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 Codeforces.R719Div3;

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

public class ProbC {
    final int mod = (int) 1e9 + 7;
    final double eps = 1e-6;
    final double pi = Math.PI;
    final long inf = Long.MAX_VALUE / 2;


    //------------> Solution starts here!!
    @SuppressWarnings("Main Logic")
    void solve() {
        for (int tc = ii(); tc > 0; tc--) {
            int n =ii();
            if (n == 1) {
                out.println(1);
                continue;
            }
            if (n == 2) {
                out.println(-1);
                continue;
            }
            if (n == 3) {
                int a[][] = {{2,9,7}, {4,6,3}, {1,8,5}};
                print(a);
                continue;
            }
            int a[][] = new int[n][n];
            int num =1;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j+=2) {
                    a[i][j] = num;
                    num++;
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = 1; j < n; j+=2) {
                    a[i][j] = num;
                    num++;
                }
            }
            print(a);
        }
    }

    void print(int a[][]) {
        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < a[i].length; j++) {
                out.print(a[i][j] + " ");
            }
            out.println();
        }
    }

    //------------> Solution ends here!!
    InputStream obj;
    PrintWriter out;
    String check = "";

    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new ProbC().main1();
                } catch (IOException e) {
                    e.printStackTrace();
                } catch (StackOverflowError e) {
                    System.out.println("RTE");
                }
            }
        }, "1", 1 << 26).start();
    }

    void main1() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
        // obj=check.isEmpty() ? new FileInputStream("/home/ankurverma1994/input.txt") : new ByteArrayInputStream(check.getBytes());
        solve();
        out.flush();
        out.close();
    }

    byte inbuffer[] = new byte[1024];
    int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) throw new InputMismatchException();
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) return -1;
        return inbuffer[ptrbuffer++];
    }

    String is() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
        {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    int ii() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    long il() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    boolean isSpaceChar(int c) {
        return (!(c >= 33 && c <= 126));
    }

    int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    float nf() {
        return Float.parseFloat(is());
    }

    double id() {
        return Double.parseDouble(is());
    }

    char ic() {
        return (char) skip();
    }

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

    long[] ila(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) a[i] = il();
        return a;
    }

    String[] isa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) a[i] = is();
        return a;
    }

    double[][] idm(int n, int m) {
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
        return a;
    }

    int[][] iim(int n, int m) {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = ii();
        return a;
    }
}