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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;


	
	
	
	
	public class COVID {
	
		static long mod = (int) 1e9 + 7;
		static PrintWriter pw;
			static int n,m;
			
			static ArrayList<Integer>[] adjList;
			
			static boolean[] isPrime;
			static ArrayList<Integer> primes;
			public static void sieve(int N) {// O( n log( log n ) )
				isPrime= new boolean[N+1];//u can save half the memory by neglecting all even numbers since they aren't primes
				primes= new ArrayList<>(N);
				Arrays.fill(isPrime, true);
				isPrime[0]=isPrime[1]=false;
				for(int i=2;i*i<=N;i++) {
					if(isPrime[i]) {
						for(int j=i*i;j<=N;j+=i) {
							isPrime[j]=false;
						}
					}
				}
				for(int i=2;i<=N;i++) {
					if(isPrime[i])primes.add(i);
				}
			}


	static int INF=(int)1e8;
	public static void main(String[] args) throws Exception {
				Scanner sc = new Scanner(System.in);
				PrintWriter pw = new PrintWriter(System.out);

				int t=sc.nextInt();
				sieve((int)1e5);
//				System.out.println(primes.size());
				while(t-->0) {
					int n=sc.nextInt();
					int id=2;
					int[][] grid =new int[n][n];
					for(int i=0;i<n;i++)
						grid[i][i]=primes.get(id++)-1;
					int limit=n;
					if(n%2!=0)limit-=3;
					for(int i=0;i<limit;i++) {
//						grid[i][i]--;
						if(i%2==0) {
							grid[i+1][i]++;
						}else {
							grid[i-1][i]++;
						}
					}
					if(limit!=n) {
						grid[n-2][n-1]++;
						grid[n-3][n-2]++;
						grid[n-1][n-3]++;
					}
					
					
					for(int i=0;i<n;i++)
					{
						for(int j=0;j<n;j++)
							pw.print(grid[i][j]+" ");
						pw.println();
					}
					
				}
				
				pw.flush();
			}
				

	
			
			static class longPair implements Comparable<longPair> {
			long x, y;
	
			public longPair(long a, long b) {
				x = a;
				y = b;
			}
	
			public int compareTo(longPair p) {
				return (p.x == x) ? ((p.y == y) ? 0 : (y > p.y) ? 1 : -1) : (x > p.x) ? 1 : -1;
			}
		}
	
	
		static class Pair implements Comparable<Pair> {
			int x;
			int y;
	
			public Pair(int a, int b) {
				this.x = a;
				y = b;
			}
	
	
			public int compareTo(Pair o) {
				return (x == o.x) ? ((y > o.y) ? 1 : (y == o.y) ? 0 : -1) : ((x > o.x) ? 1 : -1);
			}
	
			@Override
	
			public int hashCode() {
				final int prime = 31;
				int result = 1;
				result = prime * result + x;
				result = prime * result + y;
				return result;
			}
	
			@Override
	
			public boolean equals(Object obj) {
				if (this == obj)
					return true;
				if (obj == null)
					return false;
				if (getClass() != obj.getClass())
					return false;
				Pair other = (Pair) obj;
				if (x != other.x)
					return false;
				if (y != other.y)
					return false;
				return true;
			}
	
		}
	
		static class Scanner {
			StringTokenizer st;
			BufferedReader br;
	
			public Scanner(InputStream s) {
				br = new BufferedReader(new InputStreamReader(s));
			}
	
			public Scanner(String s) throws FileNotFoundException {
				br = new BufferedReader(new FileReader(s));
			}
	
			public long[] nextLongArr(int n) throws IOException {
				long[] arr = new long[n];
				for (int i = 0; i < n; i++)
					arr[i] = nextLong();
				return arr;
			}
	
			public int[] nextIntArr(int n) throws IOException {
				int[] arr = new int[n];
				for (int i = 0; i < n; i++)
					arr[i] = nextInt();
				return arr;
			}
	
			public String next() throws IOException {
				while (st == null || !st.hasMoreTokens())
					st = new StringTokenizer(br.readLine(), " ,");
				return st.nextToken();
			}
	
			public int nextInt() throws IOException {
				return Integer.parseInt(next());
			}
	
			public long nextLong() throws IOException {
				return Long.parseLong(next());
			}
	
			public String nextLine() throws IOException {
				return br.readLine();
			}
	
			public double nextDouble() throws IOException {
				String x = next();
				StringBuilder sb = new StringBuilder("0");
				double res = 0, f = 1;
				boolean dec = false, neg = false;
				int start = 0;
				if (x.charAt(0) == '-') {
					neg = true;
					start++;
				}
				for (int i = start; i < x.length(); i++) {
					if (x.charAt(i) == '.') {
						res = Long.parseLong(sb.toString());
						sb = new StringBuilder("0");
						dec = true;
					} else {
						sb.append(x.charAt(i));
						if (dec)
							f *= 10;
					}
					if (sb.length() == 18) {
						res += Long.parseLong(sb.toString()) / f;
						sb = new StringBuilder("0");
					}
				}
				res += Long.parseLong(sb.toString()) / f;
				return res * (neg ? -1 : 1);
			}
	
			public boolean ready() throws IOException {
				return br.ready();
			}
	
		}
	
		public static void shuffle(int[] a) {
			int n = a.length;
			for (int i = 0; i < n; i++) {
				int r = i + (int) (Math.random() * (n - i));
				int tmp = a[i];
				a[i] = a[r];
				a[r] = tmp;
			}
		}
	
	}