Problem: Sasha likes investigating different math objects, for example, magic squares. But Sasha understands that magic squares have already been studied by hundreds of people, so he sees no sense of studying them further. Instead, he invented his own type of square — a prime square. 

A square of size n × n is called prime if the following three conditions are held simultaneously: 

  * all numbers on the square are non-negative integers not exceeding 10^5; 
  * there are no prime numbers in the square; 
  * sums of integers in each row and each column are prime numbers. 



Sasha has an integer n. He asks you to find any prime square of size n × n. Sasha is absolutely sure such squares exist, so just help him!

Input

The first line contains a single integer t (1 ≤ t ≤ 10) — the number of test cases.

Each of the next t lines contains a single integer n (2 ≤ n ≤ 100) — the required size of a square.

Output

For each test case print n lines, each containing n integers — the prime square you built. If there are multiple answers, print any.

Example

Input


2
4
2


Output


4 6 8 1
4 9 9 9
4 10 10 65
1 4 4 4
1 1
1 1

Solution (in JAVA):

Solution:
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public final class Main
{
	static boolean[] prime;
	static void sieveOfEratosthenes(int n) 
    { 
        prime = new boolean[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
                for(int i = p*2; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
          
    } 
	static int next(int a) {
		a++;
		while(prime[a] != false) {
			a++;
		}
		return a;
	}
	public static void main (String[] args) throws java.lang.Exception
	{
		sieveOfEratosthenes(10000);
	    t = s.nextInt();
	    while(t-- > 0){
	    	int n = s.nextInt();
	    	int[][] a = new int[n][n];
	    	a[0][0] = 1;
	    	int sum = 1;
	    	for(int i =1;i<n-1;i++) {
	    		a[0][i] = next(a[0][i-1]);
	    		sum += a[0][i];
	    	}
	    	int x = 1;
	    	while(prime[sum + x] != true) {
	    		x = next(x);
	    	}
	    	a[0][n-1] = x;
	    	for(int i = 1;i<n;i++) {
	    		for(int j = 0;j<n;j++) {
	    			a[i][j] = a[0][(j+i)%n];
	    		}
	    	}
	    	
	    	for(int i = 0;i<n;i++) {
	    		for(int j =0;j<n;j++) {
	    			print(a[i][j] + " ", 0);
	    		}
	    		print("", 1);
	    	}
		}
	}
	/*
		1
		5
		1 2 2 1 3
	 */
	
	public static int t;
    
    static class InputReader
	{
		private BufferedReader br;
		private StringTokenizer st;
		
		public InputReader(InputStream stream)
		{
			br = new BufferedReader(new InputStreamReader(stream));
			st = null;
		}
		
		public String next()
		{
			while(st == null || !st.hasMoreTokens())
			{
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}
		
		public int nextInt()
		{
			return Integer.parseInt(next());
		}
		
		public long nextLong(){
		    return Long.parseLong(next());
		}
		
		public double nextDouble()
		{
			return Double.parseDouble(next());
		}
	}
	
	public static InputReader s = new InputReader(System.in);
    
    public static int[] get(int[] a){
        for(int i = 0;i<a.length;i++){
            a[i] = s.nextInt();
        }
        return a;
    }
    
    public static void print(Object o, int t){
        System.out.print(o.toString());
        if(t == 1){
            System.out.print("\n");
        }
        if(t == 2){
            System.out.print("\t");
        }
	}
    public static void print(Object[] o, int t){
        System.out.print(Arrays.toString(o));
        if(t == 1){
            System.out.print("\n");
        }
        if(t == 2){
            System.out.print("\t");
        }
	}
    
}

class Pair
{
	// Return a map entry (key-value pair) from the specified values
	public static <T, U> Map.Entry<T, U> of(T first, U second)
	{
		return new AbstractMap.SimpleEntry<>(first, second);
	}
}