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 notYourMatrix(n):
    if n == 2:
        return [[-1]]
    l=[[0 for i in range(n)] for j in range(n)]
    r=0
    s=0
    p=0
    dir =1
    for i in range(1,n*n+1):
        l[r][s]=i
        if r == n-1 or s == n-1:
            if dir ==0:
                r = p
                s = 0
                dir =1
            else:
                p+=1
                r=0
                s = p
                dir = 0
        else:
            r+=1
            s+=1
    return l
i= int(input())
l=[]
for j in range(i):
    x = int(input())
    ans = notYourMatrix(x)
    l= l+ans
for a in l:
    print(*a)