Problem: There are n bags with candies, initially the i-th bag contains i candies. You want all the bags to contain an equal amount of candies in the end. 

To achieve this, you will:

  * Choose m such that 1 ≤ m ≤ 1000

  * Perform m operations. In the j-th operation, you will pick one bag and add j candies to all bags apart from the chosen one.




Your goal is to find a valid sequence of operations after which all the bags will contain an equal amount of candies. 

  * It can be proved that for the given constraints such a sequence always exists.

  * You don't have to minimize m.

  * If there are several valid sequences, you can output any.

Input

Each test contains multiple test cases.

The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first and only line of each test case contains one integer n (2 ≤ n≤ 100). 

Output

For each testcase, print two lines with your answer. 

In the first line print m (1≤ m ≤ 1000) — the number of operations you want to take. 

In the second line print m positive integers a_1, a_2, ..., a_m (1 ≤ a_i ≤ n), where a_j is the number of bag you chose on the j-th operation.

Example

Input


2
2
3


Output


1
2
5
3 3 3 1 2

Note

In the first case, adding 1 candy to all bags except of the second one leads to the arrangement with [2, 2] candies.

In the second case, firstly you use first three operations to add 1+2+3=6 candies in total to each bag except of the third one, which gives you [7, 8, 3]. Later, you add 4 candies to second and third bag, so you have [7, 12, 7], and 5 candies to first and third bag — and the result is [12, 12, 12].

Solution (in JAVA):

Solution:
import java.util.*;
 
 
import static java.lang.Math.*;
 
import java.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.math.BigInteger; 
 
public class Main 
{ 
 
	static int mod = 1000000007;
	static int MOD = 1000000007;
	static final long M = (int)1e9+7;
 
	
	static class Pair implements Comparable<Pair>
	{
		int a, b;
		public Pair(int aa, int bb)
		{
			a = aa; b = bb;
		}
		public int compareTo(Pair p)
		{
			if(a == p.a) return b - p.b;
			return a - p.a;
		}
	}
	
	static class Reader 
	{ 
		final private int BUFFER_SIZE = 1 << 16; 
		private DataInputStream din; 
		private byte[] buffer; 
		private int bufferPointer, bytesRead; 
 
		public Reader() 
		{ 
			din = new DataInputStream(System.in); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
 
		public Reader(String file_name) throws IOException 
		{ 
			din = new DataInputStream(new FileInputStream(file_name)); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
 
		public String next() throws IOException 
		{ 
			byte[] buf = new byte[64]; // line length 
			int cnt = 0, c; 
			while ((c = read()) != -1) 
			{ 
				if (c == '\n') 
					break; 
				buf[cnt++] = (byte) c; 
			} 
			return new String(buf, 0, cnt); 
		} 
		
		public int nextInt() throws IOException 
		{ 
			int ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do
			{ 
				ret = ret * 10 + c - '0'; 
			} while ((c = read()) >= '0' && c <= '9'); 
 
			if (neg) 
				return -ret; 
			return ret; 
		}
		int[] readArray(int n) throws IOException {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
 
		public long nextLong() throws IOException 
		{ 
			long ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
			if (neg) 
				return -ret; 
			return ret; 
		} 
 
		public double nextDouble() throws IOException 
		{ 
			double ret = 0, div = 1; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
 
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
 
			if (c == '.') 
			{ 
				while ((c = read()) >= '0' && c <= '9') 
				{ 
					ret += (c - '0') / (div *= 10); 
				} 
			} 
 
			if (neg) 
				return -ret; 
			return ret; 
		} 
 
		private void fillBuffer() throws IOException 
		{ 
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
			if (bytesRead == -1) 
				buffer[0] = -1; 
		} 
 
		private byte read() throws IOException 
		{ 
			if (bufferPointer == bytesRead) 
				fillBuffer(); 
			return buffer[bufferPointer++]; 
		} 
 
		public void close() throws IOException 
		{ 
			if (din == null) 
				return; 
			din.close(); 
		}
 
		public BigInteger nextBigInteger() {
			// TODO Auto-generated method stub
			return null;
		}
 
	}
 
	
	public static boolean isPrime(int n) {
		if(n == 1)
		{
			return false;
		}
		for(int i = 2;i*i<=n;i++)
		{
			if(n%i == 0)
			{
				return false;
			}
		}
		return true;
	}
	
	public static ArrayList<Integer> sieveList(int n)
	{
	       
		ArrayList<Integer> list = new ArrayList<>();
	    boolean prime[]=new boolean[n+2];
	    for(int i=0;i<(n+1);i++)
	    {
	        prime[i]=true;
	    }
	    for(int i=2;i*i<=(n+1);i++)
	    {
	        if(prime[i]==true)
	        for(int p=i*2;p<=(n+1);p+=i)
	        prime[p]=false;
	    }
	    for(int i=2;i<=(n+1);i++)
	    {
	        if(prime[i]==true)
	        list.add(i);
	    }
	    return list;
}
	
	public static int gcd(int a, int b)
	{
		if(b == 0)
		 return a;
		
		else
		return gcd(b,a%b);
	}
	
	public static long LongGCD(long a, long b)
	{
		if(b == 0)
			 return a;
			
			else
			return LongGCD(b,a%b);
	}
 
 
	public static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
	
	public static int phi(int n)  //euler totient function
    { 
        int result = 1; 
        for (int i = 2; i < n; i++) 
            if (gcd(i, n) == 1) 
                result++; 
        return result; 
    }
	
	
	public static int[] computePrefix(int arr[], int n)
	{
		int[] prefix = new int[n];
		prefix[0] = arr[0];
		for(int i = 1;i<n;i++)
		{
			prefix[i] = prefix[i-1]+arr[i];
		}
		
		return prefix;
	}
	
	
	public static int fastPow(int x, int n) //include mod at each step if asked and in args of fn too
	{
		if(n == 0)
			return 1;
		else if(n%2 == 0)
			return fastPow(x*x,n/2);
		else
			return x*fastPow(x*x,(n-1)/2);
	}
	
	
	
	static int LowerBound(int a[], int x) {
		  int l=-1,r=a.length;
		  while(l+1<r) {
		    int m=(l+r)>>>1;
		    if(a[m]>=x) r=m;
		    else l=m;
		  }
		  return r;
		}
	
	
	static int UpperBound(int a[], int x) {
	    int l=-1,r=a.length;
	    while(l+1<r) {
	       int m=(l+r)>>>1;
	       if(a[m]<=x) l=m;
	       else r=m;
	    }
	    return l+1;
	 }
	
	
	   static int power(int x, int y, int p)
	    {
	 
	        int res = 1;
	 
	        x = x % p;
	 
	        while (y > 0) {
	            if (y % 2 == 1)
	                res = (res * x) % p;
	 
	            y = y >> 1; 
	            x = (x * x) % p;
	        }
	 
	        return res;
	    }
	 
	    static int modInverse(int n, int p)
	    {
	        return power(n, p - 2, p);
	    }
	    
	    //Fermat's little theorem for nCr % p.
	    static int nCrModPFermat(int n, int r,
	                             int p)
	    {
	 
	          if (n<r) 
	              return 0;
	        if (r == 0)
	            return 1;
	        int[] fac = new int[n + 1];
	        fac[0] = 1;
	 
	        for (int i = 1; i <= n; i++)
	            fac[i] = fac[i - 1] * i % p;
	 
	        return (fac[n] * modInverse(fac[r], p)
	                % p * modInverse(fac[n - r], p)
	                % p)
	            % p;
	    }
	    
	    
		public static void Sort(int[] a) {
			List<Integer> l=new ArrayList<>();
			for (int i:a) l.add(i);
			Collections.sort(l);
			//Collections.reverse(l);  //Use to Sort decreasingly 
			for (int i=0; i<a.length; i++) a[i]=l.get(i);
		}
		
	
	public static void main(String[] args) throws IOException 
	{ 
		Reader sc = new Reader();
		
		PrintWriter out = new PrintWriter(System.out);
		
		int t = sc.nextInt();
		while(t-- > 0)
		{
			int n = sc.nextInt();
			out.println(n);
			for(int i = 1;i<=n;i++)
			{
				out.print(i + " ");
			}
		}
		System.out.println();
	
		out.close();
	}
}