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 sys
import re
import random
import math
import copy
from heapq import heappush, heappop, heapify
from functools import cmp_to_key
from bisect import bisect_left, bisect_right
from collections import defaultdict, deque, Counter
# sys.setrecursionlimit(1000000)

# input aliases
input = sys.stdin.readline
getS = lambda: input().strip()
getN = lambda: int(input())
getList = lambda: list(map(int, input().split()))
getZList = lambda: [int(x) - 1 for x in input().split()]

INF = float("inf")
MOD = 10**9 + 7
divide = lambda x: pow(x, MOD-2, MOD)


def isprime(n):
    if n == 1:
        return False
    if n in [2,3,5,7,11,13]:
        return True
    for i in range(2, int(math.sqrt(n) + 10)):
        if n % i == 0:
            return False

    return True

nonprimes = [x for x in range(1, 100001) if not isprime(x)]

def solve(n = 0):
    if n == 0:
        n = getN()
    orn = n

    ans = 0

    for i in nonprimes:
        for j in nonprimes:
            # print(i, j, i+j + orn-2)
            if isprime(i+j + orn-2):
                ans = [i, j]
                break

        if ans:
            break

    # print(ans)
    # return

    ans = [1] * (orn-2) + ans

    ans = ans + ans

    for i in range(orn):
        print(*ans[i:i+orn])


def main():
    # print(len(primes))
    n = getN()
    for _ in range(n):
        solve()

    return
if __name__ == "__main__":
    main()
    # solve()