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C. Magic Grid

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet us define a magic grid to be a square matrix of integers of size $$$n \times n$$$, satisfying the following conditions.

- All integers from $$$0$$$ to $$$(n^2 - 1)$$$ inclusive appear in the matrix exactly once.
- Bitwise 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 $$$n \times n$$$.

Input

The only line of input contains an integer $$$n$$$ ($$$4 \leq n \leq 1000$$$). 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 $$$60$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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