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.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder();
        Combination comb = new Combination(1005);
        long mod = (long)1e9+7;
        int T = sc.nextInt();
        for(int ti = 0; ti < T; ti++){
            int n = sc.nextInt();
            int[][] ans = new int[n][n];
            int nowj = 0;
            for(int i = 0; i < n; i++){
                for(int j = 0; j < 2; j++){
                    ans[i][nowj]++;
                    nowj = (nowj+1) % n;
                }
            }
            for(int i = 0; i < n; i++){
                for(int j = 0; j < n; j++){
                    sb.append(ans[i][j]).append(" ");
                }
                pw.println(sb.toString().trim());
                sb.setLength(0);
            }
        }
        pw.flush();
    }

    static class GeekInteger {
        public static void save_sort(int[] array) {
            shuffle(array);
            Arrays.sort(array);
        }
 
        public static int[] shuffle(int[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                int randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }
 
    }
}

class Combination {
    final static long mod = (long)1e9+7;
    private static long[] fact, ifact;
    public Combination(int n){
        fact = new long[n+1];
        ifact = new long[n+1];
        fact[0] = 1;
        long ln = n;
        for (long i = 1; i <= ln; ++i){
            int ii = (int)i;
            fact[ii] = fact[ii-1]%mod * i % mod;
        }
        ifact[n] = pow(fact[n],this.mod-2);
        for (int i = n; i >= 1; --i){
            int ii = (int)i;
            ifact[ii-1] = ifact[ii]%mod*i%mod;
        }
    }
    
    public static long comb(int n, int k){
        if (k < 0 || k > n) return 0;
        return fact[n] % mod * ifact[k] % mod * ifact[n-k] % mod;
    }
    
    public static long perm(int n, int k){
        return comb(n,k) * fact[k] % mod;
    }
    
    public static long pow(long a,long b) {
        long ret = 1;
        long tmp = a;
        while(b>0) {
            if((b&1)==1){
                ret = (ret * tmp) % mod;
            }
            tmp = (tmp * tmp) % mod;
            b = b>>1;
        }
        return ret;
    }
}


class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }
    
    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}