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 bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key
import sys
input = sys.stdin.readline
M = mod = 998244353
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
 
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]

primes = [True for i in range(10 ** 5 + 19)]
for i in range(2, 10 ** 5 + 5):
    if primes[i]:
        for j in range(2 * i, 10 ** 5 + 5, i):
            primes[j] = False
mymat = [[-1 for j in range(101)] for i in range(101)]
mymat[0][0] = mymat[0][1] = mymat[0][2] = 1
mymat[1][0] = mymat[1][1] = mymat[1][2] = 1
mymat[2][0] = mymat[2][1] = mymat[2][2] = 1

# for i in range(4):
#     print(*mymat[i][:4])
        

primes = [i for i in range(10 ** 5 + 5) if primes[i]]
primeset = set(primes)
primeset.remove(0)
# print(primeset)
# print(primes[:14])

for i in range(100):
    cursum = 0
    start = i
    if i < 3:
        start = 3
        cursum = 3 
    else:
        for j in range(i):cursum += mymat[i][j]
    # print("CURRSUM", cursum)
    for j in range(start, 100):
        ind = bl(primes, cursum) + 1
        # print('Prime is : ', ind,  primes[ind])
        while (primes[ind] - cursum) in primeset:
            # print(i, j, ind, primes[ind] - cursum, cursum)
            ind += 1
        temp = primes[ind] - cursum
        mymat[i][j] = mymat[j][i] = temp
        cursum += temp
        
        
        
        
        
for i in range(100 - 1, -1, -1): 
    for j in range(100):
        mymat[j][i] = mymat[i][j]
        
        
for _ in range(val()):
    n = val()
    
    for i in range(n):
        for j in range(n):
            print(mymat[i][j], end = ' ')
        print()