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

public class P3 {
    private static class Pair<K, V>{
        K k;
        V v;
    
        Pair(K k, V v){
            this.k = k;
            this.v = v;
        }
    
        public K getKey() {
            return k;
        }
    
        public V getValue() {
            return v;
        }
    }
    
    private static class Disj{
        private int[] parent;
        private int components;
        Disj(int n){
            parent = new int[n];
            components = n;
            make_set();
        }
    
        private void make_set(){
            for (int i = 0; i < parent.length; i++) {
                parent[i] = i;
            }
        }
    
        public void union(int a, int b) {
            a = find(a);
            b = find(b);
            if(a != b) {
                parent[a] = b;
                components--;
            }
        }
    
        public int find(int x) {
            if(x != parent[x]){
                parent[x] = find(parent[x]);
            }
    
            return parent[x];
        }
    
        public int getComponentCount() {
            return components;
        }
    }
    
    private static class FastReader {
        private BufferedReader br;
        private StringTokenizer st;
    
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
    
        public FastReader(String inp) throws FileNotFoundException{
            try{
                br = new BufferedReader(new FileReader(inp));
            } catch(Exception e){
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }
    
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
    
        int nextInt() { return Integer.parseInt(next()); }
    
        long nextLong() { return Long.parseLong(next()); }
    
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
    
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] nextIntArr(int n){
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(next());
            }
            return arr;
        }

        char[] nextCharArr(int n){
            char[] arr = new char[n];
            for (int i = 0; i < n; i++) {
                arr[i] = next().charAt(0);
            }
            return arr;
        }

        String[] nextStringArr(int n){
            String[] arr = new String[n];
            for (int i = 0; i < n; i++) {
                arr[i] = next();
            }
            return arr;
        }
    }
    
    private static class Display{
        BufferedWriter bw;
        Display(){
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        public void flushOutput(){
            try {
                bw.flush();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void println(){
            try {
                bw.write("\n");
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void println(String output){
            try {
                bw.write(output + "\n");
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void println(int output){
            try {
                bw.write(output + "\n");
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void println(char output){
            try {
                bw.write(output + "\n");
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void print(String output){
            try {
                bw.write(output);
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void print(int output){
            try {
                bw.write(output);
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void print(char output){
            try {
                bw.write(output);
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public void printMatrix(int[][] arr) throws IOException{
            for (int i = 0; i < arr.length; i++) {
                for (int j = 0; j < arr[i].length; j++) {
                    print(arr[i][j] + " ");
                }
                println();
            }
            println();
        }
    
        public void printMatrix(String[][] arr){
            for (int i = 0; i < arr.length; i++) {
                for (int j = 0; j < arr[i].length; j++) {
                    print(arr[i][j] + " ");
                }
                println();
            }
            println();
        }
    
        public void printMatrix(char[][] arr){
            for (int i = 0; i < arr.length; i++) {
                for (int j = 0; j < arr[i].length; j++) {
                    print(arr[i][j] + " ");
                }
                println();
            }
            println();
        }
    
        public void printArr(int[] arr){
            for (int i = 0; i < arr.length; i++) {
                print(arr[i] + " ");
            }
            println();
        }
    
        public void printArr(String[] arr){
            for (int i = 0; i < arr.length; i++) {
                print(arr[i] + " ");
            }
            println();
        }
    
        public void printArr(char[] arr){
            for (int i = 0; i < arr.length; i++) {
                print(arr[i] + " ");
            }
            println();
        }
    }

    private static FastReader r;
    private static Display d;
    public static void main(String[] args) throws FileNotFoundException {
        r = new FastReader("input.txt");
        d = new Display();

        int t = r.nextInt();
        while(t-- > 0) {
            solve();
        }

        d.flushOutput();
    }
    
    private static void solve(){
        int n = r.nextInt();

        if(n == 2){
            d.println(-1);
            return;
        }

        var v = new ArrayList<Integer>();
        for (int i = 1; i <= n * n; i+=2) {
            v.add(i);
        }
        for (int i = 2; i <= n * n; i+=2) {
            v.add(i);
        }
        // System.out.println(v);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                d.print((v.get(0) + " "));
                v.remove(0);
            }
            d.println();
        }
    }
}