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 PYTHON):

Solution:
import sys
import math
import bisect
import atexit
import io
import heapq
from collections import defaultdict, Counter
import itertools
MOD = int(1e9+7)



# n = map(int, raw_input().split())
# input = map(int, raw_input().split())



def main():
    n = map(int, raw_input().split())[0]
    da = [['' for i in range(n)] for j in range(n)]
    st = 0
    dn = 1
    sm = [[8 ,9 ,1, 13],
          [3, 12, 7, 5],
          [0, 2, 4, 11],
          [6, 10, 15, 14]]
    mx = n/4*n/4
    db = []
    for i in range(0, mx, 2):
        db.append(i)
    for i in range(1, mx, 2):
        db.append(i)
    # print db
    idx = 0
    for i in range(n):
        for j in range(n):
            idx = i/4*(n/4) + j/4
            da[i][j] = db[idx]*16 + sm[i%4][j%4]

    dv, dh = [0 for i in range(n)], [0 for i in range(n)]
    # for i in range(n):
    #     for j in range(n):
    #         dh[i] ^= da[i][j]
    #         dv[j] ^= da[i][j]
    #         print dv,dh
    # print dv,dh
    # for i in range(n):
    #     for j in range(n):
    #         da[i][j] = int(da[i][j], base=2)
    for i in range(n):
        print ' '.join(map(str, da[i]))
    # print bin(12*12)

main()