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.util.*;
import java.io.*;

public class _1469D {
    static int[] MODS = {1000000007, 998244353, 1000000009};
    static int MOD = MODS[0];
    static long[] fact, inv;

    public static void main(String[] args) {
        sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            ArrayList<Pair> list = new ArrayList<>();
            solve(n, list);
            out.println(list.size());
            for (Pair x : list) {
                out.println(x);
            }
        }
        out.close();
    }

    static void solve(int x, ArrayList<Pair> list) {
        if (x <= 2) {
            return;
        }
        int y = Math.max(1, (int) Math.sqrt(x) - 2);
        while (y < Math.ceil(1.0 * x / y)) {
            y++;
        }
        for (int i = y + 1; i < x; i++) {
            list.add(new Pair(i, x));
        }
        list.add(new Pair(x, y));
        list.add(new Pair(x, y));
        solve(y, list);
    }

    static class Pair {
        int a, b;
        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
        public String toString() {
            return a + " " + b;
        }
    }

    public static void printArray(int[] arr) {
        for (int x : arr) {
            out.print(x + " ");
        }
        out.println();
    }

    public static long pow(long base, int power) {
        if (power == 0) {
            return 1;
        }
        long sqrt = pow(base, power / 2);
        sqrt = (sqrt * sqrt) % MOD;
        if (power % 2 == 1) {
            sqrt = (sqrt * base) % MOD;
        }
        return sqrt;
    }

    public static long inverse(long x) {
        return pow(x, MOD - 2);
    }

    public static long choose(int n, int k) {
        long ans = 1;
        for (int i = 0; i < k; i++) {
            ans = ans * (n - i);
        }
        for (int i = 1; i <= k; i++) {
            ans /= i;
        }
        return ans;
    }

    public static void precomputeFactorial(int n) {
        fact = new long[n + 1];
        inv = new long[n + 1];
        fact[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= n; i++) {
            fact[i] = (fact[i - 1] * i) % MOD;
            inv[i] = inverse(fact[i]);
        }
    }

    public static int[] sort(int[] arr) {
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < arr.length; i++) {
            list.add(arr[i]);
        }
        Collections.sort(list);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = list.get(i);
        }
        return arr;
    }

    public static void scan(long[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextLong();
        }
    }

    public static void scan(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextInt();
        }
    }

    public static MyScanner sc;
    public static PrintWriter out;

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }
    }
}