Problem: Let us define a magic grid to be a square matrix of integers of size n × n, satisfying the following conditions. 

  * All integers from 0 to (n^2 - 1) inclusive appear in the matrix exactly once. 
  * [Bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all elements in a row or a column must be the same for each row and column. 



You are given an integer n which is a multiple of 4. Construct a magic grid of size n × n.

Input

The only line of input contains an integer n (4 ≤ n ≤ 1000). It is guaranteed that n is a multiple of 4.

Output

Print a magic grid, i.e. n lines, the i-th of which contains n space-separated integers, representing the i-th row of the grid.

If there are multiple answers, print any. We can show that an answer always exists.

Examples

Input


4


Output


8 9 1 13
3 12 7 5
0 2 4 11
6 10 15 14

Input


8


Output


19 55 11 39 32 36 4 52
51 7 35 31 12 48 28 20
43 23 59 15 0 8 16 44
3 47 27 63 24 40 60 56
34 38 6 54 17 53 9 37
14 50 30 22 49 5 33 29
2 10 18 46 41 21 57 13
26 42 62 58 1 45 25 61

Note

In the first example, XOR of each row and each column is 13.

In the second example, XOR of each row and each column is 60.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.text.*;
public class Main{
    //SOLUTION BEGIN
    //Into the Hardware Mode
    void pre() throws Exception{}
    void solve(int TC)throws Exception{
        int n = ni();
        int m = n/4;
        int[][] mat = new int[n][n];
        int[][] tmp = new int[][]{
            {8, 9, 1, 13},{3, 12 ,7 ,5},{0, 2 ,4 ,11},{6, 10, 15, 14}
        };
        int c = 0;
        for(int i = 0; i< m; i++){
            for(int j = 0; j< m; j++){
                
                for(int k = 0; k< 4; k++)
                    for(int l = 0; l< 4; l++){
                        mat[i*4+k][j*4+l] = tmp[k][l]|(16*c);
                    }
                c++;
            }
        }
        for(int i = 0; i< n; i++){
            for(int j = 0; j< n; j++)p(mat[i][j]+" ");pn("");
        }
    }
    class MyTreeSet<T>{
        private int size;
        private TreeMap<T, Integer> map;
        public MyTreeSet(){
            size = 0;
            map = new TreeMap<>();
        }
        public int size(){return size;}
        public int dsize(){return map.size();}
        public boolean isEmpty(){return size==0;}
        public void add(T t){
            size++;
            map.put(t, map.getOrDefault(t, 0)+1);
        }
        public boolean remove(T t){
            if(!map.containsKey(t))return false;
            size--;
            int c = map.get(t);
            if(c==1)map.remove(t);
            else map.put(t, c-1);
            return true;
        }
        public int freq(T t){return map.getOrDefault(t, 0);}
        public boolean contains(T t){return map.getOrDefault(t,0)>0;}
        public T ceiling(T t){return map.ceilingKey(t);}
        public T floor(T t){return map.floorKey(t);}
        public T first(){return map.firstKey();}
        public T last(){return map.lastKey();}
    }
    //SOLUTION END
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    void exit(boolean b){if(!b)System.exit(0);}
    long IINF = (long)1e18, mod = (long)1e9+7;
    final int INF = (int)1e9, MX = (int)2e6+5;
    DecimalFormat df = new DecimalFormat("0.00000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-6;
    static boolean multipleTC = false, memory = false, fileIO = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        if(fileIO){
            in = new FastReader("input.txt");
            out = new PrintWriter("output.txt");
        }else {
            in = new FastReader();
            out = new PrintWriter(System.out);
        }
        //Solution Credits: Taranpreet Singh
        int T = (multipleTC)?ni():1;
        pre();
        for(int t = 1; t<= T; t++)solve(t);
        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    
    int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n()throws Exception{return in.next();}
    String nln()throws Exception{return in.nextLine();}
    int ni()throws Exception{return Integer.parseInt(in.next());}
    long nl()throws Exception{return Long.parseLong(in.next());}
    double nd()throws Exception{return Double.parseDouble(in.next());}
 
    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }
 
        String next() throws Exception{
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    throw new Exception(e.toString());
                }
            }
            return st.nextToken();
        }
 
        String nextLine() throws Exception{
            String str = "";
            try{   
                str = br.readLine();
            }catch (IOException e){
                throw new Exception(e.toString());
            }  
            return str;
        }
    }
}