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:
n=int(input())
matrix=[[None]*n for x in range(n)]
# n/4 to bnary

binary=bin(n//4)[2:]

#first squ
for x in range(2*2**len(binary)):
    for y in range(2*2**len(binary)):
        matrix[x][y] = x*2*2**len(binary) + y

sum=2*2**len(binary)
bigsum=sum**2
for i in range(1,len(binary)):
    if binary[i]=='1':
        curr=2*2**(len(binary)-i)
        for x in range(sum):
            for y in range(curr):
                matrix[x][sum+y]=bigsum
                bigsum+=1
        for y in range(sum):
            for x in range(curr):
                matrix[sum+x][y]=bigsum
                bigsum+=1
        for x in range(curr):
            for y in range(curr):
                matrix[sum+x][sum+y]=bigsum
                bigsum+=1
        sum+=curr

strs = [" ".join(list(map(str, l))) for l in matrix]
print("\n".join(strs))