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 PYTHON3):

Solution:
if(True):
    for _ in range(1):
        n=int(input())
        array=[[0]*n for i in range(n)]
        arr=[[0]*n for i in range(n)]
        x=0
        for i in range(n):
            for j in range(n):
                array[i][j]=x
                x+=1
        it=y=0
        for i in range(n):
            for j in range(n//2):
                arr[it][y]=array[j][i]
                it+=1
            if(it==n):
                it=0
                y+=1
        it=0
        y=n//2
        for i in range(n):
            for j in range(n//2,n):
                arr[it][y]=array[j][i]
                it+=1
            if(it==n):
                it=0
                y+=1
        for i in range(n):
            print(*arr[i][:])