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, exit
from bisect import bisect_left as bl, bisect_right as br

input = lambda: stdin.readline()[:-1]
intput = lambda: int(input())
sinput = lambda: input().split()
intsput = lambda: map(int, sinput())

def dprint(*args, **kwargs):
    if debugging:
        print(*args, **kwargs)


debugging = 1
# Code
t = intput()
for _ in range(t):
    n = intput()
    if n > 8:
        print(n + 5)
        for i in range(2, n):
            if i not in (4, 8):
                print(i, n)
        for j in range(6):
            print(n, 8)
        print(8, 4)
        print(4, 8)
        print(4, 8)
    else:
        inst = []
        for i in range(2, n - 1):
            inst.append((i, n))
        a, b = n - 1, n
        swap = False
        while (a, b) != (1, 2):
            b = (b + a - 1) // a
            if not swap:
                inst.append((n, n - 1))
            else:
                inst.append((n - 1, n))
            if a > b:
                swap = not swap
                a, b = b, a
        print(len(inst))
        for a, b in inst:
            print(a, b)