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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    static Integer MOD = (int) 1e9 + 7;
    static FastReader sc = new FastReader();
    static Print p = new Print();

    public static int mod_add(int a, int b) {
        return (a % MOD + b % MOD) % MOD;
    }

    public static long mod_mul(long a, long b) {
        return (a % MOD * b % MOD) % MOD;
    }


    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }

    static class Print {
        StringBuffer strb = new StringBuffer();

        public void write(Object str) {
            strb.append(str);
        }

        public void writeln(Object str) {
            strb.append(str + "\n");
        }

        public void print() {
            System.out.print(strb);
        }

        public void print(Object obj) {
            System.out.print(obj + "\n");
        }

        public void println() {
            System.out.println(strb);
        }

        public void writeln(int[] arr) {
            for (int val : arr) {
                writeln(val);
            }
        }

        public void writes(int[] arr) {
            for (int val : arr) {
                write(val + " ");
            }
        }
    }

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


    public static long factorial(long n) {
        long res = 1;
        for (int i = 1; i <= n; i++) {
            res = (i % MOD * res % MOD) % MOD;
        }
        return res;
    }

    public static void solve2() {
        int n = sc.nextInt();
        if(n == 1) {
            p.writeln(1);
            return;
        }
        if(n == 2) {
            p.writeln(-1);
            return;
        }
        int[][] res = new int[n][n];
        int curr = 1;
        if(n%2 != 0){
            for(int k=n-1; k>=0; k-=2) {
                for(int i=k,j=0; i<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
            for(int k=2; k<res.length; k+=2) {
                for(int i=0, j=k; j<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
            for(int k=n-2; k>=0; k-=2) {
                for(int i=k,j=0; i<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
            for(int k=1; k<res.length; k+=2) {
                for(int i=0, j=k; j<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
        } else {
            for(int k=n-1; k>=0; k-=2) {
                for(int i=k,j=0; i<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
            for(int k=1; k<res.length; k+=2) {
                for(int i=0, j=k; j<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
            for(int k=n-2; k>=0; k-=2) {
                for(int i=k,j=0; i<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
            for(int k=2; k<res.length; k+=2) {
                for(int i=0, j=k; j<res.length; i++, j++) {
                    res[i][j] = curr++;
                }
            }
        }
        for(int i=0; i<res.length; i++) {
            p.writes(res[i]);
            p.writeln("");
        }


    }
    public static void solve() {
        int n = sc.nextInt();
        int count = 0;
        int div = 10;
        while(n/div != 0) {
            count += 9;
            div*=10;
        }
        int copy = n;
        int min = n/(div/10);
        StringBuilder cstr = new StringBuilder();
        while(copy != 0) {
            cstr.append(min);
            copy/=10;
        }
        if(Integer.parseInt(cstr.toString()) > n) min--;
        count+= min;
        p.writeln(count);
    }

    public static void main(String[] args) {
        int t = 1;
        t = sc.nextInt();
        while (t-- != 0) {
            solve2();
        }
        p.print();
    }


    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        double[] readArrayDouble(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}