Problem: We will consider the numbers a and b as adjacent if they differ by exactly one, that is, |a-b|=1.

We will consider cells of a square matrix n × n as adjacent if they have a common side, that is, for cell (r, c) cells (r, c-1), (r, c+1), (r-1, c) and (r+1, c) are adjacent to it.

For a given number n, construct a square matrix n × n such that: 

  * Each integer from 1 to n^2 occurs in this matrix exactly once; 
  * If (r_1, c_1) and (r_2, c_2) are adjacent cells, then the numbers written in them must not be adjacent. 

Input

The first line contains one integer t (1 ≤ t ≤ 100). Then t test cases follow.

Each test case is characterized by one integer n (1 ≤ n ≤ 100).

Output

For each test case, output: 

  * -1, if the required matrix does not exist; 
  * the required matrix, otherwise (any such matrix if many of them exist). 



The matrix should be outputted as n lines, where each line contains n integers.

Example

Input


3
1
2
3


Output


1
-1
2 9 7
4 6 3
1 8 5

Solution (in PYTHON3):

Solution:
def gcd(a, b):
	if b == 0:
		return a
	return gcd(b, a%b)

t = int(input())
for test in range(t):
	n = int(input())
	if n == 1: 
		print(1)
	elif n == 2:
		print(-1)
	else:
		a = [0 for i in range(n**2)]
		value = 1
		idx = 0
		for i in range(2,n):
			if gcd(i, n**2) == 1:
				prime = i
				break
		while(value <= n**2):
			a[idx] = value
			value += 1
			idx += prime
			idx %= n**2
		#print(prime)
		for i in range(n**2):
			print(a[i],end=" ")
			if (i+1) % n == 0:
				print()