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:
import math
import sys
from typing import List

sys.setrecursionlimit(10 ** 9)


def lmi():
    return list(map(int, input().split()))


def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        return []
    prime = []
    limit = math.sqrt(n)
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        result = solve(n)
        for line in result:
            print(*line)


def solve(n) -> list:
    ans = [[1] * n for _ in range(n)]
    primes = set(get_sieve_of_eratosthenes(10 ** 5))
    cur_num = 4
    tate_sm = 0
    for i in range(n - 1):
        while (n - 1) + cur_num not in primes or cur_num in primes:
            cur_num += 1
        ans[i][-1] = cur_num
        tate_sm += cur_num

    yoko_sm = 0
    for i in range(n - 1):
        while (n - 1) + cur_num not in primes or cur_num in primes:
            cur_num += 1
        ans[-1][i] = cur_num
        yoko_sm += cur_num

    cur_num += 1
    while yoko_sm + cur_num not in primes or tate_sm + cur_num not in primes or cur_num in primes:
        cur_num += 1
    ans[-1][-1] = cur_num

    # for i in range(n):
    #     for j in range(n):
    #         assert not is_prime(ans[i][j])
    #
    # for i in range(n):
    #     assert is_prime(sum(ans[i]))
    #
    # trans_ans = trans(ans)
    # for i in range(n):
    #     assert is_prime(sum(trans_ans[i]))

    return ans


def trans(list_2d) -> list:
    return list(map(list, zip(*list_2d)))

def is_prime(x):
    if x < 2: return False
    if x == 2 or x == 3 or x == 5: return True
    if x % 2 == 0 or x % 3 == 0 or x % 5 == 0: return False

    prime = 7
    step = 4
    while prime <= math.sqrt(x):
        if x % prime == 0: return False

        prime += step
        step = 6 - step

    return True


if __name__ == '__main__':
    main()