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 hiougyf;
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
public class Solution {	
		public static void main(String[] args){  
			Scanner sc =new Scanner(System.in);
			int t=sc.nextInt();
			while(t-->0) {
				int n=sc.nextInt();
				int a[][]=new int[n][n];
				for(int i=0;i<n;i++) {
					for(int j=0;j<n;j++) {
						if(i==j) {
							a[i][j]=1;
							a[i][n-j-1]=1;
						}
					}
				}
				if(n%2!=0) {
					a[0][n/2]=1;
					a[n/2][0]=1;
				}
				for(int i=0;i<n;i++) {
					for(int j=0;j<n;j++) {
						System.out.print(a[i][j]+" ");
					}
					System.out.println();
				}
			}
		}
		 static void sieveOfEratosthenes(int n,ArrayList<Integer> a) 
		    { 
		        // Create a boolean array "prime[0..n]" and initialize 
		        // all entries it as true. A value in prime[i] will 
		        // finally be false if i is Not a prime, else true. 
		        boolean 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] is not changed, then it is a prime 
		            if(prime[p] == true) 
		            { 
		                // Update all multiples of p 
		                for(int i = p*p; i <= n; i += p) 
		                    prime[i] = false; 
		            } 
		        } 
		          
		        // Print all prime numbers 
		        for(int i = 2; i <= n; i++) 
		        { 
		            if(prime[i] == true) 
		               a.add(i);
		        } 
		    } 
	  public static int floorSqrt(int x) 
	    { 
	        // Base Cases 
	        if (x == 0 || x == 1) 
	            return x; 
	  
	        // Do Binary Search for floor(sqrt(x)) 
	        int start = 1, end = x, ans=0; 
	        while (start <= end) 
	        { 
	            int mid = (start + end) / 2; 
	  
	            // If x is a perfect square 
	            if (mid*mid == x) 
	                return mid; 
	  
	            // Since we need floor, we update answer when mid*mid is 
	            // smaller than x, and move closer to sqrt(x) 
	            if (mid*mid < x) 
	            { 
	                start = mid + 1; 
	                ans = mid; 
	            } 
	            else   // If mid*mid is greater than x 
	                end = mid-1; 
	        } 
	        return ans; 
	    } 
		static int div(int n,int b) {
			int g=-1;
			for(int i=2;i<=Math.sqrt(n);i++) {
				if(n%i==0&&i!=b) {
					g=i;
					break;
				}
			}
			return g;
		}
	 
	  
	  public static int gcd(int a, int b) 
	    { 
	        if (a == 0) 
	            return b; 
	          
	        return gcd(b%a, a); 
	    } 
	   public static int lcm(int a, int b)  
	  {  
	     return (a*b)/gcd(a, b);  
	  }  
	   public static boolean isPrime1(int n) {
           if (n <= 1) {
               return false;
           }
           if (n == 2) {
               return true;
           }
           for (int i = 2; i <= Math.sqrt(n) + 1; i++) {
               if (n % i == 0) {
                   return false;
               }
           }
           return true;
       }
       public static boolean isPrime(int n) {
           if (n <= 1) {
               return false;
           }
           if (n == 2) {
               return true;
           }
           if (n % 2 == 0) {
               return false;
           }
           for (int i = 3; i <= Math.sqrt(n) + 1; i = i + 2) {
               if (n % i == 0) {
                   return false;
               }
           }
           return true;
       }
	      
	
}