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:
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define hell 100000000000000007 //10e18+7
#define mod 1000000007//10e9+7
#define pi  3.141592653589793238
const long long N = 102; // 1e6+7

//remember the approach of suming up the element
// and when it exceeds from our radar
// try removing from the staring part
// void buildSegtree(long long s1, long long e1, long long p1)
// {
//   if (s1 == e1)
//   {
//     segtree[p1] = (arr[s1]-'0');
//     return;
//   }
//   long long mid = ((s1 + e1) / 2);
//   buildSegtree(s1, mid, 2 * p1 + 1);
//   buildSegtree(mid + 1, e1, 2 * p1 + 2);
//   segtree[p1] = ((segtree[2 * p1 + 1])+segtree[2 * p1 + 2]) ;
// }

// long long rangeQuery(long long q1, long long q2, long long s1, long long e1, long long p1)
// {
//   if (q1 <= s1 && q2 >= e1)
//     return (segtree[p1]);
//   if (q2 < s1 || q1 > e1)
//     return (0);
//   long long mid = (s1 + e1) / 2;
//   long long l1 = rangeQuery(q1, q2, s1, mid, 2 * p1 + 1);
//   long long l2 = rangeQuery(q1, q2, mid + 1, e1, 2 * p1 + 2);
//   return ((l1+l2));
// }
// void updateQuery(long long q1, long long q2, long long id, long long p1, long long val)
// {
//   if (q1 == q2)
//   {
//     segtree[p1] = val;
//     return;
//   }
//   long long mid = (q1 + q2) / 2;
//   if (id > mid)
//     updateQuery(mid + 1, q2, id, 2 * p1 + 2, val);
//   else
//     updateQuery(q1, mid, id, 2 * p1 + 1, val);
//   segtree[p1] = (segtree[2 * p1 + 1]+segtree[2 * p1 + 2]);
// }
// long long binpow(long long a, long long b, long long m)
// {
//   a %= m;
//   long long res = 1;
//   while (b > 0) {
//     if (b & 1)
//       res = res * a % m;
//     a = a * a % m;
//     b >>= 1;
//   }
//   return res;
// }
// long long inv(long long a) {
//   a %= mod;
//   if (a < 0) a += mod;
//   long long b = mod, u = 0, v = 1;
//   while (a) {
//     long long t = b / a;
//     b -= t * a; swap(a, b);
//     u -= t * v; swap(u, v);
//   }
//   if (u < 0) u += mod;
//   return u;
// }
int main()
{
#ifndef ONLINE_JUDGE
  freopen("i1.txt", "r", stdin);
  freopen("q1.txt", "w", stdout);
#endif
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ll t;
  cin >> t;
  while (t--)
  {
    ll n;
    cin >> n;
    ll a1 = 4;
    ll a2 = 16;
    ll a3 = 256;
    ll a4 = 65536;
    if (n == 3)
    {
      cout << 2 << endl;
      cout << 3 << " " << 2 << endl;
      cout << 3 << " " << 2 << endl;
    }
    else if (n == 4)
    {
      cout << 3 << endl;
      cout << 3 << " " << 4 << endl;
      cout << 4 << " " << 2 << endl;
      cout << 4 << " " << 2 << endl;
    }
    else
    {
      if (n > a1 && n <= a2)
      {
        cout << n << endl;
        for (ll i = n - 1; i >= 3; i--)
        {
          if (i != a1)
            cout << i << " " << n << endl;
        }
        cout << n << " " << 4 << endl;
        cout << n << " " << 4 << endl;
        cout << 4 << " " << 2 << endl;
        cout << 4 << " " << 2 << endl;
      }
      else if (n > a2 && n <= a3)
      {
        cout << n + 1 << endl;
        for (ll i = n - 1; i >= 3; i--)
        {
          if (i != a2 && i != a1)
            cout << i << " " << n << endl;
        }
        cout << n << " " << 16 << endl;
        cout << n << " " << 16 << endl;
        cout << 16 << " " << 4 << endl;
        cout << 16 << " " << 4 << endl;
        cout << 4 << " " << 2 << endl;
        cout << 4 << " " << 2 << endl;
      }
      else if (n > a3 && n <= a4)
      {
        cout << n + 2 << endl;
        for (ll i = n - 1; i >= 3; i--)
        {
          if (i != a2 && i != a1 && i != a3)
            cout << i << " " << n << endl;
        }
        cout << n << " " << a3 << endl;
        cout << n << " " << a3 << endl;
        cout << 256 << " " << 16 << endl;
        cout << 256 << " " << 16 << endl;
        cout << 16 << " " << 4 << endl;
        cout << 16 << " " << 4 << endl;
        cout << 4 << " " << 2 << endl;
        cout << 4 << " " << 2 << endl;


      }
      else if (n > a4)
      {
        cout << n + 3 << endl;
        for (ll i = n - 1; i >= 3; i--)
        {
          if (i != a2 && i != a1 && i != a3 && i != a4)
            cout << i << " " << n << endl;
        }
        cout << n << " " << a4 << endl;
        cout << n << " " << a4 << endl;
        cout << a4 << " " << a3 << endl;
        cout << a4 << " " << a3 << endl;
        cout << a3 << " " << a2 << endl;
        cout << a3 << " " << a2 << endl;
        cout << 16 << " " << 4 << endl;
        cout << 16 << " " << 4 << endl;
        cout << 4 << " " << 2 << endl;
        cout << 4 << " " << 2 << endl;

      }
    }

  }
}