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

@SuppressWarnings("unchecked")
public class B{

    public static boolean isPrime(int n){
        for(int i=2;i<=n/2;i++){
            if(n%i==0)return false;
        }
        return true;
    }

    public static void main(String args[])throws IOException{
        int t=sc.nextInt();

        while(t-->0){
            int n=sc.nextInt();
            // a[i] < = 10^5

            if(n==2){
                out.println("1 1");
                out.println("1 1");
                continue;
            }

            int[] a = new int[n];
            for(int i=0;i<n-1;i++)
                a[i]=1;
            int s1 = n-1;
            int sum = 113;
            
            if(isPrime(sum-s1)){
                a[0]=0;
                s1-=1;
            }
            a[n-1] = sum-s1;

            for(int i=0;i<n;i++){
                int j=i;
                do{
                    out.print(a[j]+" ");
                    j=(j+1)%n;
                }while(j!=i);
                out.println();
            }
        }
        out.close();
    }
    

    static int M=(int)Math.pow(10,9)+7;

    public static void sort(int[] arr,boolean reverse){
        ArrayList<Integer> list = new ArrayList<Integer>();
        int n =arr.length;
        for(int i=0;i<n;i++){
            list.add(arr[i]);
        }

        if(reverse)
        Collections.sort(list,Collections.reverseOrder());
        else
        Collections.sort(list);

        for(int i=0;i<n;i++){
            arr[i] = list.get(i);
        }
    }

    public static double min(double ...a){
        double min=Double.MAX_VALUE;
        for(double i : a)
        min =Math.min(i,min);
        return min;
    }

    public static long min(long ...a){
        long min=Long.MAX_VALUE;
        for(long i : a)
        min =Math.min(i,min);
        return min;
    }

    public static int min(int ...a){
        int min=Integer.MAX_VALUE;
        for(int i : a)
        min =Math.min(i,min);
        return min;
    }

    public static double max(double ...a){
        double max=Double.MIN_VALUE;
        for(double i : a)
        max =Math.max(i,max);
        return max;
    }

    public static long max(long ...a){
        long max=Long.MIN_VALUE;
        for(long i : a)
        max =Math.max(i,max);
        return max;
    }

    public static int max(int ...a){
        int max=Integer.MIN_VALUE;
        for(int i : a)
        max =Math.max(i,max);
        return max;
    }
    static class Pair{

        // Implementing equals() and hashCode()
        // Map<Pair, V> map = //...

        private final int x;
        private final int y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pair)) return false;
            Pair pair = (Pair) o;
            return x == pair.x && y == pair.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }
    }

    static FastScanner sc = new FastScanner();
    static PrintWriter out =new PrintWriter(System.out);

    static class FastScanner {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st=new StringTokenizer("");
            String next() {
                while (!st.hasMoreTokens())
                    try {
                        st=new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                return st.nextToken();
            }
            
            int nextInt() {
                return Integer.parseInt(next());
            }
            int[] readArray(int n) {
                int[] a=new int[n];
                for (int i=0; i<n; i++) a[i]=nextInt();
                return a;
            }
            long nextLong() {
                return Long.parseLong(next());
            }
            public long[] readLongArray(int n) {
                long[] a=new long[n];
                for (int i=0; i<n; i++) a[i]=nextLong();
                return a;
            }
    }
}