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:
def generate(n):
    mat = [[0 for _ in range(n)] for _ in range(n)]
    num = 0
    rev = False

    for i in range(0, n, 2):
        for j in range(0, n, 2):
            mat[i][j] = num
            mat[i][j + 1] = num + 1
            mat[i + 1][j] = num + 2
            mat[i + 1][j + 1] = num + 3

            if rev:
                mat[i][j], mat[i + 1][j] = mat[i + 1][j], mat[i][j]
                mat[i][j + 1], mat[i + 1][j + 1] = mat[i + 1][j + 1], mat[i][j + 1]

            num += 4
            rev = not rev

    return mat


if __name__ == "__main__":
    n = int(input())
    mat = generate(n)

    for row in mat:
        for num in row:
            print(num, end = " ")
        print()