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.*;

/*
polyakoff
*/

public class Main {

    static FastReader in;
    static PrintWriter out;
    static Random rand = new Random();
    static final int oo = (int) 1e9 + 10;
    static final long OO = (long) 2e18 + 20;
    static final int MOD = (int) 1e9 + 7;

    static boolean isPrime(int x) {
        if (x == 1)
            return false;
        for (int i = 2; i * i <= x; i++) {
            if (x % i == 0)
                return false;
        }
        return true;
    }

    static void solve() {
        int n = in.nextInt();

        int a = 1;
        while (!(!isPrime(a) && isPrime(a + n - 1))) {
            a++;
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (i == j)
                    out.print(a + " ");
                else
                    out.print(1 + " ");
            }
            out.println();
        }






    }


    public static void main(String[] args) {
        in = new FastReader();
        out = new PrintWriter(System.out);
//        fileInputOutput();

        int T = 1;
        T = in.nextInt();
        while (T-- > 0)
            solve();

        out.flush();
        out.close();
    }

    static void fileInputOutput() {
        try {
            in = new FastReader("input.txt");
            out = new PrintWriter(new FileOutputStream("output.txt"));
        } catch (FileNotFoundException e) {
            throw new RuntimeException(e);
        }
    }

    static void runInThread() {
        Thread thread = new Thread(null, () -> {
            int T = 1;
//            T = in.nextInt();
            while (T-- > 0)
                solve();
        }, "thread1", 1 << 28);
        thread.start();
        try {
            thread.join();
        } catch (InterruptedException e) {
            throw new RuntimeException(e);
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader() {
            this(System.in);
        }
        FastReader(String file) throws FileNotFoundException {
            this(new FileInputStream(file));
        }
        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }
        String nextLine() {
            String line;
            try {
                line = br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
    }
}