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.StringTokenizer;

public class D {
    static FastReader reader = new FastReader();
    static OutputWriter out = new OutputWriter(System.out);
    static int log(int x, int y) {
        int res = 0;
        while(x != 1) {
            if(x % y != 0) {
                x = x/y + 1;
            } else {
                x = x/y;
            }
            res++;
        }
        return res;
    }

    public static void main(String[] args) {
        int tests = reader.nextInt();
        for(int test = 1; test <= tests; test++) {
            int n = reader.nextInt();


            if(n < 9) {
                out.println(n-3 + log(n, 2));
                for(int i = 3; i <= n - 1; i++) {
                    out.println(i + " " + (i+1));
                }
                for(int i = 0; i < log(n, 2); i++) {
                    out.println(n + " " + 2);
                }
                continue;
            }
            StringBuilder res = new StringBuilder();
            int count = 0;
            for(int i = 3; i < 8; i++) {
                count++;
                res.append(i + " " + (i+1));
                res.append('\n');
            }
            for(int i = 9; i < n; i++) {
                res.append(i + " " + (i+1));
                res.append('\n');

                count++;
            }
            for(int i = 0; i < log(n, 8); i++) {
                res.append(n + " " + 8);
                res.append('\n');

                count++;
            }
            count += 3;
            res.append(8 + " " + 2);
            res.append('\n');

            res.append(8 + " " + 2);
            res.append('\n');

            res.append(8 + " " + 2);
            res.append('\n');

            out.println(count);
            out.println(res.toString());

            out.println();
        }
        out.flush();
    }


    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(char[] array) {
            writer.print(array);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void print(double[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void print(long[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void println(int[] array) {
            print(array);
            writer.println();
        }

        public void println(double[] array) {
            print(array);
            writer.println();
        }

        public void println(long[] array) {
            print(array);
            writer.println();
        }

        public void println() {
            writer.println();
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void print(char i) {
            writer.print(i);
        }

        public void println(char i) {
            writer.println(i);
        }

        public void println(char[] array) {
            writer.println(array);
        }

        public void printf(String format, Object... objects) {
            writer.printf(format, objects);
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }

        public void print(long i) {
            writer.print(i);
        }

        public void println(long i) {
            writer.println(i);
        }

        public void print(int i) {
            writer.print(i);
        }

        public void println(int i) {
            writer.println(i);
        }

        public void separateLines(int[] array) {
            for (int i : array) {
                println(i);
            }
        }
    }
}