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 PYTHON):

Solution:
import math
for _ in range(input()):
    n=input()
    safe={}
    safe[2]=1
    safe[1]=1
    safe[n]=1
    safe[100]=1
    safe[10000]=1
    safe[10]=1
    ans=[]
    for i in range(1,n+1):
        if i not in safe:
            ans.append([i,n])
    if n>10000:
        ans.append([n,10000])
        ans.append([n,10000])
        ans.append([10000,100])
        ans.append([10000,100])
        ans.append([100,10])
        ans.append([100,10])
        for i in range(4):
            ans.append([10,2])
    elif n==10000:
        ans.append([10000,100])
        ans.append([10000,100])
        ans.append([100,10])
        ans.append([100,10])
        for i in range(4):
            ans.append([10,2])
    elif n>100:
        ans.append([n,100])
        ans.append([n,100])
        ans.append([100,10])
        ans.append([100,10])
        for i in range(4):
            ans.append([10,2])
    elif n==100:
        ans.append([100,10])
        ans.append([100,10])
        for i in range(4):
            ans.append([10,2])
    elif n>10:
        ans.append([n,10])
        ans.append([n,10])
        for i in range(4):
            ans.append([10,2])
    elif n==10:
        for i in range(4):
            ans.append([10,2])
    else:
        if n>2:
            cur=float(n)
            for i in range(10):
                if cur!=1:
                    ans.append([n,2])
                    cur=math.ceil(cur/2)
    print len(ans)
    for i in range(len(ans)):
        print ans[i][0],ans[i][1]