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:

import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Map;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.Vector;
import javafx.util.Pair;

public class NewClass1{

	static long gcd(long a,long b){
		if(b==0){
			return a;
		}
		return gcd(b,a%b);
	}

	public static void main(String[] args){
		Scanner fs=new Scanner(System.in);
		int t=fs.nextInt();
		out:
		while(t-->0){
			int n=fs.nextInt();
			if(n==1){
				System.out.println("1");
			}
			else if(n==2){
				System.out.println("-1");
			} else if(n==3){
				System.out.println("1 8 3");
				System.out.println("4 2 6");
				System.out.println("7 5 9");
				/*int a[][]={{1,8,3},{4,2,6},{7,5,9}};
				
				for(int i=0;i<n;i++)
				{
				for(int j=0;j<n;j++)
				{
					System.out.print(a[i][j]+" ");
				}
					System.out.println();
				}*/
			} else{
				Vector<Integer> v[]=new Vector[n+1];
				for(int i=1;i<=n;i+=2){
					v[i]=new Vector();
					int k=i;
					for(int ii=0;ii<n;ii++){
						v[i].add(k);
						k+=n;
					}
				}
				for(int i=2;i<=n;i+=2){
					v[i]=new Vector();
					int k=i;
					for(int ii=0;ii<n;ii++){
						v[i].add(k);
						k+=n;
					}
				}
				for(int i=1;i<=n;i++)
				{
					if(i%2==0)
					{
						for(int j=0;j<v[i].size();j++)
						{
							System.out.print(v[i].get(j)+" ");
						}
						System.out.println();
					}
					
				}
				for(int i=1;i<=n;i++)
				{
					if(i%2!=0)
					{
						for(int j=0;j<v[i].size();j++)
						{
							System.out.print(v[i].get(j)+" ");
						}
						System.out.println();
					}
					
				}
			}
		}

	}
}