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 stdin,stdout                           #
import math                                            #
import heapq                                           #
                                                       #
t = 1                                                  #
def aint():                                            #
	return int(input().strip())                        #
def lint():                                            #
	return list(map(int,input().split()))              #
def fint():                                            #
	return list(map(int,stdin.readline().split()))     #
                                                       #	
########################################################
def operate(ar, x, y):
	if x!=y:
		ar[x] = (ar[x]-1)//ar[y] +1
def main():
	n=aint()
	i=n-1
	ar=[i for i in range(n+1)]
	ans = []
	while i>2:
		if i*i>=ar[n]:
			operate(ar, i, n)
			ans.append([i,n])
			i-=1
		else:
			operate(ar, n, i)
			ans.append([n,i])
	while ar[n]!=1:
		operate(ar, n, 2)
		ans.append([n,2])
	print(len(ans))
	for i in ans:
		print(*i)

	#solve

t=int(input())

########################################################
for i in range(t):                                     #
	#print("Case #"+str(i+1)+":",end=" ")		       #
	main()                                             #