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
{
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
    public static int gcd(int a,int b)
    {
        if(a>b)
        return gcd(b,a);
        if(b%a==0)
        return a;
        return gcd(b%a,a);
    }
    public static void main(String args[])throws Exception
    {
        Reader sc=new Reader();
        PrintWriter pw=new PrintWriter(System.out);
        boolean isPrime[]=new boolean[(int)1e6+1];
        Arrays.fill(isPrime,true);
        for(int i=2;i*i<isPrime.length;i++)
        {
            for(int j=i*i;j<isPrime.length;j+=i)
            isPrime[j]=false;
        }
        TreeSet<Integer> ts=new TreeSet<>();
        for(int i=2;i<isPrime.length;i++)
        {
            if(isPrime[i])
            ts.add(i);
        }
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            //int x=sc.nextInt();
            
            int arr[][]=new int[n][n];
            for(int i=0;i<n-1;i++)
            {
                for(int j=0;j<n-1;j++)
                arr[i][j]=1;
            }
            int curr=n-1,temp=n-1;
            while(ts.ceiling(curr)!=null)
            {
                int c=ts.ceiling(curr);
                if(isPrime[c-n+1])curr=c+1;
                else
                {
                    curr=c-temp;
                    break;
                }
            }
            for(int i=0;i<n-1;i++)
            arr[n-1][i]=arr[i][n-1]=curr;
            curr=(n-1)*curr;
            temp=curr;
            while(ts.ceiling(curr)!=null)
            {
                int c=ts.ceiling(curr);
                if(isPrime[c-temp])curr=c+1;
                else
                {
                    curr=c-temp;
                    break;
                }
            }
            arr[n-1][n-1]=curr;
            for(int i=0;i<n;i++)
            {
                for(int j=0;j<n;j++)
                pw.print(arr[i][j]+" ");
                pw.println();
            }
        }
        pw.flush();
        pw.close();
    }
}