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 PYTHON3):

Solution:
from collections import *
from itertools import *
from bisect import *

def inp():
    return int(input())
def arrinp():
    return [int(x) for x in input().split()]
def is_prime(n):
    if (n <= 1) : 
        return False
    if (n <= 3) : 
        return True
    if (n % 2 == 0 or n % 3 == 0) : 
        return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True
def find_prime(n):
    """
    returns prime number greater than or equal to n
    """
    if(n<=1):
        return 2
    if(is_prime(n)):
        return n
    prime = n
    found = False
    while not found:
        prime +=1
        if(is_prime(prime)):
            found = True
    return prime

def main():
    t = inp()
    for _ in range(t):
        n = inp()
        primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]
        prime_set = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199}
        if(n in prime_set):
            for i in range(n):
                temp = [1 for t in range(n)]
                print(*temp, sep = ' ')
        else:
            i = bisect_left(primes, n)
            #print('value of i', i, 'prime no at i',primes[i])
            diff = primes[i] - (n-1)
            while(diff in prime_set):
                i  += 1
                diff = primes[i] - (n-1)
            
            edge = diff*(n-1)
            #print('diff, edge:',diff, edge)
            i = find_prime(edge)
            corner_diff = i - edge
            #print('value of i', i, primes[i], 'edge candidate vala prime', corner_diff, 'edge candidate')
            while is_prime(corner_diff):
                i = find_prime(i+1)
                corner_diff = i - edge
                #print(corner_diff, 'edge candidate')
            #priniting answer using diff, 1, corner_diff
            for t in range(n-1):
                x = [1 for temp in range(n-1)] + [diff]
                print(*x, sep = ' ')
            x = [diff for temp in range(n-1)] + [corner_diff]
            print(*x, sep = ' ')
if __name__ == '__main__':
    main()