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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
  InputStream is;
  PrintWriter out;
  String INPUT = "";
  
  void solve(int TC) throws Exception {
    int n = ni();
    ArrayList<int[]> ans = new ArrayList<>();
    while(n > 2) {
      int m = (int) Math.ceil(Math.sqrt(n));
      for(int i = m+1;i<n;i++) {
        ans.add(new int[] {i, n});
      }
      ans.add(new int[] {n, m});
      ans.add(new int[] {n, m});
      n = m;
    }
    pn(ans.size());
    for(int[] i: ans) pn(i[0] + " " + i[1]);
  }
  
  boolean TestCases = true;
  public static void main(String[] args) throws Exception { new Main().run(); }
  
  void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
  static void dbg(Object... o){System.err.println(Arrays.deepToString(o));}
  
  void run() throws Exception {
    is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
    out = new PrintWriter(System.out);
    long s = System.currentTimeMillis();
    int T = TestCases ? ni() : 1;
    for(int t=1;t<=T;t++) solve(t);
    out.flush();
    if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
  }
    
  void p(Object o) { out.print(o); }
  void pn(Object o) { out.println(o); }
  void pni(Object o) { out.println(o);out.flush(); }
  
  int ni() {
    int num = 0, b;
    boolean minus = false;
    while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if(b == '-') {
      minus = true;
      b = readByte();
    }
    while(true) {
      if(b >= '0' && b <= '9'){
        num = num * 10 + (b - '0');
      } else {
        return minus ? -num : num;
      }
      b = readByte();
    }
  }
  
  long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if(b == '-') {
      minus = true;
      b = readByte();
    }
    while(true) {
      if(b >= '0' && b <= '9') {
        num = num * 10 + (b - '0');
      } else {
        return minus ? -num : num;
      }
      b = readByte();
    }
  }
    
  double nd() { return Double.parseDouble(ns()); }
  char nc() { return (char)skip(); }
  
  int BUF_SIZE = 1024 * 8;
  byte[] inbuf = new byte[BUF_SIZE];
  int lenbuf = 0, ptrbuf = 0;
  
  int readByte() {
    if(lenbuf == -1)throw new InputMismatchException();
    if(ptrbuf >= lenbuf){
      ptrbuf = 0;
      try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
      if(lenbuf <= 0)return -1;
    } return inbuf[ptrbuf++];
  }
  
  boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
  int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
  String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while(!(isSpaceChar(b))) {
      sb.appendCodePoint(b); b = readByte();
    } return sb.toString();
  }
  
  char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while(p < n && !(isSpaceChar(b))){
      buf[p++] = (char)b;
      b = readByte();
    } return n == p ? buf : Arrays.copyOf(buf, p);
  }
  
  void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}