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 JAVA):

Solution:
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

public class Main {
	public static void main (String[] args) {
	    Scanner sc = new Scanner(System.in);
	    int nt = sc.nextInt();
	    while(nt-- > 0){
	        int n = sc.nextInt();
	        if(n==2) {
	            System.out.println(-1);
	            continue;
	        }
	        int val = 1;
	        int [][]mat = new int[n+1][n+1];
	        for (int i =1;i<=n;i++){
	            for (int j=1; j<=n; j++){
	                if((i+j)%2==0) mat[i][j] = val++;
	            }
	        }
	        for (int i =1;i<=n;i++){
	            for (int j=1; j<=n; j++){
	                if(mat[i][j]==0){
	                    System.out.print(val + " ");
	                    val++;
	                } 
	                else {
	                    System.out.print(mat[i][j]+ " ");
	                }
	            }
	            System.out.println();
	        }
	   }
	        
	}
}