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:
import functools
import math
import sys
from collections import defaultdict

# input = sys.stdin.readline
rt = lambda: map(int, input().split())
ri = lambda: int(input())
rl = lambda: list(map(int, input().split()))


def main():
    n = ri()
    pattern = [[0, 4, 8, 12], [13, 9, 5, 1], [2, 6, 10, 14], [15, 11, 7, 3]]

    a = [[0 for _ in range(n)] for _ in range(n)]
    blocks = n*n//16
    posX = 0
    posY = 0
    for x in range(blocks):
        for i in range(4):
            for j in range(4):
                a[posX+i][posY+j] = pattern[i][j]+x*16
        posX += 4
        if posX >= n:
            posX = 0
            posY += 4

    for row in a:
        print(' '.join(map(str, row)))


if __name__ == '__main__':
    main()