints.append(2)

	endpoints.reverse()
	#print (endpoints)
	res = list()
	operations = 0
	for i in range(1, len(endpoints)):
		for j in range(endpoints[i-1]+1, endpoints[i]):
			res.append(str(j) + " " + str(endpoints[i]))
			operations += 1

	#print (endpoints)
	for i in range(len(endpoints)-1, 0, -1):
		res.append(str(endpoints[i]) + " " + str(endpoints[i-1]))
		
		res.append(str(endpoints[i]) + " " + str(endpoints[i-1]))
		endpoints[i] = int(ceil(endpoints[i]/endpoints[i-1]))
		endpoints[i] = int(ceil(endpoints[i]/endpoints[i-1]))
		operations += 2
		#endpoints[i] = int(ceil(endpoints[i]/endpoints[i-1]))

	
	print (operations)
	for item in res:
		print (item)
	#print (endpoints)