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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class Main{
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int t=sc.nextInt();
        while (t-->=1){
            int n=sc.nextInt();
            int a[][]= new int[n][n];
            if (n==2){
                for (int i=0;i<2;i++){
                    for (int j=0;j<2;j++)
                    a[i][j]=1;
                }
            }
            else if (n>=3){
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        if (i == j) {
                            a[i][j] = 1;
                        } else if ((i + j) == n - 1) {
                            a[i][j] = 1;
                        } else if (n % 2 != 0 && (i + j) == n - 1) {
                            a[i][j] = 1;
                        } else {
                            a[i][j] = 0;
                        }


                    }
                }
                int x = n / 2;
                a[x][x + 1] = 1;
                a[x - 1][x] = 1;
            }

            for (int i=0;i<n;i++){
                for (int j=0;j<n;j++){
                    System.out.print(a[i][j]+" ");
                }
                System.out.println();
            }

        }
        out.flush();
    }
    //-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    static class Binary implements Comparable<Binary>{
        int num;
        int val;
        Binary(int n,int v){
            num=n;
            val=v;
        }
        public int compareTo(Binary o){
            return val-o.val;
        }
    }
    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static class Pair{
        int i,j;
        Pair(int i,int j){
            this.i=i;
            this.j=j;
        }
    }
    static int mod=(int)1e9+7;
    static long mod(long x){
        return ((x%mod+mod)%mod);
    }
    static long add(long x,long y){
        return mod(mod(x)+mod(y));
    }
    static long mul(long x,long y){
        return mod(mod(x)*mod(y));
    }
    static int[] find(int n,int start,int diff){
        int a[]= new int[n];
        a[0]=start;
        for (int i=1;i<n;i++)a[i]=a[i-1]+diff;
        return a;
    }
    static void swap(int a,int b){
        int c=a;
        a=b;
        b=c;
    }

    static void printArray(int a[]){
        for (int i=0;i<a.length;i++){
            System.out.print(a[i]+" ");
        }
    }
    static boolean sorted(int a[]){
        int n=a.length;
        boolean flag=true;
        for (int i=0;i<n-1;i++){
            if (a[i]>a[i+1])flag=false;
        }
        if (flag)return true;
        else  return false;
    }
    public static int findlog(long n){
        if(n == 0)
            return 0;

        if(n == 1)
            return 0;
        if(n == 2)
            return 1;
        double num = Math.log(n);
        double den = Math.log(2);
        if(den == 0)
            return 0;
        return (int)(num/den);
    }
    public static long gcd(long a,long b){
        if(b%a == 0)
            return a;
        return gcd(b%a,a);
    }
    public static int gcdInt(int a,int b){

        if(b%a == 0)
            return a;

        return gcdInt(b%a,a);

    }

    static void sortReverse(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
//        Collections.sort.(l);
        Collections.sort(l,Collections.reverseOrder());
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    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[] readArrayLong(long n) {
            long[] a=new long[(int)n];
            for (int i=0; i<n; i++) a[i]=nextLong();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }


}