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 CPP):

Solution:
//2020 SEORII®. All right reserved.
//Code created on 2020-12-29

#include <bits/stdc++.h>

using namespace std;

void f() {
    int n;
    cin >> n;
    vector<int> v;
    v.push_back(n);
    while (v.back() != 2) {
        for (int i = 2;; ++i) {
            if (i * i >= v.back()) {
                v.push_back(i);
                break;
            }
        }
    }
    cout << v.size() + n - 3 << '\n';
    auto li = v;
    for (int i = 2; i < n; ++i) {
        if (v.back() == i) {
            v.pop_back();
        } else cout << i << ' ' << n << '\n';
    }
    for (int i = 0; i < li.size() - 1; ++i) {
        cout << li[i] << ' ' << li[i + 1] << '\n';
        cout << li[i] << ' ' << li[i + 1] << '\n';
    }
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int t;
    cin >> t;
    while (t--) f();
    return 0;
}