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:
import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))

numbers=[2,4]
while numbers[-1]<200000:
    numbers.append(numbers[-1]*numbers[-2])
#[2, 4, 8, 32, 256, 8192, 2097152]

t=int(input())
for _ in range(t):
    n=int(input())
    if n==1 or n==2:
        print(0)
    elif n==3:
        print(2)
        print('3 2')
        print('3 2')
    else:
        ans=[]
        #optimal to retain 2 numbers, say a and b.
        for i in range(len(numbers)-1):
            if numbers[i+1]>n:
                b=numbers[i]
                a=numbers[i-1]
                break
        for i in range(2,n):
            if i!=a and i!=b: #set to 1
                ans.append([i,n])
        if n!=b: #set n to 1
            ans.append([n,b])
            ans.append([n,b])
        aa=a
        bb=b
        while not (aa==1 or bb==1):
            if bb>aa:
                ans.append([b,a])
                bb=(bb+aa-1)//aa
            else:
                ans.append([a,b])
                aa=(aa+bb-1)//bb
#        print(a,b)
        print(len(ans))
        multiLineArrayOfArraysPrint(ans)