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Fill a Special Grid

You are given a non-negative integer n representing a 2n x 2n grid.

You are given a non-negative integer n representing a 2n x 2n grid. You must fill the grid with integers from 0 to 22n - 1 to make it special. A grid is special if it satisfies all the following conditions:

Return the special 2n x 2n grid.

Note: Any 1x1 grid is special.

Example 1

Input: n = 0

Output: [[0]]

Explanation: The only number that can be placed is 0, and there is only one possible position in the grid.

Example 2

Input: n = 1

Output: [[3,0],[2,1]]

Explanation: The numbers in each quadrant are: Since 0 < 1 < 2 < 3 , this satisfies the given constraints.

Example 3

Input: n = 2

Output: [[15,12,3,0],[14,13,2,1],[11,8,7,4],[10,9,6,5]]

Explanation: The numbers in each quadrant are: This satisfies the first three requirements. Additionally, each quadrant is also a special grid. Thus, this is a special grid.

Constraints

  • 0 <= n <= 10

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