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 sys

n = int(input())
# def fun(c):
# 	global n
# 	_ = []
# 	b = 1
# 	half_n = int(n/2)
# 	for i in range(n)[:half_n:1]:
# 		_.append(b)
# 		b <<= 1
# 	for i in range(n)[half_n::1]:
# 		_.append(_[i-half_n]+b)
# 	for i in range(n):
# 		_[i] += c

# 	for i in _[:-1:]:
# 		print("{:}".format(i), end = " ")
# 	print("{:}".format(_[-1]), end = '\n')

# left = []
# b = 1
# half_n = int(n/2)
# for i in range(n)[:half_n:1]:
# 	left.append(b)
# 	b <<= 1
# for i in range(n)[half_n::1]:
# 	left.append(left[i-half_n]+b)

# for j in left:
# 	# print("j = {:b}".format(j))
# 	fun(j<<n)
_ = []
for i in range(n):
	# print("i = {}, (i+1)%n = {}".format(i, (i+1)%n))
	k = int((i%n)/4)
	_.append(i+(n-1)*4*k)

def fun(mass,d = 0):
	for i,j in enumerate(mass):
		if (i+1)%n != 0:
			print(f"{j+d}", end = " ")
		else:
			print(f"{j+d}", end = "\n")

for i in range(n):
	fun(_,i*4)